Author: factsonscience
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biographies sciences
biographies of scientists
John hebert 5/15/18
CONTENTS OF BIOGRAPHIES—
MATH
PHYSICS
CHEMISTRY
GEOLOGISTS
ASTRONOMY
ROCKET SCIENTISTS
INVENTORS
BIOLOGISTS
BIOCHEMISTS
GENETICISTS
EVOLUTIONARY BIOLOGISTS
ZOOLOGISTS
ANTHROPOLOGISTS
CULTURAL ANTHROPOLOGISTS
ARCHEOLOGISTS
PALEONTOLOGISTS
SOCIOLOGISTS
PSYCHOLOGISTS
MATHEMATICIAN
PYTHAGORAS c. 570495 BC. He is known for the Pythagorean theorem, credited to him, was known to the babylonians and Indians before him. It states that the squares of each side of a right triangle add together is equal to the square of the hypotenuse of the triangle.
ZENO c. 490c. 430 bc. He is best known for his paradoxes, particularly zeno’s paradox.
THEAETETUS c. 417c. 368 BC. His principle contributions to math were on irrational lengths, which were included in Euclid’s work, and in proving that there are precisely 5 regular convex polyhedra.
EUCLID mid4th century BCmid3rd century BC. (fl. 300 BC). Greek mathematician often referred to as the father of geometry. His work, the elements, is one of the most influential works in the history of mathematics. He deduced the principles of what is now called Euclidean geometry. He wrote about perspective, conic sections, spherical geometry, number theory, and rigor. Although best known for its geometrical results, the elements also includes number theory. It considers the connection between perfect numbers and Mersenne primes (known as the EuclidEuler theorem), the infinitude of prime numbers, Euclid’s lemma on factorization, which leads to the fundamental theorem of arithmetic on the uniqueness of prime factorizations, and the Euclidean algorithm for finding the greatest common divisor of 2 numbers. Euclid’s geometry was considered the only geometry possible, until noneuclidean geometry was discovered in the 19th century.
EUDOXUS 355 bc. Developed the method of exhaustion, a precursor to integral calculus. He was very familiar with geometry and number theory. He used the theory of proportions to allow the possibility of irrational numbers.
ARCHIMEDES c. 287c. 212 BC. Regarded as one of the leading scientists in classical antiquity. He anticipated modern calculus and analysis by applying concepts of infinitesimal and the method of exhaustion, to derive and rigorously prove a range of geometric theorems, including the area of a circle, the surface area and volume of a sphere, and the area under a parabola. Other mathematical achievements include deriving an accurate approximation of pi, defining and investigating the Archimedean spiral, and creating a system using exponentiation for expressing very large numbers. He also applied the method of exhaustion similar to integral calculus to answer problems involving finding areas. He concluded that the number of grains of sand needed to fill the universe would be 8×10^63 grains.
APOLLONIUS late 3rd centuryearly 2nd century. Known for his theories on the topic of conic sections.
HIPPARCHUS c. 190c. 120 BC. He was the first mathematician to possess trigonometric tables used to compute the eccentricity of the orbits of the Sun and Moon.
HERON C. 10C. 70. He described how to compute square roots iteratively, but is best known for hero’s formula, which gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin. The formula is— area=sqrt(s(sa)x(ab)x(sc)), where sides are lengths a, b, and c, and s=(a+b+c)/2.
NICOMACHUS c. 60c. 120. He was more interested in the mystical properties of numbers than their mathematical properties. He put significance in prime and perfect numbers.
DIOPHANTUS 201/215285/299. Sometimes called the father of algebra. He was the first greek mathematician to recognize fractions as numbers. Diophantine equations are named after him for usually algebraic equations with integer coefficients in which integer solutions are sought.
PAPPUS c. 290c. 350. One of the last great Greek mathematicians. He is known for his Pappus’s hexagon theorem in projective geometry.
HYPATIA c. 350415. She is known for her intense interest and reverence of mathematics.
ARYABHATA 476550. He is known for the sinusoidal functions, solution of the single variable quadratic equation, calculating pi to 4 decimal places, and measuring the circumference of the Earth with 99.8% accuracy.
BRAHMAGUPTA c. 598after 685. First to gives rules to compute zero. He solved ax^2+bx=c and came up with x=(sqrt(4ac)/2a and x=((sqrt(ac+b^2/4)b/2)/a. He also calculated a/c+b/d*a/c=a(d+b)/cd, and a/cb/d*a/c=a(db)/cd. He provided a formula for generating pythagorean triples.the formula isa=mx is one leg of the right triangle. b=m+d is the other leg of the right triangle. M and x are rational numbers d=mx/(x+2), And c=m(1+x)d. You can generate pythagorean triples with the previous formulas and arrive at pythagorean triples of a^2+b^2=c^2. He also went on to give a recurrence relation for generating solutions to certain instances of Diophantine equations of the 2nd degree as nx^2+1=y^2, called pell’s equation. Brahmagupta most famous result in geometry is his formula for cyclic quadrilaterals. Given the lengths for the sides of any cyclic quadrilateral, he gave an approximate and exact formula for the figure’s area.the formula is let the lengths be: p,q,r and s. The approximate area is (p+r)/2, q+s)/2, and t=(p+q+r+s)/2, and the exact formula is sqrt((tp)(tq)(tr)(ts)). Heron’s formula is a special case of this formula and it is derived by setting one of the sides equal to zero.he also provided a way to determine pi with very little margin of error. He presented a sine table using names of objects to represent the digits of placevalue numerals. In 665, he devised and used a special case of the NewtonSterling interpolation formula of the second order to interpolate new values of the sine function and other values.
BHASKARA 1 c. 600c. 680. He was the first to write numbers in the Hindu decimal system with a circle for the zero, and he gave a remarkable and unique rational approximation of the sine function.
ALKHWARIZMI c. 780c. 850. He is credited with the first systematic solution of linear and quadratic equations in Arabic. He is considered one of the fathers of algebra. He also did innovative work in trigonometry.
ALKARAJI c. 953c. 1029. He was influenced by Diophantus, and be began the freeing of algebra from geometry. He systematically studied the algebra of exponent and was the first to realize that the sequence x, x^2, x^3…, and its reciprocal can be extended indefinitely. He wrote on the binomial theorem and Pascal’s triangle.
ABU AHAYTHAM c. 965c. 1040. He worked on the beginning of the link between algebra and geometry. He explored Euclid’s parallel postulate, using the concept of motion into geometry using a proof by contradiction. He worked on perfect numbers, where 2^(n1)x(2^n1) is a perfect number where 2^n1 is prime. He found the volume of a paraboloid.
OMAR KHAYYAM
May 18, 1048December 4, 1131. He worked on the theory of parallels, geometric algebra, and the binomial theorem and extraction of roots. He developed general methods for solving cubic equations and equations of
higher order.
BHASKARA 2 11141185. He proved the Pythagorean theorem by calculating the same area in 2 different ways and then cancelling out terms to arrive at a^2+b^2=c^2. He solved quadratic equations with more than one unknown, and found negative and irrational solutions. He arrived at preliminary concepts of mathematical analysis and infinitesimal calculus, conceived differential calculus, after discovering an approximation of the derivative and differential coefficient, stated Rolle’s theorem, developed spherical trigonometry, and found methods of solving Pell’s equation.
FIBONACCI c. 1175c. 1250. Considered the most talented mathematician of the Middle Ages. He popularized the HinduArabic numeral system in the west. in his book, liber abaci, he introduced the sequence of fibonacci numbers and also discussed irrational and prime numbers. The golden ratio is the limit of the ratio of consecutive numbers in the fibonacci sequence.
NASIR ALDIN ALTUSI February 18, 1201June 26, 1274. He was the first to list the six distinct cases of a right triangle in spherical trigonometry. He stated the law of sines
for plane and spherical triangles and the law of tangents for spherical triangles along with proof for all of these.
QIN JIUSHAO 12021261. He produced indeterminate equations and numerical solutions of certain polynomial equations up to the 10th order, a general form of the Chinese remainder theorem, and a formula for finding the area of a triangle from the given lengths of 3 sides, also known as Heron’s formula proved by Heron about 60 BC. He also found ways for finding sums of arithmetic series.
JORDANUS SE NEMORE fl. 13th century. He wrote wonderful treatise on practical arithmetic, pure arithmetic, algebra, and geometry.
NOCOLE ORESME c. 1320July 11, 1382. he is known for the proof of the divergence of the harmonic series.
REGIOMONTANUS June 6, 1436July 6, 1476. He did work on arithmetic and symbolic algebra.
DEL FERRO February 6, 1465November 5, 1526. He provided a solution of the depressed cubic equation.
MICHAEL STIFEL 1487April 19, 1567. He was the first to use the term ‘exponent’ and give a few of the exponential laws. He was the first who used a standard model to solve quadratic equations.
NICCOLO FONTANA TARTAGLIA 1499/1500December 13, 1557. He is best known for his conflicts with Gerolamo Cardano, where Cardano cajoled Tartaglia into revealing his solution to the cubic equation by promising not to publish them. Cardano saw an unpublished preTartaglian solution to the cubic equation by del ferro who independently came up with the same solution as Tartaglia, so cardamon broke his promise to Tartaglia and published Tartaglia’s solution. Both Tartaglia and cardano are credited with solving the cubic equation, which is now known as the CardanoTartaglia formula. He is also known for giving the volume of a tetrahedron.
GEROLAMO CARDANO September 24, 1501September 21, 1576. One of the most influential mathematicians of the renaissance, and was one of the key figures in the foundation of probability and the earliest introducer of the binomial coefficient and the binomial theorem to the western world. He made the first systematic use of negative numbers, published solutions from other mathematicians for the cubic and quartic equations, acknowledged the existence of imaginary numbers, and made the first systematic treatment of probability.
LODOVICO FERRAI February 2, 1522October 5, 1565. Was mainly responsible for solving quartic equations. He proved the intermediate value theorem for polynomials, using the procedure of conquer and divide by subdividing the interval into equal parts. His decimals were an inspiration to Newton.
RAPHAEL BOMBELLI January 20, 15261572. He authored a treatise on algebra and is a central figure in the understanding of imaginary numbers. He gave a comprehensive account of the algebra known at the time, and was the first European to write down the way of performing computations with negative numbers. He made monumental contributions to complex numbers. He saw that imaginary numbers were crucial and necessary to solving quartic and cubic equations.
FRANCOIS VIETE 1540February 23, 1603. He is known for the first notation of new algebra (symbolic notation).
SIMON STEVIN 15481620. Brought to the western world for the first time the general solution to the quadratic equation.
JOHN NAPIER February 1, 1550April 4, 1617. Best known for discovering logarithms.
HENRY BRIGGS February 1561January 26, 1630. He changed the original logarithms invented by Napier into common base 10 logarithms.
GALILEO GALILEI
February 15, 1564January 8, 1642. He made original contributions to the science of motion through an innovative combination of
experiment and mathematics. He was one of the first modern thinkers to clearly state that the laws of nature are mathematical. Galileo showed a modern appreciation of the proper relationship between mathematics, theoretical physics, and experimental physics. He understood the parabola, both in terms of conic sections, and in terms of the ordinate (y) varying as the square of the abscissa (x). He asserted that a parabola was the theoretical ideal trajectory of a uniformly accelerated projectile in the absence of air resistance.
MARIN MERSENNE September 8, 1588September 1, 1648. He is known for Mersenne primes of the form M(n)=2^n1.
GIRARD DESARGUES February 21, 1591September 1661. He is one of the founders of projective geometry, and known for Desargues theorem and Desargues graph.
Albert Girard 1595December 8, 1632. He had early thoughts on the fundamental theorem of algebra and gave the inductive definition for the Fibonacci numbers. He showed that the area of a spherical triangle depends on the interior angles, a result called Gerard’s theorem.
RENE DESCARTES
March 31, 1596February 11, 1650. He is mainly known in mathematics for his cartesian coordinate system.
BONAVENTURA CAVALIERI 1598November 30, 1647. He is known for his work on indivisibles, the precursor to infinitesimal calculus, and the introduction of logarithms into Italy. Cavalieri’s principle in geometry partially anticipated integral calculus.
GILLES PERSONNE DE ROBERVAL August 10, 1602October 27, 1675. Just before the invention of calculus, he worked with problems which are soluble by some method involving limits and infinitesimals. He coined the term trochoid.
PIERRE DE FERMAT
October 31 to December 6, 1607January 12, 1665. He is given credit for the early developments that led to infinitesimal
calculus and did work analogous to that of differential calculus, then unknown. He also did research into number theory,, and made notable contributions to analytic geometry and probability. He is known for Fermat’s last theorem, proved in 1994, and Fermat’s little theorem.
JOHN PELL March 1, 1611December 12, 1685. He is known for the Pell number and the Pell’s equation.
JOHN WALLIS December 3, 1616November 8, 1703. he was given partial credit for the development of infinitesimal calculus, and is also credited with the introduction of the infinity symbol. He made significant contributions to trigonometry, calculus, geometry, and the analysis of infinite series. He introduced the term continued fraction. He published a treatise on conic sections which were defined analytically. He is also known for the Wallis product.
BLAISE PASCAL June 19, 1623August 19, 1662. Helped create 2 major new areas of research: projective geometry at t6 and probability theory with Fermat. He a provided convenient tabular presentation of binomial coefficients, now called pascal’s triangle. Pascal used a probabilistic argument, pascal’s wager, to justify belief in God and a virtuous life.
ISAAC BARROWS October 1630May 4, 1677. Generally credited for the early development of infinitesimal calculus, especially the fundamental theorem of calculus.
His work was on tangents, and he was the first to calculate the tangents of kappa curves. Newton was his student who went on to develop calculus in its modern form.
JAMES GREGORY November 1638October 1675. He discovered infinite series representations for several trigonometric functions and he formulated the Taylor’s series. He was influential with trigonometric series.
ISAAC NEWTON
December 25, 1642march 20, 1727. Known for his book Principia Mathematica, invention of infinitesimal calculus, binomial series.
SEKI TAKAKAZU 1642December 5, 1708. He has been described as japan’s newton. He did work on infinitesimal calculus and Diophantine equations independently of newton. He is credited with the discovery of Bernoulli numbers, and the resultant and determinant are attributed to him.
GOTTFRIED LEIBNIZ July 1, 1646 November 14, 1716. Coinventor of calculus.
MICHEL ROLLE April 21, 1652November 8, 1719. he is best known for Rolle’s theorem, which states that any realvalued differentiable function that attains equal values at 2 distinct points must have a stationary point somewhere between them.
THE BERNOULLI FAMILY OF MATHEMATICIANS Daniel, Jacob, Jacob(2), Johann, Johann(2), Johann(3), Nicolaus, Nicolaus(2)
JACOB BERNOULLI December 27, 1654August 16, 1705. Sided with Leibniz against newton in the calculus inventor controversy. He made numerous contributions to calculus, including being one of the inventors of the calculus of variations. He discovered the mathematical constant ‘e’. He has numerous mathematical discoveries to his name.
DE L’HOSPITAL 1661February 2, 1704. He is associated with L’Hospital’s rule, a way of calculating limits involving indeterminate forms 0/0 and infinity/infinity. This rule did not originate with him.
GIOVANNI SACCHERI September 5, 1667October 25, 1733. His geometric work resulted in the basis of elliptic geometry and theorems of hyperbolic geometry.
ABRAHAM DE MOIVRE May 26, 1667 November 27, 1754. He is known for de Moivre’s formula that links complex numbers and trigonometry, for his work on the normal distribution and probability theory, and for the theorem of de MoivreLaplace..
JOHANN BERNOULLI August 6, 1667 January 1, 1748. One of the many prominent mathematicians in the Bernoulli family, he made many contributions to infinitesimal calculus, and educated Euler in his youth.he is known for the brachistochrone problem, which is a curve which has the fastest descent.
JACOPO RICCATI May 28, 1676April 14, 1754. He introduced the hyperbolic functions, and studied the Riccati equation, which is a firstorder differential equation that is used to refer to matrix equations with an analogous quadratic term, which occurs in both continuoustime and discretetime linear quadraticgaussian control. Introduced hyperbolic functions.
ROGER COTES July 10, 1682June 5, 1716. Invented the quadrature formulas and introduced the Euler formula.
TAYLOR BROOK August 18, 1685December 1731. Best known for Taylor series and the Taylor’s theorem.
NICOLAUS BERNOULLI October 21, 1687November 29, 1759. He is one of the many prominent mathematicians of the Bernoulli family. He did work in probability, differential equations, and geometry.
JAMES STERLING May 1692December 5, 1770. He. Is known for sterling numbers, sterling permutations, sterling approximations, and he proved the correctness of newton’s classification of cubics.
CHRISTIAN GOLDBACH March 18, 1690November 20, 1764. Known for Goldbach’s conjecture.
COLIN MACLAURIN February 1, 1698June 14, 1746. The Maclaurin series, a special case of the Taylor series, is named after him. He was influential in trigonometric series.
DANIEL BERNOULLI February 8, 1700March 17, 1782. One of the prominent mathematicians in the Bernoulli family, he applied math to mechanics, especially fluid mechanics, and did pioneering work in probability and statistics. He is known for the Bernoulli principle, which in fluid dynamics, states that an increase in the speed of a fluid occurs simultaneously with an decrease in pressure or a decrease in the fluid’s potential energy. This principle explains why an airplane wing provides lift and enables airplane flight.
THOMAS BAYES c. 1701April 7, 1761. Bayes theorem is named after him, dealing with probability theory, and led to Bayesian probability.
GABRIEL CRAMER July 31, 1704January 4, 1752. He is known for Cramer’s rule (an explicit formula for the solution of a system of linear equations with as many equations as unknowns and is valid whenever the system has a unique solution), Cramer’s paradox, and Cramer’s theorem for algebraic curves.
LEONARD EULER April 15, 1707September 18, 1783. Swiss mathematician Leonard Euler is one of the most eminent mathematicians of the 18th century and it held as one of the greatest in history. He is also one of the very few that were the most prolific ones. He worked in almost all areas of mathematics, from geometry, infinitesimal calculus, trigonometry, algebra, and number theory. The number ‘e’ is named after him, being equal to 2.71828…, as is the EulerMascheroni constant (gamma), which is equal to approximately .57721, and it is not know whether this number is rational or irrational. The concept of a function and summations originated from him.He worked in the power series and proved the power series expansions for ‘e’ and the inverse tangent function along with the Basel function (summation of 1/n^2=pi^2/6 in 1735. He introduced the use of the exponential function and logarithms into analytic proofs. He is known for the Euler identity e^(I*pi)+1=0. It was voted in 1988 the most beautiful formula ever. Euler is responsible for 3 to the top 5 formulas in 1988.De movire’s formula resulted directly from Euler’s formula. He elaborated on the theory of higher transcendental functions by introducing the gamma function. He used new methods to sole quartic equations. He foreshadowed the development of complex analysis and invented the calculus of variations, including its best known result, the EulerLagrange equation. He incorporated complex numbers into trigonometry. He did pioneering work in the use of analytic methods to solve number theory problems. He introduced analytic number theory, and created the theory of hypergeometric series, qseries, hyperbolic trigonometric functions and the analytic theory of continued fractions. He used the divergence of the harmonic series to prove the infinitude of primes, and used analytic methods to gain understanding of the way prime numbers are distributed. His work led to the development of the prime number theorem. He proved that the sum of the reciprocals of primes diverges. Doing this, he discovered the connection between the Riemann zeta function and the primes. This is
known as the Euler product formula for the Riemann zeta function. Euler proved newton’s identities, format’s little theorem, Fermat’s theory on sums of 2 squares, and made distinct contributions to lag range’s 4square theorem. He invented the totient function, using properties of this function to generalize format’s little theory in what is now known as ruler’s theorem. He proved the relationship shown between Mersenne primes and perfect numbers earlier proved by Euclid was 1to1, known as EuclidEuler theory. He conjectured about the law of quadratic reciprocity, which is fundamental to number theory. Gauss used these ideas. In 1772, Euler proved that 2^3112,147,483,647 is a Mersenne prime, and remained so until 1867. In 1735, he proved that the 7 brides of Konigsberg problem in graph theory is not possible. He discovered the formula VE+F=2 for the number of vertices, edges, and faces of a convex polyhedron, and hence a planar graph. Its constant is known as the Euler characteristic. The study and generalization of this formula, by Cauchy and l’hillier is the origin of topology. He described many applications of the Bernoulli numbers, Fourier series, Euler numbers, and the constants e and pi, continued fractions, and integrals. He integrated Leibniz’s and Newton’s differential calculus. He made great progress in improving numerical approximation of integrals, inventing Euler approximations. Some of these approximation are ruler’s method and the EulerMaclaurin formula. He facilitated the use of differential equations, in particular introducing the Euler Mascheroni constant. He calculated with great accuracy the orbits of comets and other celestial bodies, and calculated the parallax of the sun.he did work in set theory and logic.
THOMAS SIMPSON August 20, 1710May 14, 1761. He is the inventor of Simpson’s rule, used to approximate definite integrals.
ALEXIS CLAIRAUT May 13, 1713May 17, 1765. He is known for Clairaut’s theorem, which helped to establish Newton’s principles and results. He is also credited with Clairaut’s equation and Clairaut’s relation.
JEAN LE ROND D’ALEMBERT November 17,1717October 29, 1783. He is known for d’Alember’s principle concerning dynamics as related to newton’s 3rd law of motion, applying calculus to vibrating strings, and his research in integral calculus where he devised relationships of variables by means of rate of change of their numerical value.
MARIA AGNESI May 16, 1718January 9, 1799. first woman to write a mathematics handbook on both differential and integral calculus.
JOHANN LAMBERT August 26, 1728September 25, 1777. He was the first to prove that pi is an irrational number. He is also known for the Lambert w function, and he introduce hyperbolic functions.
ALEXANDRETHEOPHILE VANRMONDE (28 February 1735 – 1 January 1796) was a French mathematician, musician and chemist who worked with Bezout and Lavoisier; his name is now principally associated with determinant theory in mathematics. He was born in Paris, and died there.
JOSEPH LOUIS LAGRANGE January 25, 1736 April 10, 1813. He made significant contributions to the fields of analysis, number theory, and both classical and celestial mechanics. He invented Lagrange multipliers.
GASPARD MONGE May 9, 1746July 28, 1818. Inventor of descriptive geometry, the mathematical basis of technical drawing. (father of descriptive geometry.)
PIERRE SIMON DE LAPLACE March 23, 1749March 5, 1827. He wrote a 5 volume Mechanique Celeste (17991825).it translates the geometric study of celestial mechanics to one based on calculus. In statistics, bayesian interpretation of probability was developed by him. He is known for Laplace’s equation, Laplacian, Laplace transform, block holes, and the nebular hypothesis of the solar system’s formation.
ADRIENMARIE LEGENDRE September 18, 1752 January 10, 1833. He is known for Legendre transformation, Legendre polynomials, Legendre transform, and elliptic functions.
PAOLO RUFFINI September 22, 1765May 10, 1822. He is known for an incomplete proof that quintic and higher ordered equations cannot be solved by radicals (Abel Ruffini theorem), the Ruffini rule, and a fast method for polynomial division. He made contributions to group theory, probability, and the quadrature of a circle.
JOSEPH FOURIER March 21, 1768 May 16, 1830. Known for initiating the investigation of Fourier series and their application to problems of heat transfer and vibrations. The Fourier transform and Fourier’s law are named in his honor.
SOPHIE GERMAIN April 1, 1776June 27, 1831. She did work in differential geometry, number theory, and is known for Sophie Germain prime numbers along with proving format’s last theorem for one of its exponents.
FRIEDRICH GAUSS April 30, 1777February 23, 1855. He contributed significantly to many fields, including number theory, algebra, statistics, analysis, differential geometry, mechanics, matrix theory, and astronomy.
MARY FAIRFAX SOMERVILLE December 26, 1780November 29, 1872. She studied math and astronomy and her writings influenced James Clerk Maxwell. She was a polymath.
SIMON POISSON June 21, 1781April 25, 1840. He is known for the Poisson distribution, poisson regression, poisson summation, poisson algebra, and much more.
BERNARD BOLZANO October 5, 1781December 18, 1848. He is known for Bolzano’s theory, the first purely analytical proof of the intermediate value theorem.
JEANVICTOR PONCELET July 1, 1788December 22, 1867. He is considered a reviver of projective geometry and did notable work in this area. He developed the concept of parallel lines meeting at infinity, and aided in the development of complex numbers.
AUGUSTIN LOUIS CAUCHY August 21, 1789 May 23, 1857. He made pioneering work in analysis and was one of the first to star and prove theorems of calculus rigorously. He almost singlehandedly founded complex analysis and the study of permutation groups in abstract algebra.
AUGUST MOBIUS November 17, 1790September 26, 1868. He is known for the Mobius strip, Mobius transform, Mobius function, and more.
NIKOLAI LABACHEVSKY November 20, 1792February 12, 1856. He is known primarily for his work on hyperbolic/Labachskian geometry (nonEuclidean).
GEORGE GREEN July 14, 1793May 31, 1841. He is known for Green’s theorem (the idea of potential functions as currently used in physics), Green’s functions, Green’s identity, and more.
JULIUS PLUCKER June 16, 1801May 22, 1868. He made fundamental contributions to analytic geometry. He vastly extended the study of lame curves. He is known for the plucker formula.
MIKHAIL OSTROGRADSKY September 24, 1801January 1, 1862. A disciple of Euler and one of the leading mathematicians in imperial Russia. He gave the first general proof of the divergence theorem, created the Ostrogradsky equation, , and method for integrating rational functions.
JANOS BOLYAI December 15, 1802January 27, 1860. He is one of the founders of nonEuclidean geometry.
CARL JACOBI December 10, 1804February 18, 1851. He made fundamental contributions to elliptical functions, differential equations, and number theory. He is known for the Jacobean, Jacobi’s elliptical functions, Jacobi ellipsoid, Jacobi transform, Jacobi polynomials, and more.
NIELS ABEL August 5, 1802April 6, 1829. His most famous single result is the first complete proof demonstrating the impossibility of solving general quintic equations by radicals. He was also an innovator in the field of elliptic functions, discoverer of abelian functions.
PETER DIRICHLET February 13, 1805 May 5, 1859. He made deep contributions to number theory, including creating analytic number theory, the theory of Fourier series, and other topics of mathematical analysis. He gave the modern formal definition of a function. He is known for much in math, such as the Dirichlet series, the Dirichlet distribution, the Dirichlet integral, the Dirichlet space, and much more.
WILLIAM HAMILTON August 4, 1805 September 2, 1865. In pure mathematics, he is best known for the inventor of quanternions.
AUGUSTUS DE MORGAN June 27, 1806March 18, 1871. He formulated De Morgan’s law and introduced the term mathematical induction. He is known for De Morgan’s laws, De Moran algebra, relational algebra, and universal algebra.
Johann Benedict Listing (25 July 1808 – 24 December 1882) was a German mathematician.
J. B. Listing was born in Frankfurt and died in Göttingen. He first introduced the term “topology”, in a famous article published in 1847, although he had used the term in correspondence some years earlier. He (independently) discovered the properties of the halftwisted strip at the same time (1858) as August Ferdinand Möbius, and went further in exploring the properties of strips with higherorder twists (paradromic rings). He discovered topological invariants which came to be called Listing numbers.
In ophthalmology, Listing’s law describes an essential element of extraocular eye muscle coordination.
JOSEPH LIOUVILLE March 24, 1809September 8, 1882. He is best remembered for Liouville’s theorem, a basic result in complex analysis, and in number theory, he was the first to prove the existence of transcendental numbers by construction using continued fractions (liouville numbers).
HERMANN GRASSMANN April 15, 1809September 26, 1877. He is known for multilinear algebra.
ERNST KUMMER January 29, 1810May 14, 1893. He is known for Bessel functions, Kummer surfaces, and Kummer theory.
EVARISTE GALOIS October 25, 1811May 31, 1832. While still a teen, he was able to determine the necessary and sufficient condition for a polynomial to be solved by radicals, solving a 350 year problem. His work laid the foundations of group theory and Galois theory, two major branches of abstract algebra.
Pierre Alphonse Laurent (18 July 1813 – 2 September 1854) was a French mathematician and Military Officer best known as the discoverer of the Laurent series, an expansion of a function into an infinite power series, generalizing the Taylor series expansion.
Ludwig Schläfli (15 January 1814 – 20 March 1895) was a Swiss mathematician, specializing in geometry and complex analysis (at the time called function theory) who was one of the key figures in developing the notion of higherdimensional spaces. The concept of multidimensionality has come to play a pivotal role in physics, and is a common element in science fiction.
JAMES SYLVESTER September 3, 1814 March 15, 1897. He made fundamental contributions to matrix theory, invariant theory, number theory, partition theory, and combinatorics. He is known for the Sylvester constant, the Sylvester sequence, the Sylvester formula, the Sylvester determinant theorem, and more.
KARL WEIERSTRASS October 31, 1815 February 19, 1897. The father of modern analysis. He formalized the definition of the continuity of a function, proved the intermediate value theorem and the Bolzano Weierstraus theorem, and used the properties of the latter to study the properties of continuous functions on closed bounded intervals. He brought soundness and rigor to calculus, as did caught earlier. He made significant advancements in the field of calculus of variations.he discovered a function that is continuous, but had no derivative at any point.
GEORGE BOOLE November 2, 1815December 8, 1864. He worked in the fields of differential equations and algebraic logic, and for Boolean logic, which laid the foundation for the Information Age.
SIR GEORGE STOKES August 13, 1819 February 1, 1903. He made seminal contributions to fluid dynamics, including the NavierStokes equations. He is known for Stoke’s theorem, and contributed to the theory of asymptotic expansions.
PAFNUTY CHEBYSHEV May 16, 1821Decemebr 8, 1894. He worked on probability, statistics, analytical geometry, and number theory. He is known for Chebyshev’s theorem in which there is always a prime number between n and 2n.
ARTHUR CAYLEY August 16, 1821 January 26, 1895. He helped found the modern British school of mathematics. He is known for algebraic geometry, group theory, the CayleyHamilton theorem, the Cayley Dickerson construction, and Cayley algebra (octonion).
CHARLES HERMITE December 24, 1822January 14, 1901. He did research on number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, and algebra. He is known for the proof the ‘e’ is a transcendental number.
GOTTHOLD EISENSTEIN April 16, 1823October 11, 1852. He specialized in number theory and analysis and proved several results in which Gauss could not solve. He provided 2 proofs of the law of quadratic reciprocity, and analogous laws of cubic and quartic reciprocity.
Enrico Betti October 21, 1823August 11, 1892. He wrote a paper in topology in 1871 that led to the later naming after him of the Betti numbers. He also worked on the theory of equations, giving early expositions of Galois theory, he also discovered Betti’s theory, a result in the theory of elasticity, and is known for Betti’s theorem.
LEOPOLD KRONECKER December 7, 1823December 29, 1891. He is known for the kronecker product, the kronecker theorem, the kronecker lemma, and other discoveries.
BERNARD RIEMANN September 17, 1826 July 20, 1866. He made contributions to analysis, number theory, and differential geometry. He rigorously formulated the Riemann integral, worked on Fourier series, contributed to complex analysis, notably the introduction of Riemann surfaces, laid the foundation of the mathematics of general relativity, and in his famous 1859 paper on the primecounting function, contained the Riemann hypothesis, one of the most famous unsolved problems in pure mathematics.
HENRY SMITH November 2, 1826February 9, 1883. He is known for the Smith MinkowskiSiegel mass formula and Smith normal form.
JAMES CLERK MAXWELL June 13, 1831 November 5, 1879. Did work in mathematical physics,, his most notable achievement was to formulate the classical theory of electromagnetic radiation, bringing together for the first time electricity, magnetism, and light as manifestations of the same phenomenon in his 4 differential equations (Maxwell’s equations).
RICHARD DEDIKIND October 6, 1831February 12, 1916. He made important contributions to abstract algebra, particularly ring theory, algebraic number theory, and the definition of real numbers. He is known for the Dedikind cut, a method of construction of real numbers.
LAZARUS FUCHS May 5, 1833April 26, 1902. Known for fuchsian groups and fuchsia’s theorem.
JOHN VENN August 4, 1834April 4, 1923. Logician who introduced the Venn diagram, used in set theory, logic, statics, and computer science.
EUGENIO BELTRAMI November 16, 1835February 18, 1900. He was the first to prove the consistency of nonEuclidean geometry by modeling it on a surface of constant curvature, the pseudosphere, and the interior of an ndimensional unit sphere, the socalled BeltramiKlein model. He also developed singular decomposition for matrices, and used differential calculus for problems of mathematical physics indirectly influencing the development of tensor calculus developed by Gregorio RicciCurbastro and Tullio LeviCivita.
CAMILLE JORDAN January 5, 1838January 22, 1922. He is known for his foundational work in group theory, Jordan curve theorem, Jordan matrix, and more.
JOSIAH WILLARD GIBBS February 11, 1839April 28, 1903. Made important theoretical contributions to physics, chemistry, and math. Together with James clerk maxwell and Ludwig Boltzmann, he created statistical mechanics explaining the laws of thermodynamics as consequence of the statistical properties of ensembles of a physical system composed of many particles. He invented modern vector calculus independently of Oliver Heaviside.
FRANCOIS LUCAS April 4, 1842October 3, 1891. He studied the Fibonacci sequence, and the Lucas sequence and Lucas numbers are named after him. He is known for the cannonball problem, Lucas primes, and Lucas’ theorem. Also, a proof using elliptic functions was found which as relevance to the boson string theory in 26 dimensions.
SOPHIUS LIE December 17, 1842february 18, 1899. He largely created the theory of continuous symmetry and applied it to the study of geometry and differential equations.he is known for Lie groups, lie theory, and Lie algebra, among much more.
GREGOR CANTOR March 3, 1845January 6, 1918. He invented set theory, which became a fundamental theory in mathematics,
established the importance of onetoone correspondence between two sets, defined infinite and well=ordered sets, and proved that the real numbers are more numerous than the natural numbers. He showed that there are an infinity of infinities. He defined cardinal and ordinal numbers and their arithmetic.
GOSTA MITTGLEFFLER March 16, 1846July 7, 1927. He is known chiefly for his connection with the theory of functions, today known as complex analysis.
FERDINAND GEOG FROBENIUS October 26, 1849August 3, 1917. He is best known for his contributions to the theory of elliptical functions, differential equations, and group theory. He is known for his determinants identities, known as FrobeniusStickelberger formulae, governing elliptic functions, and for developing the theory of biquadratic forms. He was the first to introduce the notion of rational approximations of functions, known as Made approximates, and to give a full proof of the CayleyHamilton theorem. He is also known for Frobenius manifolds, which are differentialgeometric objects.
SOPHIA KOVALEVSKAYA 18501891. Made noteworthy contributions to analysis, partial differential equations, and mechanics. She is known for the CauchyKowalevski theorem.
OLIVER HEAVISIDE May 18, 1850February 3, 1925. Adapted complex numbers to the study of electrical circuits, invented mathematical techniques for the solution of differential equations, equivalent to Laplace transforms, reformulated Maxwell’s equations in terms of electric and magnetic forces and energy flux, and independently coformulated vector analysis. He is known for the Heavisidestep function, among other achievements.
CARL LINDEMANN April 12, 1852March 6, 1939. He is noted for his proof of pi being a transcendental number (a number which is not a root of any polynomial with rational coefficients.).
HENRI POINCARE April 29, 1854July 17, 1912. A polymath and described the last universalist in mathematics. He is known for the poincare conjecture (which was solved in 2003), the threebody problem, special relativity, HilbertPoincare series, chaos theory, coining the term ‘Betti number’, and the power fixedpoint theorem.
EMILE PICARD July 24, 1856December 11, 1941. He is known for Painieve transcendentals, Picard group, and Picard theorem, which states that an analytic function with an essential singularity takes every value infinitely often, and perhaps one exception, in any neighborhood of the singularity.
KARL PEASON March 27, 1857April 27, 1938. He is credited with establishing the discipline of mathematical statistics. He is known for the Pearson distribution, phi coefficient, and Pearson’s chisquared test.
GIUSEPPE PEANO August 27, 1858April 20, 1932. He wrote over 200 books and papers, and was a founder of mathematical logic and set theory, to which he contributed much notation.the axiomatization of natural numbers is named the Peano numbers. He also made key contributions to the modern rigorous and systematic treatment of the method of mathematical induction.
Giulio Ascoli (20 January 1843, Trieste – 12 July 1896, Milan) was an Italian mathematician. He made contributions to the theory of functions of a real variable and to Fourier series. For example, Ascoli introduced
equicontinuity in 1884, a topic regarded as one of the fundamental concepts in the theory of real functions.[1] In 1889, Italian mathematician Cesare Arzelà generalized Ascoli’s Theorem into the Arzelà–Ascoli theorem, a practical sequential compactness criterion of functions.[
DAVID HILBERT January 23, 1862February 14, 1943. He is recognized as one of the most influential and universal mathematicians if the 19th and 20th centuries. He discovered and developed ideas in many areas, including invariant theory and the axiomatization of geometry, one of the foundations of functional analysis. He is known as one of the founders of proof theory and mathematical logic. He put forth his famous 23 problems in 1900 to hopefully be solved in the 20th century.
GOTTLOB FREGE November 8, 1848July 26, 1925. He is considered a major figure in mathematics, and responsible for the development of modern logic. He is known for predicate calculus, Frege’s theorem, the FregeGeach problem, and more.
CHRISTIAN FELIX KLEIN April 25, 1849June 22, 1925. Known for his work in group theory, complex analysis, nonEuclidean geometry, and on the connection of geometry and group theory. He classified geometries by their underlying symmetry groups. He is known for a Klein bottle. It is a one sided surface which, if traveled upon, could be followed back to the post of origin while flipping the traveler upside down. it is a one sided bottle.
GREGORIO RICCICUBASTRO January 12, 1853August 6, 1925. He invented tensor calculus, an extension of vector calculus to tensor fields (tensors that may vary over a manifold I.e. spacetime).
THOMAS STIELTJES December 29, 1856December 31, 1894. he pioneered in the field of moment problems and contributed to the study of continued fractions.
GRACE CHISHOLM YOUNG March 15, 1858March 29, 1944. she worked in calculus and is known for the DenjoyYoungSaks theorem.
Vito Volterra (3 May 1860 – 11 October 1940) was an Italian mathematician and physicist, known for his contributions to mathematical biology and integral equations,[2][3] being one of the founders of functional analysis. He is known for the lotkavolterra equations.
CHARLES JEAN DE LA VALLEEPOUSSIN august 14, 1865march 2, 1962. he is best known for providing a proof of the prime number theorem.
ERIK IVAR FREDHOLM april 7, 1866august 17, 1927. Worked on integral equations and operator theory which foreshadowed hillier spaces.
JACQUES HADAMARD December 8, 1866October 17, 1963. He made contributions in number theory, complex function theory, differential geometry, and partial differential equations. He proved the prime number theorem, and is known for the Hadamard product and Hadamard matrices.
FELIX HAUSDORFF November 8, 1868January 26, 1942. He is one of the founders of modern topology and contributed significantly to set theory, descriptive set theory, measure theory, function theory, and functional analysis. He is known for the Hausdorff Dimension, the Hausdorff space, the Hausdorff paradox, and other achievements. RIP
ELIE CARTAN April 9, 1869May 6, 1951. He made significant contributions to mathematical physics, differential geometry, and group theory. He is known for Lie groups and differential forms.
BOREL january 7, 1871february 3, 1956. He is known for founding work in the areas of measure theory and probability.
Ernst Steinitz (13 June 1871 – 29 September 1928) was a German mathematician. Steinitz’s 1894 thesis was on the subject of projective configurations; it contained the result that any abstract description of an incidence structure of three lines per point and three points per line could be realized as a configuration of straight lines in the Euclidean plane with the possible exception of one of the lines. He axiomatically studies the properties of fields and defines important concepts like prime field, perfect field and the transcendence degree of a field extension. Steinitz proved that every field has an algebraic closure. He also made fundamental contributions to the theory of polyhedra: Steinitz’s theorem for polyhedra is that the 1skeletons of convex polyhedra are exactly the 3connected planar graphs.
ERNST ZERMELO July 27, 1871May 21, 1953. A logician, his work had major implications in the foundation of mathematics, and he is best known for developing the ZermeloFraenkel axiomatic set theory, and his proof of there wellordering theorem.
BERTRAND RUSSELL May 18, 1872February 2, 1970. He is known for his work in mathematical logic, paradoxes of set theory, Russell’s paradox, the barber’s paradox, prepositional logic, and much more.
Issai Schur (January 10, 1875 – January 10, 1941) was a Jewish mathematician who worked in Germany for most of his life. As a student of Frobenius, he worked on group representations (the subject with which he is most closely associated), but also in combinatorics and number theory and even theoretical physics. He is perhaps best known today for his result on the existence of the Schur decomposition and for his work on group representations (Schur’s lemma).
TEIJI TAKAGI April 21, 1875February 28, 1960. He is best know for proving the Takagi existence theorem in class field theory. He worked on the Blanomange curve, a graph that is nowhere differentiable but a uniformly continuous function.
HENRI LEBESGUE june 28, 1875july 26, 1941. He is most famous for his theory of integration, which is summing the area between an axis and the curve of a function defined for that axis.
HARDY february 7, 1877december 1, 1947. He is known for his achievements in number theory and analysis, and for the hardyweinberg principle, hardyramanujan asymptotic formula, and the hardylittlewood circle method. He is the mathematician who discovered ramanujan.
EDMUND LANDAU February 14, 1877February 19, 1938. He worked in number theory and complex analysis. He is known for his work in the distribution of prime numbers and the Landau prime ideal theorem.
Maurice Fréchet 2 September 1878 – 4 June 1973) was a French mathematician. He made major contributions to the topology of point sets and introduced the entire concept of metric spaces. He also made several important contributions to the field of statistics and probability, as well as calculus. His dissertation opened the entire field of functionals on metric spaces and introduced the notion of compactness. Independently of Riesz, he discovered the representation theorem in the space of Lebesgue square integrable functions.
Guido Fubini (19 January 1879 – 6 June 1943) was an Italian mathematician, known for Fubini’s theorem and the Fubini–Study metric.
LIPOT FEJER February 9, 1880october 15, 1959. He is known for research in harmonic analysis, in particular, Fourier series.
OSWALD VEBLEN June 24, 1880August 10, 1960. A geometer and topologist, he applied these to atomic physics and the theory of relativity. He proved the Jordan curve theorem in 1905.
LUITZEN BROUWER february 27, 1881 December 2, 1966. He worked in topology, set theory, measure theory, and complex analysis.he was the founder of mathematical intuitionism. He is known for the Brouwer fixedpoint theory and the hairy ball theorem
WACLAW SIERPINSKI march 14, 1882october 21, 1969. He is known for outstanding contributions to set theory, research on the axiom of choice and the continuum hypothesis, number theory, the theory of functions, and topology.
EMMY NOETHER March 23, 1882April 14, 1935. She is known for her landmark contributions to abstract algebra and theoretical physics. One of the leading mathematicians, she developed the theories of rings, fields, and algebras, and explained the connection between, symmetry and conservation laws.
GEORGE BIRKHOFF March 21, 1884November 12, 1944. He is best known for what is now known as the ergodic theorem. He also proved Poincare’s ‘Last Geometric Theorem’, a special case of the threebody problems, and proved that the Schwarzschild geometry is the unique symmetric solution of the Einstein field equation.
SOLOMON LEFSCHETZ September 3, 1884October 5, 1972. He did fundamental work on algebraic topology and its applications to algebraic geometry, and on the theory of nonlinear ordinary differential equations. He is known for the Lefschetz hyperplane theorem, the Lefschetz number. The Lefschetz fixed point theorem, among other acheivements.
JOHN LITTLEWOOD june 9, 1885september 6, 1977. He is best known for achievements in analysis, number theory, and differential equations. He attempted to solve the Riemann hypothesis by showing that if it were true then the prime number theorem follows and obtains the zero term. He is known for the 1st and 2nd hardy littlewood theorems, the 1st is a strong form of the twin prime conjecture.
HERMANN WEYL November 9, 1885december 8, 1955. He is known for well algebra, well transform, the well lemma (a very weak form of the Laplace transform), the well tensor, and other discoveries.
LUDWIG BIEBERBACH december 4, 1886september 1, 1982. German mathemetician known for bieberbach conjecture.
GEORGE POLYA December 13, 1887september 7, 1985. He made fundamental contributions to combinatorics, number theory, numerical analysis, and probability theory. He is known for the poly conjecture, the ploy enumeration theorem, the Hilbert polya theorem, among other accomplishments.
RAMANUJAN december 22, 1887april 26, 1920. A mathematical genius. With almost no formal training in pure mathematics, made substantial contributions to analysis, number theory, infinite series, and continued fractions, including solving problems considered unsolvable.
RICHARD COURANT January 8, 1888January 27, 1972. He is known for the Courant number and the Courant minimax principle. He published in 1943 the finite element method, which is his numerical treatment of the plain torsion problem for multiply connected domains, and is now one of the ways to solve partial differential equations numerically.
LOUIS MORDELL january 28, 1888march 12, 1972. he is known for pioneering research in number theory.
STEFEN BANACH
March 30, 1892August 31, 1945. He is generally considered one one of the world’s most important and influential mathematicians of the 20th century. He is known for the BanachTarski paradox, the BanachSteinhaus theorem, and for functional analysis, which he founded.
GASTON JULIA february 3, 1893march 19, 1978. he devised the formula for the Julia set.
NORBERT WIENER November 26, 1894 March 18, 1964. He developed Tauberian theorems ( which deals with infinite series) in summability theory, most of which could be encapsulated in a principle from harmonic
analysis. He is also known for abstract Wiener space, a mathematical object in measure theory, and realvalued continuous paths on the unit interval known as classical Wiener space.
EMIL ARTIN march 3, 1898december 20, 1962. One of the leading mathematicians in the 20th century known for his work on algebraic number theory, contributing largely to class field theory and a new construction of Lfunctions. he also contributed to the pure theories of rings, groups, and fields.
OSCAR ZARISKI April 24, 1899July 4, 1986. One of the most influential algebraic geometers of the 20th century. He is known for Zariski theory on holomorphic functions.
MARY CARTRIGHT december 17, 1900april 3, 1998. she was the first to analyze a dynamical system of chaos.
ANTONI ZYGMUND decemeber 25, 1900may 30, 1992. Considered one of the greatest analysts of the 20th century. his main interest was harmonic analysis.
ALFRED TARSKI
January 14, 1901October 26, 1983. A prolific author who did work in model theory, metamathematics, algebraic logic, abstract algebra, topology, geometry, measure theory, mathematical logic, and set theory. He is known for his work on the foundations of modern logic, Tarski’s undefinability theory, and the BanachTarski paradox, which states that a ball can be decomposed into a finite number of point sets and reassembled into 2 balls of the original.
Bartel Leendert van der Waerden February 2, 1903 – January 12, 1996) was a Dutch mathematician and historian of mathematics. Van der Waerden is mainly remembered for his work on abstract algebra. He also wrote on algebraic geometry, topology, number theory, geometry, combinatorics, analysis, probability and statistics, and quantum mechanics (he and Heisenberg had been colleagues at Leipzig). In his later years, he turned to the history of mathematics and science.
FRANK RAMSEY february 22, 1903january 19, 1930. He is known for Ramsey theory, a branch of mathematics that studies the conditions under which order must appear.
VON NEUMANN December 28, 1903 february 8, 1957. He had a phenomenal memory. He made major contributions to functional analysis, topology, numerical analysis, quantum mechanics, quantum statistical analysis, game theory, computing, linear programming, selfreplicating machines, and statistics. He is known for a great numbers of achievements.
ANDREY KOLMOGOROV April 25, 1903October 20, 1987. He is known for work in probability theory, topology, intuitional logic, turbulence studies, classical mechanics, mathematical analysis, Kolmogorov complexity, KAM theorem, and then KPP equation.
ALONZO CHURCH June 14, 1903august 11, 1995. Made major contributions to mathematical logic and to the foundation of theoretical computer science. He is best known for the lambda calculus and the churchrosser theorem.
W.V.D. HODGE June 17, 1903july 7, 1975. He was specifically a geometer. He discovered far reaching topological relations between algebraic geometry and differential geometry, and an area now called hodge theory, and pertaining more generally to Mahler manifolds.
RENATO CACCIOPPOLI
january 20, 1904may 8, 1959. he is known for his contributions to mathematical
analysis, including the theory of functions of several complex variable, functional analysis, and measure theory. RIP.
HENRI CARTAN July 8, 1904August 13, 2008. He made substantial contributions to algebraic topology. He is known for Cartan’s theorems A and B.
KURT GODEL April 28, 1906January 14, 1978. Considered the greatest logician in history along with Aristotle, Tarski, and Frege. He published 2 incompleteness theorems in 1931 in mathematical logic, which he proved, that demonstrate the inherent limitations of every formal axiomatic system containing basic arithmetic. the theorems show that finding a complete and consistent set of axioms for all of mathematics is impossible.
OLGA TAUSSKYTODD august 30, 1906october 7, 1995. She wrote more than 300 research papers in algebraic number theory, integral matrices, and matrices in algebra and analysis.
HAROLD COXETER February. 9, 1907march 31, 2003. he is regarded as one of the greatest geometer of the 20th century.
STANISLAW ULAM april 13, 1909may 13, 1984. He invented the Monte Carlo method of computation, suggested nuclear pulse space propulsion, proved some theorems, and proposed several conjectures.
PAL TURAN
august 18, 1910september 26, 1976. Worked primarily in number theory. he is known for the power sum method and extremal graph theory.
SHIINGSHEN CHERN october 26, 1911december 3, 2004. known for the cern simony theory, chernweil theory, and the Chern class.
ALEN TURING June 23, 1912June 7, 1954. He provided a formalization of the concept of the algorithm and computation with a turning machine, the model of a general purpose computer. He is also considered the father on theoretical computer science and artificial intelligence. He is known for the Turning proof and the Turing test.
PAUL ERDOS march 26, 1913september 20, 1996. One of the most prolific mathematicians ever, he is known for his social approach to mathematics and he collaborated with over 500 mathematicians in proving and conjecturing.
PAUL ERDOS GROUP FROM N IS A NUMBER FILM—
FAN CHUNG, RONALD GRAHAM, BELLA BELLOBAS, VERA SOS, JOEL SPENCER, HERB WILF
SAMUEL EILENBERG
September 30, 1913January 30, 1998. Cofounded category theory with Saunders Mac Lane. He is also known for the EilenbergSteenrod axioms.
MARJORIE LEE BROWNE september 9, 1914october 19, 1979. One of the first africanamerican women to earn a Ph.D in mathematics. her work on classical groups demonstrated simple proofs of important topological properties of the relations between classical groups. Her work in general focused on linear and matrix algebra.
MARTIN GARDNER October 21, 1914may 22, 2010. An American mathematics popularizer and regarded as the dean of mathematical puzzles.
GEORGE DANTZIG
november 8, 1914may 13, 2005. Known for his development of the simplex method, and algorithm for solving linear problems. he also solved 2 open problems in statistical theory.
LAURENT SCHWARTZ march 5, 1915july 4, 2002. He pioneered the theory of distributions, which gives a welldefined meaning to objects such as the Dirac delta function.
PAUL HALMOS
march 3, 1916october 2, 2006. he made fundamental advances in mathematical logic, probability theory, statistics, operator theory, ergodic theory, and functional analysis, especially hilbert spaces.
CLAUDE SHANNON
april 30, 1918february 24, 2001. Cryptographer known as the father of information theory. He demonstrated that electrical applications of Boolean algebra could construct any logical, numerical relationship. He is also known for the Shannon number, Shannon expansion, power inequality, binary code, and much more.
ABRAHAM ROBINSON October 6, 1918april 11, 1974. He is widely known for the development of nonstandard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were reincorporated into modern mathematics.
RAYMOND SMULLYAN may 25, 1919february 6, 2017. A mathematical logician who popularized mathematical logic problems.
JULIA ROBINSON December 8, 1919,July 30, 1985. She is best known for her work on decision theory and Hilbert’s 10th problem.
LOTFI A. ZADEH february 4, 1921. Proposed fuzzy concepts:ets, logic, algorithms, semantics, languages, control, systems, probabilities, events, and information.
ALFRED REYNI
march 20, 1921february 1, 1970. Made contributions in combinatorics, graph theory, number theory, and mostly probability theory.
JOSEPH B. KELLER july 31, 1923september 7, 2016. he specialized in applied math and is known for his work on the geometrical theory of diffraction, and the einsteinbrilouinkeller method.
RENE THOM september 2, 1923october 25, 2002. Made a reputation as a topologist and was involved in singularity theory. Founder of catastrophe theory.
EVELYN BOYD GRANVILLE may 1, 1924. Second africanAmerican woman to earn a Ph.D. in mathematics.
ISADORE SINGER may 3, 1924. Proved the atiyahsinger index theorem, which paved the way for new interactions between pure math and theoretical physics.
CHRISTOPHER ZEEMAN February 4, 1925february 13, 2016. known for catastrophe theory, geometric topology, and singularity theory. he described a new theory named dihomology, an algebraic structure associated to a topological space, containing both homology and cohomology, introducing what is now known as the Zeeman spectral sequence, to see how singularities in a space perturb poincare duality.
LOUIS NIRENBERG February 28, 1925. One of the outstanding analysts of the 20th century. he made fundamental contributions to linear and partial differential equations and their application to complex analysis and geometry. His contributions include the gagliardonirenberg interpolation inequality, which is important in the solution of the elliptical partial differential equations, that arise in many areas of math, and the formalization of the bounded mean oscillation known as johnnirenberg space, which is used to study the behavior of both elastic materials and games of chance as martingales. his work on partial differential equations was described as about the best that can be done towards solving the naiverstokes existence and smoothness problem in fluid mechanics and turbulence.
JOHN TATE March 13, 1925. he is known for many fundamental contributions in algebraic number theory, arithmetic geometry, and algebraic geometry. he is known also for Fourier analysis in number fields which is one of the ingredients in the modern theory of automorphic forms and their lfunction, notably by its use in the Adele ring and ts selfduality and harmonic analysis on it. He gave a cohomological treatment of global class field theory using techniques of group cohomology applied to the dale class group and Galois cohomology. This treatment made more transparent some of the algebraic structures in the previous approaches in class field theory which used central field algebras to compute the Brauer group of a global field. he also made a number of important contributions to padic theory. he invented rigid analytic spaces which led to the field of rigid analytic geometry. he found a padic analogue of hodge theory, known as hodgetare theory, a central technique of modern algebraic number theory. he also created the Tate curve parametrization for certain padic elliptic curves and the p divisible (tatebarsotti) groups. the classification of abelian varieties over finite fields and led to the hondatate theorem. he is known for the Tate conjecture and the Tate module. a special case of the Tate conjecture was involved in the proof of the morsel conjecture.
PETER LAX may 1, 1926. has worked in pure and applied mathematics and made important contributions to integratabtle systems, fluid dynamics and shock waves, solijtronic physics, hyperbolic conservation laws, and mathematics and computer science.
JEANPIERRE SERRE september 15, 1926. He made contributions to algebraic topology, algebraic geometry, and algebraic number theory. he was awarded the fields medal, won the wolf prize (2000( and the Abel prize (2003). Together with cartoon, serve established the technique of using eilenbergmaclane spaces for computing homotopy groups of seres, at that time a major problem in topology.
YUTAKA TANIYAMA
novemeber 12, 1927novemebr 17, 1958. he is known for the taniyamashimura conjecture. RIP.
LENNART CARLESON march 18, 1928. Known as a leader in the field of harmonic analysis. He proved lusin’s conjecture. he also solved the probability problem of stopping times. In the theory of hardy spaces, he contributed the corona theorem, and established the almost everywhere convergence of fourier series for squareintegratabtle functions, now known as Carleson’s theorem. he is also known for the theory of Carleton measures. In the theory of dynamical systems, he has worked in complex dynamics.
ALEXANDER GROTHENDIECK March 28, 1928November 13, 2014. Leading figure in the creation of algebraic geometry. He is considered by many to be the greatest mathematician in the 20th century.
JOHN NASH june 13, 1928may 23, 2015. He won the 1994 Nobel prize in economics for his producing mathematics of the highest quality. RIP
MICHAEL ATIYAH april 22, 1929.known for the AtiyahSinger index theorem
GORO SHIMURA
february 23, 1930. he is known for the modularity theorem, previously known as the taniyamashimura conjecture.. he extended the theory of complex multiplication and modular forms to higher dimensions.he brought to the concept of higher dimension equivalent of modular curve. They bear the same relation to general hodge structures as modular curves do to elliptic curves.
STEPHEN SMALE July 15, 1930. He researches toplogy, dynamical systems, and mathematical economics.
JACQUES TITS august 12, 1930. works on group theory and incidence geometry, and introduced the tits buildings, the tits alternative, and the tits group.
JOHN MILNOR february 20, 1931. he is known for his work in differential topology, ktheory, dynamical systems, exotic spheres, farymilnor theorem, milnor’s theorem, milnorthurston kneading theory, and surgery theory.
HEISUKE HIONAKA april 9, 1931. he proved that singularities of algebraic varieties admit resolutions in characteristic zero. he also showed that a deformation of kahler manifolds need not be kahler.
KLAUS ROTH october 29, 1925november 10, 2015. Known for his work on diophantine approximation, the large sieve, discrepancy theory, and irregularities of distribution.
HERBERT WILF June 13, 1931january 7, 2012. Specialized in combinatorics and graph theory.
ROGER PENROSE – August 8, 1931. he is known for his work in mathematical physics and contributions to general relativity and cosmology.
VIVIENNE MALONESMAYES 19321995. the 5th africanamerican woman to earn a Ph.D in math. she studied the properties of functions.
TAIRA HONDA June 2, 1932may 15, 1975. he worked in number theory and proved the hondatate theorem classifying abelian varieties over finite fields. RIP.
KENNETH APPEL October 8, 1932april 19, 2013. he solved the 4color problem in 1976.
JOHN GRIGGS THOMPSON october 13, 1932. noted for his work in the field of finite groups, introducing new techniques in solving the nilpotency of Frobenius kernels problem. he made major contributions to the inverse Galois problem, and found a criterion for a finite group to be a Galois group, which implies that the monster simple group is a Galois group. the Thompson group the is the 26 sporadic finite simple group.
PAUL COHEN april 2, 1934march 23, 2007. He is best known for the proofs that the continuum hypothesis and the axiom of choice are independent from zermelofraenkel set theory.
NICOLAS BOURBAKI a group of mainly French mathematicians aimed at reformulating mathematics on an extremely abstract and formal but selfcontained basis in set theory by writing a series of books beginning in 1935.
YAKOV SINAI september 21, 1935. Contributed to the modern metric theory of dynamical systems and connected the world of deterministic (dynamical) systems with the world of probabilistic (stochastic) systems. he has worked on mathematical physics and probability theory and his efforts have provided the groundwork for advances in the physical sciences.
DONALD KNUTH january 10, 1936. a mathematical and computer scientist, he is known for the knuthmorrispratt algorithm, knuthbendix completion algorithm, and the robinsonschenstedknuth correspondence.
ROBERT LANGLANDS october 6, 1936.known for the ganglands program
C.T.C. WALL december 14, 1936.known for the Brauerwall group, Wall’s conjecture, Surgery on compact manifold.
YURI MANIN 1937. has worked in algebraic geometry and diophantine geometry.
DAVID MUMFORD june 11, 1937. he is known for distinguished work in algebraic geometry, the mumfordshah functional, and research into vision and pattern theory.
BARRY MAZUR december 19, 1937. he is known for diophantine geometry, generalized schoenflies conjecture, Mazur swindle, and Mazur torsion theorem.
JAMES HARRIS SIMONS 1938. He developed the chernsimons form, and contributed to the development of string theory by providing a theoretical framework to combine geometry and topology with quantum field theory.
C.P. RAMANUJAM
january 9, 1938october 27, 1974. he worked in the fields of number theory and
algebraic geometry. He worked on waring’s problem in algebraic number fields and made contributions to number theory. RIP.
SERGEI NOVIKOV march 20, 1938. noted for work in algebraic topology and soliton theory. he has worked in ciborium theory. he showed how the Adams spectral sequence, used in calculating homotopy groups, could be adapted to cohomology theory typified by cobordism and ktheory. This required the development of the idea of cohomology operations in the general setting, since the basis of spectral sequence is the initial data of ext functors taken with respect to a ring of such operations, generalizing the steered algebra. the resulting adamsnovikov spectral sequence is now a basic tool in stable homotopy theory.
ALAN BAKER august 19, 1939. Known for his work on effective methods in number theory, in particular those arising from transcendental number
theory. He is also known for work in diophantine equations and for baker’s theorem.
SRINIVAS VARADHAN january 2, 1940. Known for his fundamental contributions to probability theory and in particular for creating a unified theory of large deviations.
ENDRE SZEMERELI august 21, 1940.known for Szemeredi’s theorem, the Szemeredi regularity lemma, the ErdosSzemeredi theorem, the HajnalSzemeredi theorem, and the SzemerediTrotter theorem
ENRICO BOMBIERI november 26, 1940. He is known for large sieve method in analytic number theory, bombierilang conjecture, bomber norm, bombierivinogtadov theorem, heights in diophantine geometry, siege’s lemma, and bomierifriedlanderiwaniec theorem.
KAREN UHLENBECK august 24, 1942. Known for work in the calculus of variations.
MIKHAIL GROMOV December 23, 1943. he has made revolutionary contributions to geometry.
PIERRE DELIGNE October 3, 1944. he is known for work on the Weil conjectures, leading to a complete proof in 1973.
MITCHELL FEIGENBAUM december 19, 1944. Pioneering work in chaos theory and discoverer of the Feigenbaum constants.
PERCI DIACONIS january 31, 1945. – known for tackling math problems involving randomization, such as coin flipping and shuffling playing cards.
GRIGORY MARGULIS february 24, 1946. Known for work on lattices in lie groups, and the introduction to methods from ergodic theory into diophantine approximations.he is also known for the super rigidity theorem, arithmeticity theorem, expander graphs, and the Oppenheimer conjecture.
WILLIAM THURSTON October 30, 1946August 21, 2012. he has made contributions to the study of 3manifolds.
ALAIN CONNES april 1, 1947. Known for the baumconnes conjecture, noncompetitive geometry, and operator algebras.
JOHN BALL 1948. He has researched elasticity, the calculus of variations, and infinite dimensional dynamical systems.
LASZLO LOVASZ march 9, 1948. he is best known for his work in combinatorics.
SHINGTUNG BYAU april 4, 1949. he has worked mainly in differential geometry, especially geometric analysis. his proof of the positive energy theorem in general relativity demonstrated that einstein’s theory is consistent and stable. his proof of the calami conjecture allowed physicists to show, using calaiyau compactification, that string theory is a viable candidate for a unified theory of nature. Calaiyau manifolds are part of the standard toolkit for string theorists today.
CHARLES FEFFERMAN april 18, 1949.he received his phd from princeton at age 20 in computer, mathematical, and natural sciences. his primary field of research is mathematical analysis. He contributed innovations that revised the study of multidimensional complex analysis by finding fruitful generalizations of classical lowdimensional results. His work on partial differential equations, fourier analysis, in particular convergence, multipliers, divergence, singular integrals and hardy spaces earned him the fields medal in 1978. His work also included a study of the asymptotics of the Bergman kernel off the boundaries of pseudo convex domains in c^m. He has studied mathematical physics, harmonic analysis, fluid dynamics, neural networks, geometry, and spectral analysis.
FAN CHUNG October 9, 1949. Works mainly in spectral graph theory, extremal graph theory, and random graphs, in particular in generalizing the erdosrenyi model for graphs with general distribution (including powerlaw graphs in the study of large information networks.)
FRANK KELLY December 28, 1950. he specializes in optimization, queueing theory, and network theory, and has researched random processes, networks, and optimization, especially in very largescale systems such as telecommunications or transportation networks.
MICHAEL FREEDMAN april 21, 1951. He worked on the poincare conjecture in dimension 4, and showed that exotic R^4 manifolds exist.
EDWARD WITTEN August 26, 1951. he is known for work in mathematical physics dealing with string theory, quantum gravity, and supersymmetric quantum field theories.
PETER HALL november 20, 1951janusry 9, 2016known for nonparametric statistics and the bootstrap method
BERNARD SILVERMAN february 22, 1952. a statistician known for density estimation, nonparametric regression, and functional data analysis.
BRIAN D. RIPLEY April 29, 1952. he has made contributions to the fields of spacial statistics and pattern recognition, and his work on artificial neural networks.
VAUGHN JONES december 31, 1952. he is known for his work on von Neumann algebras, discovery of the jones polynomial, knot polynomials, and increased interest in lowdimensional topology..
ANDREW WILES april 11, 1953. He proved fermat’s last theorem, which was proposed in the 1600s, in 1994. he is also known for proving the TaniyamaShimura conjecture for semistable elliptic curves, proving the main conjecture of Iwasawa theory
PETER SARNAK December 18, 1953. he is known for his work in analytic number theory, and the hafnersamakmccurley constant.
VLADIMIR DRINFELD february 14, 1954. his work is in algebraic geometry over finite fields with number theory, especially the theory of automorphic forms, through the notions of elliptic module and the theory of the geometric ganglands correspondence. he is known for quantum groups, geometric ganglands correspondence, the drinfelfsokolovwilson equation, and the manindrinfeld theorem.
JEAN BOURGAIN febraury 28, 1954. he is known for work in analytic number theory, harmonic analysis, ergodic theory, Banach spaces, and partial differential equations.
GERD FALTING july 28, 1954. Known for his work in algebraic geometry, and for the morsel conjecture and the faltings’ product theorem.
INGRID DAUBECHIES august 17, 1954.known for wavelets.
EFIM ISAAKOVICH ZELMANOV september 7, 1955. he is known for his work on combinatorial problems in non associative algebra and group theory, including his solution of the restricted burnside problem. he has worked on jordan algebras in the case of infinite dimensions, and has shown that the glennie’s identity in a certain sense generated all identities that hold. he then showed that the engel identity for lie algebras implies nilpotent, in the case of infinite dimensions.
DORIN ANDRICA march 12, 1956. Known for the andrica’s conjecture, which deals with the gaps between prime numbers.
NOGA ALON february 17, 1956. he contributed to combinatorics and computer science.
PIERRELOUIS LIONS august 11, 1956. he has worked on partial differential equations. he was the first to give a complete solution to the boltzmann equation with proof. he is known for the mean field game theory.
JEANCHRISTOPHE YOCCOZ may 29, 1957september 3, 2016. he is known for dynamical systems and the yoccoz puzzle.
SIMON DONALDSON August 20, 1957. he is known for his work on topology of smooth (differentiable) 4dimensional manifolds, Donaldson theory, and donaldsonthomas theory.
CURT MCMULLEN may 21, 1958. he is known for work in complex dynamics, hyperbolic geometry, and telchuller theory.
RICHARD BORCHERDS November 29, 1959. Currently working on quantum field theory. he is known for work on lattices, number theory, group theory, and infinite dimensional algebras. he is also known for Borcherds algebra. he pioneered the classification of unimodular lattices, and introduced new algebraic objects, most notably vertex algebras and BorchersKacMoody algebras. these ideas came together in his vertex algebraic construction and analysis of the fake monster lie algebra. He resolved the conwaynorton monstrous moonshine conjecture, which describes an intricate relation between the monster group and modular
functions on the complex upper halfplane. To prove this conjecture, he drew on theories of vertex algebras and borcherdskacmoody algebras along with string theory, and applied them to the moonshine module, a vertex operator algebra with monster symmetry.additional work in moonshine concerned mod p variants of this conjecture, and were known as modular moonshine. He also produced the theory of borcherds product, which are holomorphic automorphic forms on O(n,2) that have well behaved infinite product expansions at cusps.he used this theory to resolve some long standing conjectures about affineness of certain moduli spaces of algebraic surfaces. he has also put perturbative renormalization, in particular the 1hooftveltman proof of perturbative renormalizability of gauge theory, into rigorous mathematical language.
JOHN BAEZ June 12, 1961. a mathematical physicist.
TIM GOWERS november 20, 1963. he is known for work in functional analysis and combinatorics.
MAXIM KONTSEVICH august 25, 1964 his work concentrates on geometric aspects of mathematical physics, most notably knot theory, quantization, and mirror symmetry. one of his results is a formal deformation quantization that holds for any poisson manifold. he also introduced knot invariants defined by complicated integrals analogous to feynman integrals. In topological field theory, he introduced the moduli space of stable maps, a rigorous formulation of the feynman integral for topological string theory.
VLADIMIR VOEVODSKY june 4, 1966. Worked on developing homotopy theory for algebraic varieties and formulated motivic cohomology. he proved the minor conjecture and motivic blochkato conjecture. He is also known for the invariant foundations of mathematics and homotopy type theory.
PERELMAN june 13, 1966. Made landmark contributions to Riemann geometry and geometric topology. He proved the poincare conjecture in 2003, one of the millennial prizes, but refused to accept the 1 million dollar award for solving the problem.
NOAM DAVID ELKIES august 25, 1966. he extended school’s algorithm to create the schoolelkiesatkin algorithm, proved that an elliptic curve over the rational numbers is super singular at infinitely many primes, and he found a counterexample of ruler’s sum of powers conjecture for fourth powers.
LAURENT LAFFORGUE november 6, 1966. made outstanding contributions to langlands’ program in the fields of number theory and analysis. He proved the ganglands conjectures for the automorphism group of a function field. he proved the question of the construction of compactifications of certain moduli stacks of shtukas.
WENDELIN WERNER September 23, 1968. Works on random walks, brownian motion, schrammloewner evolution, and related theories in probability theory and mathematical physics. he won the fields medal for his contributions to the development of stochastic loewner evolution, the geometry of 2dimensional brownian motion, and conformal field theory.
SHINICHI MOCHIZUKI march 29, 1969. He is the leader of and the main contributor to one of the major parts of modern number theory, anabelian geometry. he solved the grothendieck conjecture in anabelian geometry about hyperbolic curves over number fields. He initiated and developed absolute anabelian geometry, monoanabelian geometry, and combinatorial anabelian geometry. He introduced padic teichmuller theory and hodge arakelov theory. his recent theories include the theory of trobenioids,
anabelioids and the stale thetafunction theory. He is author of the inter universal theichmuller theory also referred to as the arithmetic deformation theory or mochizuki theory. It supplies a new conceptual view on numbers, by using groups of symmetries such as the full absolute Galois groups and arithmetic fundamental groups. Its applications provide solutions to problems such as the spire conjecture, the hyperbolic Volta conjecture, and
the abs conjecture and its generalization over arbitrary number fields.
RAVI VAKIL February 22, 1970.algebraic geometer, known for GromovWitten theory, worked on Schubert calculus, he proved that all Schubert problems are enumerative over the real numbers
ANDREI OKOUNKOV july 26, 1969. Works on representation theory of infinite symmetric groups and its applications to algebraic geometry, mathematical physics, probability theory and special functions, the statistics of plane partitions, and quantum cohomology of the hilbert scheme of points in the complex plane. He formulated wellknown conjectures relating the gromovwitten invariants and donaldsonthomas invariants of threefold. he bridged probability, representation theory, and algebraic geometry.
ELON LINDERSTRAUSS august 1, 1970. Works in the area of dynamics, particularly the area of ergodic theory and its applications to number theory, has made progress on the Littlewood conjecture and major progress on Peter saran’s arithmetic quantum unique ergodicity conjecture, studied the distributions of torus periodic orbits of some arithmetic spaces, generalizing theorems by Hermann Minkowski and Yuri link, and has studied systematically the invariant of mean dimension introduced in 1999 by mikhail gromov.
ISLAV SMIMOV september 3, 1970. His research includes complex analysis, dynamical systems, and probability theory. he did work on critical percolation theory, where he proved the cary’s formula for critical percolation on the triangular lattice, and deduced conformal invariance. the smimov’s theorem has led to a fairly complete theory for percolation on the triangular lattice and its relationship to the schrammloewner evolution, and established conformality for there randomcluster model and Ising model in 2 dimensions.
NGO BAO CHAU june 28, 1972. Best known for proving the fundamental lemma for unitary groups/automorphic forms.the general strategy was to
understand the local orbital integrals appearing in the fundamental lemma in terms of affine springer fibers arising in the hitching vibration. This allowed the use of geometric representation theory, the theory of perverse sheaves, to study what was initially a combinatorial problem in a number theoretic nature. he proved the fundamental lemma for lie algebras. he completed the proof of the fundamental lemma in all cases.
CEDRIC VILLANI october 5, 1973. Works primarily on partial differential equations, Riemann geometry, and mathematical physics. he is known for work on boltzmann equation, kinetic theory, landau damping, transportation theory, and ottovillain theorem.
MANJUL BHARGAVA august 8, 1974. known for the gauss composition laws, 290 theorems, factorial function, ranks of elliptic curves, geometric number theory, representation theory, padic analysis
TERRENCE TAO july 17, 1975. know for the GreenTao theorem, Tao’s inequality, Kakeya conjecture, Horn conjecture
MARTIN HAIRER november 14, 1975. works in the field of stochastic analysis, particularly stochastic partial differential equations. He made fundamental advances in many important directions such as the study of variants of hormander’s theorem, systematization of the construction of Lyapunov functions for stochastic systems, development of a general
theory of egodicity for nonmarkovian systems, multi scale analysis techniques, theory of homogenization, theory of path sampling and, most recently, theory of rough paths and the newly introduced theory of regularity structures.
BEN GREEN february 27, 1977.known for the GreenTao theorem, proof of the CameronErods conjecture, combinatorics, and number theory
MARYAM MIZAKHANI may 3, 1977july 14, 2017. Research topics included teichmuller theory, hyperbolic geometry, ergodic theory, and symplectic geometry. she won the fields medal for her work in the dynamics and geometry of Riemann surfaces and their moduli spaces.
1978LEONARD ALDEMAN december 31, 1945.,RONALD RIVEST may 6, 1947., ADI SHAMIR july 6, 1952. creators of the Ursa encryption algorithm.
ARTUR AVILA june 29, 1979. Works primarily on dynamical systems and special theory. he proved the conjecture of the 10 martinis, which explains mathematical physicist Barry Simon’s theory about the behavior of schrodinger operators, mathematical tools related to quantum physics.
1994 PAUL WOLFSKEHL June 30, 1856September 13, 1906, TANIYAMA november 12, 1927november 17, 1958, GORO SHIMURA february 23, 1930., BARRY MAZUR December 19, 1937., NICK KATZ December 7, 1943., JOHN COATES january 26, 1945., KEN KIBET june 28, 1948., ANDREW WILES april 11, 1953., RICHARD TAYLOR may 19, 1962. The people mainly responsible for the proving of fermat’s last theorem.
PHYSICISTS
MIGUEL ALCUBIERRE march 28, 1964. Mexican theoretical physicist known for the Alcubierre drive, a speculative warp drive for a spacecraft that can travel faster then the speed of light.
ALHAZEN c. 965c. 1040. widely considered the 1st theoretical physicists as a proponent of the scientific method.
LUIS ALVAREZjune 13, 1911september 1, 1988. One of the most brilliant and productive experimental physicists of the 20th century. he devised a set of experiments to observe kelectron capture, predicted by the beta decay theory but never before observed. he produced tritium using a cyclotron and measured its halflife. he also measured the magnetic moment of a neutron.
ANDRE MARIE AMPERE january 22, 1775june 10, 1836. founded and named the science of electrodynamics, now known as electromagnetism. the unit of electric current, the ampere, is named after him.
CARL ANDERSON september 3, 1905january 11, 1991. he discovered the positron.
ANDERS ANGSTROM august 13, 1814june 21, 1874. One of the founders of the science of spectroscopy. the angstrom, a unit 10^10 meters long, in which the wavelength of light is measured, is named after him.
ARCHIMEDES c. 287 bcc. 212 bc. he is known for the archimedes’ screw and the archimedes principle.
ARISTARCHUS c. 310 bcc. 230 bc. One of the first to predict the rotation of the earth, and he placed the sun at the center of the universe.
AMEDEO AVOGADRO august 9, 1776july 9, 1856. He is most noted for his contribution to molecular theory now known as avogadro’s law and for the avagadro constant.
JOHANN BALMER may 1, 1825march 12, 1898. the Balmer lines (spectral line emissions of the hydrogen atom) and Balmer series are named after him.
JOHN BARDEEN may 23, 1908january 30, 1991. Known for the invention of the transistor and for a fundamental theory of conventional superconductivity known the bfs theory.
HENRI BECQUEREL december 15, 1852august 25, 1908. the 1st person to discover evidence of radioactivity.
ALEXANDER GRAHAM BELL march 3, 1847august 2, 1922. Crated the telephone.
DANIEL BERNOULLI february 8, 1700march 17, 1782. Known for his applications of math to mechanics, especially fluid mechanics. he is known for the Bernoulli principle,
an example of the conservation of energy, underlying the carburetor and the airplane wing.
NIELS BOHR october 7, 1885novemebr 18, 1962. Made foundational contributions to understanding atomic structure and quantum theory. he developed the Bohr model of the atom, which proposed that energy levels of electron are discrete and that electrons revolve in stable orbits around the atomic nucleus but can jump from one energy level, or orbit to another
LUDWIG BOLTZMANN february 20, 1844september 5, 1906. he developed statistical mechanics, which explains and predicts how the properties of atoms, such as mass, charge, and structure, determine the physical properties of matter, such as viscosity, thermal conductivity, and diffusion. RIP
MAX BORN december 11, 1882january 5, 1970. Instrumental in the development of quantum mechanics. He proved that schrodinger’s wave equation could be interpreted as giving statistical rather than exact productions of variable.
SATYENDRA NATH BOSE january 1, 1894february 4, 1974. he is best known for his work on quantum mechanics, providing the foundation for boseeinstein statistics and the theory of the bose einstein condensate.
ROBERT BOYLE january 25, 1627december 31, 1691. One of the pioneers of modern experimental scientific method. he is best
known for boyle’s law, which describes how the pressure of a gas tends to increase as the volume of the container decreases.
WILLIAM HENRY BRAGG July 2, 1862march 12, 1942. he is known for the analysis of crystal structure by xrays.
WILLIAM LAWRENCE BRAGG march 31, 1890july 1, 1971. he discovered bragg’s law of xray diffraction, which is basic for the determination of crystal structure.
PERCY WILLIAMS BRIDGMAN april 21, 1882august 20, 1961. he is known for his work in high pressure physics. RIP
LOUIS VICTOR DE BROGLIE august 15, 1892march 19, 1987. he made groundbreaking contributions to quantum theory. he postulated the wave nature of electrons and suggested that all matter has wave properties (known as the de Broglie hypothesis), which is an example of waveparticle duality, and forms a central part of the theory of quantum mechanics.
SADI CARNOT June 1, 1796august 24, 1832. Described as the father of thermodynamics. he gave the 1st successful theory of the maximum efficiency of heat engines. His work led to the 2nd law of thermodynamics and the the law of entropy.
HENDRIK CASIMIR july 15, 1909may 4, 2000. he is known for the casimr effect, which in quantum field theory are physical forces arising from a quantized field.
HENRY CAVENDISH october 10, 1731 february 24, 1810. he is known for the discovery of hydrogen and for measuring the density of the earth.
JAMES CHADWICK october 20, 1891july 24, 1974. Known for the discover of the neutron.
OWEN CHAMBERLAIN july 10, 1920february 28, 2006. Discovered the antiproton.
PAVEL CHERENKOV july 28, 1904january 6, 1990. he is known for Cherenkov radiation, which are charged atomic particles which move at a greater velocity than light.
RUDOLF CLAUSIUS january 2, 1822august 24, 1888. One of the founders of the science of thermodynamics. He restated the Carnot cycle as a theory of heat, and he stated the 2nd law of thermodynamics.
JOHN COCKCROFT may 27, 1897september 18, 1967. He split the atom, which was instrumental in the development of atomic power.
ARTHUR COMPTON september 10, 1892march 15, 1962. he discovered the Compton effect, which demonstrated the particle nature of electromagnetic radiation.
EDWARD CONDON march 2, 1902march 26, 1974. a pioneer in quantum mechanics and a participant in the development of radar.
CHARLESAUGUSTIN DE COULOMB CharlesAugustin de Coulomb
june 14, 1736august 23, 1806. he is best known for developing coulomb’s law, which states the force of attraction of repulsion between charged particles.
SIR WILLIAM CROOKE june 17, 1832april 4, 1919. he was a pioneer in the development of the crooks tube, a vacuum tube.
MARIE CURIE november 7, 1867july 4, 1934. She conducted pioneering work in radioactivity, and discovered the elements polonium and radium.
JOHN DALTON september 6, 1766july 27, 1844. he enunciated gaylussac’ law (pertains to thermal expansion of gasses and the relationship between temperature, volume, and pressure) and dalton’s law, concerning the law of partial pressure (in a mixture of
nonreacting gasses, the total pressure exerted is equal. to the sum of the partial pressures of the individual gases).
TsungDao Lee November 24, 1926) is a ChineseAmerican physicist, known for his work on parity violation, the Lee Model, particle physics, relativistic heavy ion (RHIC) physics, nontopological solitons and soliton stars. Lee, at the age of 30, won the Nobel Prize in Physics with Franklin C N Yang for their work on the violation of the parity law in weak interactions, which Chien Shiung Wu experimentally verified.
CLINTON DAVISSON october 22, 1881february 1, 1958. Discovered electron diffraction.
PAUL DIRAC august 8, 1902october 20, 1984. Made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics. he made significant contributions to the reconciliation of general relativity with quantum mechanics. he formulated the Dirac equation which describes the behavior of fermions and he predicted the existence of antimatter.
CHRISTIAN DOPPLER November 29, 1803march 17, 1853. He discovered the principle of the doppler effect, which says that the observed frequency of a wave depends on the relative speed of the source and the observer.
FREEMAN DYSON December 15, 1923. Physicist known for his work in quantum electrodynamics and solidstate physics. he developed a description of quantum physics based on m and m array of totally random numbers.
WILLIAM ECCLES august 23, 1875april 29, 1965. Pioneered the development of radio communication.
PAUL EHRENFEST january 18, 1880september 25, 1933. Made major contributions to the field of statistical mechanics and its relation to quantum mechanics, including his theory of phase transition and the Ehrenfest theorem.
ALBERT EINSTEIN Albert Einstein
march 14, 1879april 18, 1955. Developed the theories of general and special relativity, the law of photoelectric effect, brownian movement, and the massenergy equivalence formula: e=mc^2.
LORAND EOTVOS july 27, 1848april 8, 1919. Remembered for his work on gravitation and surface tension, and the invention of the torsion pendulum.
CORNELIUS EVERETT worked with stanislaw ulam to find amount of tritium needed for to hbomb.
DANIEL GABRIEL FAHRENHEIT may 24, 1686september 16, 1736. Laid the foundation for the era of precision thermometry by inventing the mercuryinglass thermometer. the fahrenheit temperature scale is named after him.
MICHAEL FARADAY september 22, 19791august 25, 1867. he contributed to the study of electromagnetism and electrochemistry, and discovered the principles of electromagnetic induction, diamagnetism, and electrolysis.
ENRICO FERMISeptember 29, 1901november 28, 1954. Creator of the 1st nuclear reactor. he induced radioactivity by neutron bombardment, and discovered transuranic elements. he made significant contributions to the development of quantum theory, nuclear and particle physics, and statistical mechanics.
RICHARD FEYNMAN may 11, 1918february 15, 1988. Known for his work in the path integral formulation of quantum mechanics, the theory of quantum electrodynamics, the physics of superfluidity of supercooled liquid helium, and particle physics where he proposed the Parton model.
GEORGE FRANCIS FITZGERALD august 3, 1851february 22, 1901. he is known for his work in electromagnetic theory and for the lorentzfitzgerald contraction, which became an integral part of einstein’s special theory of relativity.
LEON FOUCAULT september 18, 1819february 11, 1868. known for his demonstration of the Foucault pendulum, which demonstrates the effect of earth’s rotation. he also made an early measurement of the speed of light.
BENJAMIN FRANKLIN january 17, 1706april 17, 1790. he was the 1st to label electric charges as positive and negative, and he discovered the principle of conservation of charge. he invented the lightning rod.
JOSEPH VON FRAUNHOFER march 6, 1787june 7, 1826. He discovered and studied the dark absorption lines in the spectrum of the sun that are now known as Fraunhofer lines.
AUGUSTINJEAN FRESNEL may 10, 1788july 14, 1827. He is the inventor of the Fresnel sense, and he formulated the fresnel equation which is the basis for many applications in computer graphics.
DENNIS GABOR june 5, 1900february 9, 1979. He invented holography.
GALILEO GALILEIfebruary 15, 1564january 8, 1642. He is known for kinematics and dynamics in the physics of falling bodies.
CARL FRIEDRICH GAUSS april 30, 1777february 23, 1855. he is known for gauss’s law of magnetism, which is one of Maxwell’s 4 equations that underlie classical electrodymamics.
JOSEPH LOUIS GAYLUSSAC december 6, 1778may 9, 1850. he is known for gay lussac’s law, which pertains to thermal expansion of gasses and the relationship between temperature, volume, and pressure.
HANS GEIGER september 30, 1882september 24, 1945. best known as coinventor of the geiger counter and the geiger marsden experiment which discovered the atomic nucleus.
MURRAY GELLMANN september 15, 1929. know for his work on the theory of elementary particle physics. the coined the term ‘quark’.
JOSIAH WILLARD GIBBS february 11, 1839april 28, 1903. he was cocreator of stistical mechanics that explained the laws of thermodynamics as consequences of the stistical properties of ensembles of the possible states of a physical system composed of many particle.
MARIA GOEPPERTMAYER june 28, 1906february 20, 1972. Proposed a nuclear shell model of the atomic nucleus.
BRIAN GREENE february 9, 1963. Worked on mirror symmetry, relating 2 different calaiyau manifolds (concretely, relating the conifold to one of its orbifolds). he also described the flop transition, a mild form of topology change, showing the topology in string theory can change at the conifold point.
FEZA GURSEY april 7, 1921april 13, 1992. Turkish mathematician physicist who worked on the chiral model and on su(6).
OTTO HAHN march 8, 1879july 28, 1968. Pioneer in the field of radioactivity. he provided proof of nuclear fission.
EDWIN HALLnovemebr 7, 1855november 20, 1938. Discovered the hall effect, the production of a voltage difference (hall voltage) across an electric conductor, transverse to an electric current in the conductor and the applied magnetic field perpendicular to the current.
STEPHEN HAWKING january 8, 1942march 2018. the 1st to set out a theory of cosmology explained by a union of the general theory of relativity and
quantum mechanics. he strongly supports the many worlds interpretation of quantum mechanics.
OLIVER HEAVISIDE may 18, 1850february 3, 1925. he reformulated Maxwell’s field equations in terms of electric and magnetic forces and energy flux.
WERNER HEISENBERGHeisenberg in 1933, as professor at Leipzig University december 5, 1901february 1, 1976. on of the key pioneers of quantum mechanics. he he developed a matrix formulation of quantum mechanics. he formulated the Heisenberg uncertainty principle, which says that there is a fundamental limit to the precision in which a particle’s position and momentum can be known.
HERMANN VON HELMHOLTZ august 31, 1821september 8, 1894. Known for his theories on the conservation of energy, work in electrodynamics, chemical thermodynamics, and on the mechanical foundation of thermodynamics.
JOSEPH HENRY december 17, 1797may 13, 1878. Discovered the electromagnetic phenomenon of selfinductance. the unit of inductance, the Henry, is named after him.
HEINRICH HERTZ february 22, 1857january 1, 1894. he proved the existence of electromagnetic waves. the unit of frequency, the hertz, is named after him.
PETER HIGGS Nobel laureate Peter Higgs at a press conference, Stockholm, December 2013 may 29, 1929. he proposed that broken symmetry in electroweak theory could explain the origin of mass of elementary particles the general and of the w and z bosons in particular. This Higgs mechanism, predicts the existence of a new particle, the Higgs boson.
ROBERT HOOKE july 28, 1635march 3, 1703. he is known for hooke’s law, which states that the force needed to extend or compress a spring by some distance x is proportional to that distance.
SHIRLEY ANN JACKSON august 5, 1946. the first African American woman to earn a ph.d. in nuclear physics.
JOHANNES HANS DANIEL JANSEN june 25, 1907february 11, 1973. he is co proposer of the nuclear shell model of the atomic nucleus.
IRENE JOLIOTCURIE september 12, 1897march 17, 1956. Discoverer of artificial radioactivity.
PASCAL JORDANoctober 18, 1902july 31, 1980. Made significant contributions to quantum mechanics and quantum field theory. he contributed much to the mathematical form of matrix mechanics, and developed canonical anti commutation relations for fermions. Jordon algebra is used to study the mathematical and conceptual foundations of quantum theory.
JAMES PRESCOTT JOULE december 24, 1818october 11, 1889. He studied the nature of heat, and discovered its relationship to mechanical work. this led to the law of conservation of energy, which led to the development of the 1st law of thermodynamics. the joule, a unit for energy, is named after him.
PYOTR KAPITSA july 8, 1894april 8, 1984. Best known for his work in low temperature physics.
GUSTAV ROBERT KIRCHHOFF march 12, 1824october 17, 1887. he contributed in a fundamental way to understanding the emission of blackbody radiation by heated objects. kirchoff’s law of thermal radiation refers to wavelengthspecific radiation emission and absorption by a material body in thermodynamic equilibrium, including radiative exchange equilibrium.
MILOTO KOBAYASHI april 7, 1944. Known for his work on cp violation. He discovered the origin of the broken symmetry which predicted the existence of at least 3 families of quarks in nature.
WILLIS LAMB july 12, 1913may 15, 2008. he determined the precise magnetic moment of the electron.
LEV LANDAU January 22, 1908april 1, 1968. he is known for the density matrix method in quantum mechanics, the quantum mechanical theory of diamagnetism, the theory of superconductivity, the theory of fermi liquid, the explanation of landau damping in plasma physics, the damping in quantum electrodynamics, the 2 component theory of neutrinos, and the landau equations for s matrix singularities.
PAUL LANGEVIN january 23, 1872december 19, 1946. he is known for the twin paradox, Langevin dynamics, and the Langevin equation.
ERNEST LAWRENCE august 8, 1901august 27, 1958. Inventor of the cyclotron.
TSUNGDAO LEE november 24, 1926. Known for his work on parity violation, the lee model, particle physics, and relativistic heavy ion physics.
HENDRIK LORENTZ july 18, 1853february 4, 1928. he is known for the Lorentz for in magnetism, his discovery and theoretical explanation of the Zeeman effect, and deriving the transformation equations which form the basis of the special theory of relativity.
ERNEST MACH february 18, 1838february 19, 1916. the mach number is named after him, which is a shock wave and is the ratio of ones speed to that sound.
THEODORE MAIMAN july 11, 1927may 5, 2007. He in vented the first working laser, the ruby laser.
GUGLIELMO MARCONI april 25, 1874july 20, 1937. did Pioneering work in long distance radio communication and for his development of marconi’s law (the relation between height of antennas and maximum signaling distance of radio transmission) and the radio telegraph system.
JOHN MATHERS august 7, 1946. he is known for his work on the cosmic background explorer satellite and research into cosmic microwave background radiation.
JAMES CLERK MAXWELL june 13, 1831novemeber 5, 1879. he formulated the classical theory of electromagnetic radiation, bringing together for the first time electricity, magnetism, and light as manifestations of the same phenomenon.
LISE MEITNER november 7, 1878october 27, 1968. Discovered the nuclear fission of uranium when it absorbed an extra neutron.
ALBERT MICHELSON december 19, 1852may 9, 1931. Known for his work on the measurement of the speed of light.
ROBERT MILLIKAN march 22, 1868december 19, 1953. he measured the elementary electronic charge and worked on the photoelectric effect.
HENRY MOSELEY november 23, 1887august 10, 1915. he is known for the concept of the atomic number and moseley’s law, an empirical law concerning the characteristic xrays that are emitted by atoms.
SETH NEDDERMEYER september 15, 1907january 29, 1988. Codiscoverer of the muon.
YUVAL NE’EMAN may 14, 1925april 26, 2006. In 1961, he discovered the classification of hadrons through the su(3) flavor symmetry, now called the eightfold way.
JOHN VON NEUMANN December 28, 1903february 8, 1957. he established a rigorous mathematical framework for quantum mechanics.
SIR ISAAC NEWTONdecember 25, 1642march 20, 1727. he laid the foundations of classical mechanics and formulated the laws of motion and universal gravitation.
EMMY NOETHERmarch 23, 1882april 14, 1935. She produced norther’s theorem, which explains the connection between symmetry and conservation laws.
GEORG OHM march 16, 1789july 6, 1854. he formulated ohm’s law, which says that there is a direct proportionality between the potential difference (voltage) applied across a conductor and the resultant electric current.
HANS CHRISTIAN ORSTED august 14, 1777march 9, 1851. he discovered that an electric current creates a magnetic field.
BLASE PASCAL june 19, 1623august 19, 1662. he made important contributions to the study of fluids, and clarified the concepts of pressure and vacuum.
WOLFGANG PAULIapril 25, 1900december 15, 1958. he is known for the Pauli exclusion principle (states that 2 or more identical fermions, particles with 1.2 integer spin, cannot occupy the same quantum state within a quantum system simultaneously) which involves spin theory, the basis of a theory of the structure of matter.
MARTIN PERL june 24, 1927september 30, 2014. he discovered the tau lepton.
MAX PLANCKapril 23, 1858october 4, 1947. he has a primary role as the originator of quantum theory and his discovery of the energy quanta. Ke is known for Planck’s constant and Planck’s law of black body radiation, which describes the spectral density of electromagnetic radiation emitted by a body of thermal equilibrium at a given temperature.
HENRI POINCAREapril 29, 1854july 17, 1912. a mathematical physicist, he was the first to present the Lorentz transformations in their modern symmetrical form.
EDWARD PURCELL august 30, 1912march 7, 1997. he discovered nuclear magnetic resonance, which became widely used to study the molecular structure of pure materials and the composition of mixtures,
HELEN QUINN may 19, 1943. she made major contributions as a particle physicist, such as the perceivedquint theory, which implies a corresponding symmetry of nature (related to matter antimatter symmetry and the possible source of the dark matter that pervades the universe) and her contributions to the search for a unified theory for the 3 types of particle interactions: strong, electromagnetic, and weak.
ISIDOR RABI july 29, 1898janulary 11, 1988. he discovered nuclear magnetic resonance imaging, and was on of the first to work on the cavity magnetron, which is used in microwave radar and microwave ovens.
CHANDRASEKHARA RAMAN novemebr 7, 1888november 21, 1970. he did ground breaking work in the field of light scattering. he discovered that when light traverses a transparent material, some of the deflected light changes wavelength, which is known as the Raman effect.
LISA RANDALLjune 18, 1962. She researches elementary particles, fundamental forces and extra dimensions of space, the standard model, supersymmetry, possible solutions to the hierarchy problem
concerning the relative weakness of gravity, cosmology of extra dimensions, baryogenesis, cosmological inflation, and dark matter.
LORD RAYLEIGH november 12, 1842june 30, 1919. He discovered argon, Rayleigh scattering, which can explain why the sky is blue, and he predicted the existence of the surface waves known as Rayleigh waves.
OWEN RICHARDSON april 26, 1879february 15, 1959. he worked on thermionic emission which led to richardson’s law, which states that the current from a heated Wire sees to depend exponentially on the temperature of the wire in a form similar to the Arrhenius equation.
ROBERT RICHARDSON june 26, 1937february 19, 2013. he did research in sub millikelvin temperature studies of helium3.
WILHELM RONTGENmarch 27, 1845february 10, 1923. Discovered xrays.
ABDUS SALAMjanuary 29, 1926november 21, 1996. he worked on electroweak unification theory.
ARTHUR SCHAWLOW may 5, 1921april 28, 1999. Coinventor of the laser.
JULIAN SCHWINGER february 12, 1918july 16, 1994. Best known for his work on the theory of quantum electrodynamics, in particular for developing a relativistically invariant perturbation theory, and for renormalizing red to one loop order.
ARNOLD SOMMERFELD december 5, 1868april 26, 1951. he introduced the 2nd quantum number (azimuthal quantum number ) and the 4th quantum number ( spin quantum number). he also introduced the fine structure constant.
CHARLES PROTEUS STEINMETZapril 9, 1865october 26, 1923. he fostered the development of alternating current that made possible the expansion of the electrical power industry in the united states. he also formulated mathematical theories for engineers and made groundbreaking discoveries in the understanding of hysteresis that enabled engineers to design better electromagnetic apparatus equipment including especially electric motors for use in industry.
GEORGE STOKES august 13, 1819february 1, 1903. Made a seminal contribution to fluid dynamics including the naviesstokes equations.
LEO SZILARD february 11, 1989may 30, 1964. he conceived the nuclear chain reaction.
RICHARD TAYLOR november 2, 1929. Did pioneering investigations concerning deep inelastic scattering of electrons, which was of essential importance in the development of the quark model in particle physics.
EDWARD TELLER january 15, 1908september 9, 2003. he is known for the jahnteller effect and the ashkinteller model, the 2nd of which may help one to gain insight into the behavior of ferromagnets and certain other phenomenon in solidstate physics.
NIKOLA TESLAjuly 10, 1856january 7,1943. he is best know for his contributions to the design of the modern alternating current electrical supply systems.
J.J. TOMSON december 18, 1856august 30, 1940. he discovered the electron.
WILLIAM TOMSON (LORD KELVIN) june 26, 1824december 17, 1907. he did important work in the formulation of the 1st and 2nd laws of thermodynamics and helped unify physics into its modern form. the temperature scale, the kelvin, is named in his honor.
SAMUEL CHAO CHUNG TING january 27, 1936. He discovered the subatomic particle, the j/psi particle.
SINITIRO TOMANAGA march 31, 1906july 8, 1979. he was very influential in the development of quantum electrodynamics, the relativistic quantum field theory of electrodynamics.
EVANGELISTA TORRICELLI october 15, 16080ctober 25, 1647. he invented the barometer, which measures atmospheric pressure.
CHARLES TOWNES july 28, 1915january 27, 2015. he invented the maser.
JOHANNES DIDERIK VAN DER WAALS november 23, 1837 march 8, 1923. Primarily associated with the van Der Waals equation of states that describe the behavior of gases and their condensation to the liquid phase.
STEPHEN WEINBERG may 3, 1933. Contributed to the unification of the weak force and electromagnetic interaction between elementary particles.
HERMANN WEYL november 9, 1885december 8, 1955. he was one of the 1st to conceive of combining general relativity with the laws of electromagnetism.
EUGENE WIGNER november 17, 1902january 1, 1995. he contributed to the theory of the atomic nucleus and the elementary particles, particularly through the discovery and application of fundamental symmetry principles.
JAMES WATT january 30, 1736august 25, 1819. He improved on Thomas newcomer’s steam engine with his watt steam engine. the unit of power, the watt, is named after him.
WILHELM WEBER october 24, 1804june 23, 1891. Coinventor of the 1st electromagnetic telegraph. the unit for magnetic flux, the weber, is named after him.
EDWARD WITTEN august 26, 1951. he researches string theory, quantum gravity, supersymmetric quantum field theories, and other areas of mathematical physics.
EMIL WOLF july 30, 1922. he has made advancements in physical optics, including diffraction, coherence properties of optical fields, spectroscopy, and the theory of direct scattering and inverse scattering.
FRED ALAN WOLF december 3, 1934. he specializes in quantum physics and the relationship between physics and consciousness.
CHIENSHIUNG WU may 31, 1912february 16, 1997. she is best known for her experiment which contradicted the hypothetical law of conservation of parity.
CHEN NING YANG october 1, 1922. He works on statistical mechanics and particle physics. he did work on parity non conservation of weak interaction.
THOMAS YOUNG june 13, 1773may 10, 1829. he is known for the wave theory of light and the doubleslit experiment.
HIDEKI YUKAWA january 23, 1907september 8, 1981. He proposed a theory of mesons in 1935, which explains the interaction between protons and neutrons.
PIETER ZEEMAN may 25, 1865october 9, 1943. he discovered the Zeeman effect, which is the splitting of a spectral line into several components in the presence of a static magnetic field.
Physicists research and study physical phenomena in our universe. Their findings help to explain why the material universe exists and behaves the way that it does. Physicists cover issues ranging from subatomic particles to quantum mechanics, and many others. This is a list of some of the world’s most famous physicists and their great contributions to science and humanity.
CHEMISTS
Svante Arrhenius february 19, 1859october 2, 1927. One of the founders of physical chemistry. He was the 1st to use basic principles of physical chemistry, the study of matter in terms understood by physics, to calculate estimates of the extent to which increases in atmospheric carbon dioxide increase earth’s surface temperature through the Arrhenius effect, leading to what we now understand as global worming caused by human caused carbon dioxide emissions.
Amedeo Avogadro august 9, 1776july 9, 1856. he is known for avogadro’s law, which states that equal volumes of gases under the same conditions of temperature and pressure will contain equal numbers of molecules. Avogado constant is named for him which is the number of atoms, molecules, ions, or other particles in 1 mole (the amount of chemicals as there are in 12 grams of carbon12) of a substance, 6.002140857×10^23 in number.
Leo baekelandnovember 14, 1863february 23, 1944. he is known as the father of the plastic industry for his invention of bakelite, an inexpensive, nonflammable and versatile plastic, that marked the beginning of the modern plastics industry.
Adolf von Baeyer october 31, 1835august 20, 1917. he synthesized indigo, and developed a nomenclature for cyclic compounds.
Johann Konrad Beilstein february 17, 1838october 18, 1906. Founder of the famous handbook of organic chemistry, now known as the beilstein database.
Friedrich Joachim Becher may 6, 1635october 1682. an alchemist known for the development of his phlogiston theory of combustion, which means that a firelike element called phlogiston is contained within combustible bodies and released during combustion.
Marcellin berthelot october 25, 1827march 18, 1907. Known for the thomsenberthelot principle of thermochemistry (hypothesis that argues that all chemical changes are
accompanied by the production of heat where the most heat is produced. he synthesized many organic compounds from inorganic substances.
Carolyn r. Bertozzi october 10, 1966. she is known for biorthogonal chemistry, which means that any chemical reaction that can occur inside of living systems without interfering with native biochemical processes.
Jons jakob berzellus august 20, 1779august 7, 1846. One of the founders of modern chemistry, along with Robert Boyle, john dalton, and Antoine Lavoisier. he is noted for his determination of atomic weights. his experiments led to a more complete depiction of the principles of stoichiometry, or the field of chemical combining proportions. he also showed the power of an electrochemical cell to decompose chemicals into pairs of electrically opposite constituents. he discovered or isolated several new elements, including cerium and thorium. in Sweden, he is known as the father of Swedish chemistry.
Wallace Carothers April 27, 1896april 29, 1937. a leader in organic chemistry, he invented nylon. RIP
Henry Cavendishoctober 10, 1731february 24, 1810. he discovered oxygen, and he described the density of what he called flammable air, which formed water on combustion.
Michelle chang 1977. Researches in biosynthesis of biofuels and pharmaceuticals.
Ernst cohenknown for his work on the allotropy (metals that exist on 2 or more different forms) of metals. murdered in auchwitz. RIP
Gerry cori august 15, 1896october 26, 1957. she is known for extensive research on carbohydrate metabolism, she described the cori cycle (the lactic acid cyclethe metabolic pathway in which lactate produced by anaerobic glycosides in the muscles moves to the liver and is converted to glucose, which then returns to the muscles and is metabolized back to lactate.), and identified glucose 1phosphate.
Archibald scott couper march 31, 1831march 11, 1892. he developed the concept of tetravalent carbon atoms linking together to form larger molecules, and that the bonding order of the atoms in a molecule can be determined from chemical evidence.
William crookes june 17, 1832april 4, 1919. he discovered the new element thallium.
Marie curienovember 7, 1867july 4, 1834. she discovered polonium and radium.
pierre curie may 15, 1859april 19, 1906. he was a pioneer in crystallography.
john dalton september 6, 1766july 26, 1844. he is best known for proposing the modern atomic theory.
Humphry davy december 17, 1778may 29, 1829. he isolated the elements: potassium, sodium, calcium, strontium, barium, magnesium, boron, and discovered chlorine and iodine.he also invented the new field of electrochemistry.
Jean baptiste dumas july 14, 1800april 10, 1884. he is best known for organic synthesis and analysis, determining atomic and molecular weights by measuring vapor densities, and he developed a method for the analysis of nitrogen in compounds.
Henry eyring february 20, 1901december 26, 1981. his primary contribution to chemistry was the study of chemical reaction rates and intermediates.
Michael faradayseptember 22, 1791august 25, 1867. he contributed to the study of electrochemistry.
he discovered benzene, investigated the clathrate hydrate of chlorine, invented the early form of the bunsen burner, the system of oxidation numbers, and popularized the terms anode, cathode, electrode, and ion.
Hermann von Fehling june 9, 1812july 1, 1856. known for developing fehling’s solution used for estimation of sugar.
enrico fermi september 29, 1901november 28, 1954. Discovery of transuranic elements.
Franz Joseph Emil Fischer march 19, 1877december 1, 1947. Discoverer of the fischertropsch process (a collection of chemical reactions that convert mixture of carbon monoxide and hydrogen into liquid hydrocarbons) and developing the Fischer assay.
Edward frankland january 18, 1825august 9, 1899. he is one of the originators of organometallic chemistry and introduced the concept of combining power or valence.
Rosalind Franklin july 25, 1920april 16, 1958. a crystallographer who used xray diffraction on dna fibers and provided key insights into dna structure.
Charles freidel march 12, 1832april 20, 1899. Developed the dreidelcrafts alkylation and acylation reaction.
Joseph louis gayLussac december 6, 1778may 9, 1850. known for his discovery that water is made of 2 parts hydrogen and 1 part oxygen, known for 2 laws related to gases and his work on alcohol water mixtures.
Charles Frederic Gerhardt august 21, 1816august 19, 1856. He came up with the notation for the chemical formulas for acetylsalicylic acid.
Josiah willard Gibbs february 11, 1839april 28, 1903. He converted a large part of physical chemistry from an empirical into a deductive science.
Lawrence glendenin november 8, 1918november 22, 2008. Codiscoverer of the element promethium.
Moses gomberg february 8, 1866february 12, 1947. he is known for radical chemistry (concerning a free radical, an atom, molecule, or ion that is an unpaired valence electron). he successfully prepared tetraphenylmethane, an organic compound consisting of a methane core with 4 phenyl substituents.
Carl grabe february 24, 1841january 19, 1927. Known for the first synthesis of an economically important dye, alizarin. he also contributed to the fundamental nomenclature of organic chemistry.
Thomas graham december 20, 1805september 16, 1869. Pioneered work in dialysis and the diffusion of gases. the is regarded as the father of colloid chemistry.
Fritz haber december 9, 1868january 29, 1934. he invented the haberbosch process, a method used in industry to synthesize ammonia from nitrogen gas and hydrogen gas.
otto Hahn march 8, 1879july 28, 1968. he is known for radiochemistry and is referred to as the father of nuclear chemistry.
Charles martin hall december 6, 1863december 27, 1914. he invented an inexpensive way of producing aluminum.
Charles Hatchett january 2, 1785march 10, 1847. Discovered the element niobium.
Dorothy Hodgkinmay 12, 1910july 29, 1994. She developed protein xray calistography. To determine the 3dimensional structures of biomolecules, she discovered the strucure of penicillin, insulin, and vitamin b12.
Albert Hoffmann january 11, 1906april 29, 2008. Synthesized LSD, psilocybin, and psilocin.
August Wilhelm hofmann april 8, 1818may 5, 1892. His research on aniline helped lay the basis of the anilinedye industry and laid the groundwork for others to extract benzene and toluene and convert them into nitro compounds and amines.he established the structural relationship of ammonia to ethlyamines and tetrathylammonia. he discovered formaldehyde, hydrazobenzene, the isonitriles, and allyl alcohol.he made a number of processes which were investigated, including hofmann rearrangement, the hofmannmartius rearrangement, hofmann elimination, and the hofmannloffler reaction.
Darlene hofmannnovember 8, 1926. Nuclear chemist who confirmed the existence of element 106, seaborgium.
Frederick lowland hopkins june 20, 1861may 16, 1947. Discovered vitamins and the amino acid tryptophan.
Linda hsiehwilson she combines organic chemistry and neurobiology to understand the molecular basis of fundamental processes. she applies the tools of organic synthesis, biochemistry, molecular and cell biology, biophysics, and neurobiology to manipulate and understand small molecules, proteins and molecular interactions critical to neuronal communication, development, learning, and memory.
Amir hoveyda he studies asymmetric catalysis, and is particularly noted for his work on developing catalysts for asymmetric olefin metathesis. he has worked extensively with nheterocyclic carbenes as ligands. he focuses research on coppercatalyzed allelic alkylations and conjugate additions using these ligands.
Vladimir ipatieff november 21, 1867november 29, 1952. he made important contributions in the field of petroleum chemistry.
Frederic and Irene joliotcuriechemists who discovered artificial radioactivity.
August kekule
september 7, 1829july 13, 1896. Principle founder of the theory of chemical structure. he is known for the tetravalent of carbon and the structure of benzene.
Izaak kolthoff february 11, 1894march 4, 1993. Analytical chemist who was highly influential. Considered the father of analytical chemistry. he developed a cold process for producing synthetic rubber.
Hans krebaugust 25, 1900november 22, 1981. Biochemist who pioneered study of cellular respiration, the biochemical pathway in cells for production of energy. he is best known for discovering the urea cycle and the citric acid cycle, the later a sequence of metabolic reactions that produce energy in cells (also known as the kern cycle).
Irving Langmuir january 31, 1881august 16, 1957. he is known for his concentric theory of atomic structure. He also invented the gas filled incandescent lamp.
August laurent november 14, 1807april 15, 1853. Founded organic chemistry with the discoveries of anthracene, ophthalmic acid, and carbolic acid. he devised a systematic nomenclature for organic chemistry based on structural groupings of atoms within molecules to determine how the molecules combine in organic reactions.
Antoine lavoisier august 23, 1743may 8, 1794. Widely considered the father of modern chemistry. He understood the role oxygen plays in combustion, opposed the phlogiston theory, recognized the names oxygen and hydrogen, helped construct the metric system, compiled the first list of the elements, helped reform chemical nomenclature, predicted the existence of silicon, and was the first to establish that sulfur was and element and not a compound. RIP
Willard libby december 17, 1908september 8, 1980. an American physical chemist, he is known for the development of radiocarbon dating, which revolutionized archaeology and paleontology.
Jacob marinsky april 11, 1918september 1, 2005. Codiscoverer of the element promethium.
Jean charles galissard de marginar april 24, 1817april 15, 1894. His work with atomic weights suggested the possibility of isotopes and the packing fraction of nuclei. his study of rare earth elements led to the discovery of ytterbium and the codiscovery of Gadolinium.
Alan marshall 1944. Known for the scientific technique of fourier transform ion cyclotron resonance mass spectrometry, which is way to determine the massto charge ratio of ions based on cyclotron frequency of the ions in a fixed magnetic field.
Julius lothar meyer august 19, 1830april 11, 1895. a pioneer in the development of the first periodic table of the chemical elements.
Stanley miller march 7, 1930may 20, 2007. he carried out the millerurea experiment, which showed that complex organic molecules could be synthesized from inorganic precursors. this experiment provided support for the idea that the chemical evolution of the early earth had led to the natural synthesis of chemical building blocks of life from inanimate inorganic molecules.. the is considered the father of prebiotic chemistry.
Eilhardt mitscherlich january 7, 1794august 26, 1863. Best remembered for his discovery of isomorphism (crystallography) in 1819.
Karl Friedrick mohrnovember 4, 1806september 28, 1879. he is known for his early statement of the principle of the conservation of energy. ammonium ion(ii) sulfate is named moor’s salt after him.
Henry Gwen Jeffrey Moseleynovember 23, 1887august 10, 1915. he is known for proposing that the atom contains
in its nucleus a number of positive charges that is equal to its atomic number in the periodic table. he is also known for moseley’s law, an empirical law concerning the characteristic xrays that are emitted by atoms. RIP
Paul muller january 12, 1899october 13, 1965. Discovered insecticidal qualities and the use of ddt in the control of vector diseases such as malaria and yellow fever.
robert nalbandyan 19372002. Codiscoverer of photosynthetic protein plantacyanin and pioneer in the field of free radicals.
John Alexander reina newland november 26, 1837july 29, 1898. Worked on the development of the periodic table of the elements.
Julius nieuwland february 14, 1878june 11, 1936. he is known for contributions to acetylene research, the use of one type of synthetic rubber, which led to the invention of neoprene.
Joan oro october 26, 1923september 2, 2004. His research was important in understanding the origin of life.
Paracelsus 1493/1494september 24, 1541. the father of toxicology.
Rudolph Pariser december 8, 1923. a polymer chemist best known for the method of molecular orbital computation.
Robert parr september 22, 1921march 27, 2017. Developed a method of computing approximate molecular orbitals for pi electron systems.
Louis pasteur december 27, 1822september 26, 1895. he is known for microbial fermentation and
pasteurization (the process that kills microbes in food and drink, such as milf, juice, and canned food).
Eugenemelchlor peligot march 24, 1811april 15, 1890. Isolated the first sample of uranium.
Roy plunkett june 26, 1910may 12, 1994. Discovered polytetrafluoroethylene.
Joseph priestley(17331804) One of the founding fathers of chemistry. stumbled across photosynthesis, is credited with the discovery of oxygen and accidentally brought us soda water.
Ilya Prigogine january 25, 1917may 28, 2003. Known for his discovery that importation of energy into chemical systems could reverse the maximization of entropy rule imposed by the 2nd law of thermodynamics.
Joseph louis proust september 26, 1754july 5, 1826. Discovered the law of constant composition, stating that chemical compounds always combine in constant proportions.
Francois marie Raoul may 10, 1830april 1, 1901. he is known for raoult’s law, which states that the partial vapor pressure of each component of an ideal mixture of liquids is equal to the vapor pressure of the pure component multiplied by its mole fraction in the mixture.
Jeremias benjamin richter march 10, 1762april 14, 1807. Introduced the term stoichiometry.
Andres manuel del rio november 10, 1764march 23, 1849. Discovered compounds of vanadium.
Pierre jean robiquet january 13, 1780april 29, 1840. Identified amino acids, the first of them asparagine, and adopted industrial dyes with the identification of alizarin.
Ernest Rutherford august 30, 1871october 19, 1937. he proved that radioactive halflife involved the nuclear transmutation of one chemical element to another.
Frederick Sangeraugust 13, 1918november 19, 2013. he worked on the structure of protein, especially insulin, and determined the base sequences of nucleic acids.
Carl Scheeledecember 9, 1742may 21, 1786. Discover oxygen, and identified molybdenum, tungsten, barium, hydrogen, and chlorine. he also discover tartaric, oxalic, uric, lactic, and citric organic acids.
Christian friederich Schonbein 18 October 1799 – 29 August 1868 was a German Swiss chemist who is best known for inventing the fuel cell (1838)[1] at the same time as William Robert Grove, Robert Cumming and his discoveries
of guncotton[2] and ozone.[3]
Nevil vincent sidgwick may 8, 1873march 15, 1952. Theoretical chemist who made significant contributions to valency and chemical bonding. he demonstrated the existence and wideranging importance of the hydrogen bond.
Oktay Sinanoglufebruary 25, 1935april 19, 2015. Internationally renowned turkish physical chemist and molecular biochemist. Using simple pictures, chemists could predict the ways in which complex chemical reactions would proceed, and solve complex problems in quantum chemistry.
Susan solomanjanuary 19, 1956. the first to propose chlorofluorocarbon free radical reaction mechanism that is the cause of the antarctic ozone hole.
Alfred stock july 16, 1876august 12, 1946. did pioneering research on the hayrides of boron and silicon, coordination chemistry, mercury, and mercury poisoning.
Friedrich august kekule von stradonitzseptember 7, 1829july 13, 1896. he established the foundation for the structural theory in organic chemistry.
Louis Jacques thenard may 4, 1777june 21, 1857. he did important researches in ethers, sebacic acid, and bile. he discovered hydrogen peroxide.
Harold Clayton Urey april 29, 1893january 5, 1981. Did pioneering work in isotopes. he discovered deuterium.
Louis Nicolas vauquelin may 16, 1763november 14, 1829. Discovered beryllium and chromium.
Alessandro Giuseppe Antonio Anastasio Voltafebruary 18, 1745march 5, 1827. Developed the field of electrochemistry.
Friedich wohlerjuly 31, 1800september 23, 1882. he synthesized urea and the first to isolate several chemical elements.
William hyde wollaston august 6, 1766december 22, 1826. Discovered the elements palladium and rhodium. He also developed a way to process platinum ore into malleable ingots.
Robert woodward april 10, 1917july 8, 1979. he made many key contributions, especially the synthesis of complex natural products to determine their molecular structure. he also did theoretical studies of chemical reactions. he synthesized quinine, cholesterol, cortisone, strychnine, lysergic acid, reserpine, chlorophyll, vitamin B12, cephalosporin, and colchicine.
Ahmed zewall february 26, 1946august 6, 2016. father of femtochemistry, the study of chemical reactions in extremely short timescales (10^15 seconds).
Geologists
James Hutton (1726–1797) is considered by many to be the father of modern geology. He was the first to develop the idea of uniformitarianism, which was popularized by Charles Lyell years later. He also dismantled the universally accepted view that the Earth was just a few thousand years old.
Charles Lyell (17971875) he was a revolutionary in his time for his radical ideas regarding the Earth’s age.
Lyell wrote Principles of Geology, his first and most famous book. Lyell was a proponent of James Hutton’s idea of uniformitarianism, and his work expanded upon those concepts. This stood in contrast to the thenpopular theory of catastrophism. His ideas greatly influenced the development of Charles Darwin’s theory of evolution.
Alfred Wegener (18801930), a German meteorologist and geophysicist, is best remembered as the originator of the theory of continental drift. Initially, the theory was widely criticized before being verified by the discovery of midocean ridges in the 1950s. It helped spawn the theory of plate tectonics.
Inge Lehmann (18881993), discovered the core of the Earth and was a leading authority on the upper mantle. Lehmann began studying how seismic waves behaved as they moved through the interior of the Earth and, in 1936, published a paper based on her findings she proposed a threeshelled model of the Earth’s interior, with an inner core, outer core and mantle. Her idea was later verified in 1970 with advances in seismography.
Georges Cuvier (17691832), regarded as the father of paleontology, was a prominent French naturalist and zoologist. Cuvier was a believer in catastrophism and a vocal opponent of the theory of evolution.
Louis Agassiz (18071873) was a SwissAmerican biologist and geologist that made monumental discoveries in the fields of natural history. He is considered by many to be the father of glaciology for being the first to propose the concept of ice ages. Agassiz would spend much of his career promoting and defending Cuvier’s work on geology and the classification of animals. Enigmatically, Agassiz was a staunch creationist and opponent of Darwin’s theory of evolution.
Florence Bascom (18621945): American geologist and first female hired by the USGS; expert in petrography and mineralogy who focused on the crystalline rocks of the United States Piedmont.
Marie Tharp (19202006): American geologist and oceanographic cartographer who discovered midocean ridges.
John Tuzo Wilson (19081993): Canadian geologist and geophysicist that proposed the theory of hotspots and discovered transform boundaries.
Friedrich Mohs (17731839): German geologist and mineralogist that developed the qualitative Mohs scale of mineral hardness in 1812.
Charles Francis Richter (19001985): American seismologist and physicist that developed the Richter
magnitude scale, the way that earthquakes were quantitatively measured.
Eugene Merle Shoemaker (19281997): American geologist and founder of astrogeology; codiscovered Comet ShoemakerLevy 9 with his wife Carolyn Shoemaker astronomer David Levy.
ASTRONOMERS
John Couch Adams June 5, 1819January 21, 1892. Predicted the existence and position of Neptune, using only mathematics, and his calculations were made to explain the discrepancies with Uranus’s orbit and the laws of Kepler and Newton.
Anders Jonas Angstrom August 13, 1814June 21, 1874. One of the developers of spectroscopy.
Aristarchus C. 310C. 230BC. The first known person who placed the sun at the center of the known universe with the earth revolving around it, and was also the first to predict the rotation of the earth on its axis.
Halton Arp March 21, 1927December 28, 2013. He is known for his 1966 atlas of peculiar galaxies which catalogues many examples of interacting and merging galaxies. He was a critic of the Big Bang theory and advocated a non standard cosmology incorporating intrinsic redshift.
Aryabhata 476550 CE. He is known for explaining the lunar eclipse and solar eclipse, the rotation of the earth on its axis, reflection of light by the moon, and he measured the circumference of the earth to 99.8% accuracy.
Hans BetheJuly 2, 1906March 6, 2005. Won the 1967 Nobel prize for his work on
nucleosynthesis, and did work on supernovas, neutron stars, and black holes. He did the calculations to detect the gravitational waves from merging neutron stars and black holes using the LIGO (laser interferometer gravitationalwave observatory).
Bhaskara 2 11141185. Measured the length of time for the earth to go around the sun, and he was accurate by a difference of just 3.5 minutes.
Walter Baade March 24, 1893June 25, 1960. He discovered 944 Hidalgo, the first of a class of minor planets (Centaurs) which cross the orbits of the giant planets. He made the distinction between population 1 and population2 stars, he discovered 2 types of cepheid variable stars which he used to recalculate the size of the universe and doubled the size Hubble came up with in 1929. He identified supernovas as a new category of astronomical objects and proposed a new class of stars that result from supernovas. He discovered an optical counterpart of
radio sources, including Cygnus A. He discovered the Apollo class of asteroids, which orbit closer than Mercury’s orbital distance.
Jocelyn Bell born July 15, 1943. Astrophysicist who discovered the first radio pulsar in July 1967.
Friedrich Wilhelm Bessel– July 22, 1784March 17, 1846. He was the first to determine the distance to another star using the parallax method.
Johann Ebert Bode January 19, 1747November 23, !826. Astronomer who predicted the orbit of Uranus and reformulated and popularized the Titius Bode law, which predicts pretty well the orbital distances of the planets.
Bart Bok April 28, 1906August 5, 1983. Discoverer of Bok globules, small densely dark clouds of interstellar gas and dust, and it is suggested that it is here where stars contract before forming.
Thomas Bopp October 15, 1949january 5, 1918. Codiscoverer of Comet HaleBopp with Alan Hale in 1995.
Tycho Brahe December 14, 1564October 24, 1601. He made comprehensive and accurate observations as an astronomer, especially of the planets. Johannes around the sun, but incorrectly the sun going around the earth. Supernova 1572 (SN1572) was named after him as Tycho’s Star.
Brahmagupta C. 598after 665. Explained that the moon was closer to us than the sun, developed methods for calculating the position of heavenly bodies over time, and calculating lunar and solar eclipses.
Michael BrownJune 5, 1965. Discovered many transNeptunian objects, notably the dwarf planet Elis.
William Brook June 11, 1844May 3, 1921. The most prolific comet discoverer of all time.
Geoffrey Burbridge September 24, 1925 January 26, 2010. Described the process of stars burning lighter elements into successively heavier atoms which are then expelled Ito form other structures in the universe, including other stars and planets. He also proposed the quasi steady state theory where the universe is oscillatory and expands and contracts periodically over infinite time
Margaret Burbridge August 12, 1919. She hypothesized with husband Geoffrey, William Fowler, and Fred Hoyle that all elements are made in stars by nuclear reactions (stellar nucleosynthesis). Also she was the first person to measure the rotation curves of galaxies and one of the pioneers in the study of quasars.
Robert Burnham JrJune 16, 1931March 20, 1993. Best known for writing an excellent classic 3 volume Burnham’s Celestial Handbook.
Annie Jump Cannon December 11, 1863April 13, 1941. She developed a stellar classification system according to the temperatures and spectral types of the stars.
Giovanni Cassini June 8, 1625September 14, 1712. He discovered 4 moons of the planet Saturn, and he noted the division in the rings of Saturn, called the Cassini Division.
Subrahmanyan Chandrasekhar October 19, 1910August 21, 1995. Known for the Chandrasekhar limit, where a white dwarf’s mass can not exceed 1.44 times the sun’s mass.
Nicolaus Copernicus February 19, 1473May 23, 1543. Formulated a model of the universe where the sun, rather than the earth, was the center of the universe.
John Dobson September 14, 1915January 1, 2014. Best known for the Dobsonian
telescope, and his efforts to promote awareness in astronomy and his unorthodox views in physical cosmology.
Christian Doppler November 29, 1803March 17, 1853. Best known for an influential principle called the Doppler effect, where if a stellar body is moving away from earth, there is a red shift in the spectrum of the object, and if moving towards us, there is a blue shift. This principle has been used to support the Big Bang theory.
Frank Drake May 28, 1930. He is one of the pioneers in the search for extraterrestrial life, including founding SETI, with the first observational attempts to detect extraterrestrial communications in 1960 in Project Ozma. He also is the creator of the Drake equation, which estimates the probable likelihood
of extraterrestrial civilizations, and he is the creator of the Arecibo Message with a description of earth astronomically and biologically and its lifeforms that were transmitted to a globular star cluster.
Henry Draper March 7, 1837November 20, 1882. Pioneer in astrophotography.
Ron Drever October 26, 1931March 7, 2017. He was instrumental in the first detection of gravitational waves in September 2015.
Arthur Eddington (1882–1944) December 28, 1862November 22, 1944. Popularizer of Einstein’s general theory of relativity.
Albert Einstein March 14, 1879April 18,1955. He applied general relativity to model the large scale structure of the universe. He is known for the cosmological constant, which was added to the general theory of relativity to hold back gravity to achieve a static universe, which was the accepted view at the time.
George Ellis August 11, 1939. he worked for many decades on anisotropic cosmologies and inhomogeneous universes.
Johann Encke September 23, 1791August 26, 1865. German astronomer who worked on calculations of the periods of comets and asteroids, measured the distance from the Earth to the sun, and made observations on the planet Saturn.
Eratosthenes c. 276BCc. 195/194 BC. First person known to calculate the circumference of the earth, the tilt of the earth’s axis, and the distance to the sun.
Sandra Faber December 28, 1944. She made important discoveries linking the brightness of galaxies to the speed of the stars in them.
John Flamsteed August 19, 1646December 31, 1719. He catalogued over 3,000 stars. He accurately calculated the solar eclipses of 1666 and 1668. He also is responsible for several of the earliest recorded sightings of the planet Uranus which he mistook for a star and catalogued as the star 34 Tauri. In 1681, he proposed that the 2 great comets were the same comet, first traveling towards the sun and later away from it.
Joseph von Fraunhofer March 6, 1787June 7, 1826. Known for the discovery of dark absorption lines known as Fraunhofer lines in the sun’s spectrum.
Alexander Friedmann June 18, 1888September 16, 1925. He is best known for his pioneering theory that the universe was expanding, governed by a set of equations he developed now known as the Friedmann equations.
R. Jay GaBany September 17, 1954. Astrophotographer and produced long exposures images of ancient galactic merger remnants around nearby galaxies which were previously undetected or suspected.
Galileo Galilei February 15, 1564January 8, 1642. He used the newly invented telescope to confirm the phases Venus goes through, discover the 4 major moons of the planet Jupiter, and observed and analyzed sunspots. He championed the Copernican heliocentric view of the universe which said that the earth moves around the sun.
Johann Gottfried GalleJune 9, 1812July 10, 1910. He was the first person to view the Planet Neptune and know what he was looking at. Urban Le Verrier had predicted its existence and position and sent its coordinates to Galle, and Galle found it the same night within 1 degree of the predicted position. This was a remarkable event was one of the most remarkable events in 19thcentury science and a dramatic validation of celestial mechanics.
George Gamow March 4, 1904August 19, 1968. Said that the present levels of hydrogen and helium in the universe, which make up over 99% of all matter, could be explained by reactions that occurred during the Big Bang. He also made an estimate of the residual cosmic microwave background radiation, predicting that the afterglow of the Big Bang would have cooled after billions of years, filling thee universe with a radiation about 5 degrees above absolute zero.
Carl Friedrich Gauss April 30, 1777February 23, 1855. Calculated the orbit of the asteroid Ceres in 1801.
Margaret Geller December 8, 1947. Did pioneering work in mapping the nearby universe, studies of the relationship between galaxies and their environment, and the development and application of methods for measuring the distribution of matter in the universe.
Thomas Gold May 22,1920June 22, 2004. He was one of the 3 scientists to propose the now abandoned steady star theory hypothesis of the universe.
Brian Greene February 9, 1963. Working on string cosmology, especially the imprints of trans Planckian physics on the cosmic microwave background, and branegas cosmologies that could explain why space around us has 3 large dimensions, expanding on the suggestion of a black hole electron, that the electron may be a black hole.
Jesse Greenstein October 15, 1909October 21, 2002. He did important work in determining the abundances of the elements in stars, and was among the first to recognize that quasars are compact, very distant sources as bright as galaxies.
Allen Guth February 27, 1947. He did pioneering work in cosmic inflation in the just born universe when it passed through a phase of expansion driven by positive vacuum energy density (negative vacuum pressure).
Alan Hale. March 7, 1958. Codiscoverer of Comet Hale Bopp along with amateur astronomer Thomas Bopp.
George Ellery Hale. June 29, 1968February 21, 1938. Solar astronomer best known for discovery of magnetic fields in sunspots.
Asaph Hall October 15, 1829November 22, 1907. Discovered the 2 moons of Mars, Deimos and Phobos in 1877. He determined the orbits of other planet satellites and of double stars, the rotation of Saturn, and the mass of Mars.
Edmund Halley November 29, 1656January 1, 1742. Computed the orbit of Halley’s Comet. William Hartmann June 6, 1939. The first to convince the scientific mainstream that the earth had once been hit by a planet sized body (The) creating both the moon and the earth’s 23.5 degree tilt.
Stephen Hawking January 8, 1942march 2018. He has worked on gravitational relativity theorems in the framework of general relativity and the theoretical prediction that black holes emit radiation, called Hawking radiation. He was the first to set out a theory of the theory of cosmology explained by the union of the general theory of relativity and quantum mechanics. He is a vigorous supporter of the many interpretation of quantum mechanics.
John Herschel March 7, 1792May 11, 1971. He named 7 moons of Saturn and 4 of Uranus.
William Herschel November 15, 1738August 25, 1822. He discovered the planet Uranus and catalogued 5,000 stellar objects.
Caroline Herschel March 16, 1750January 9, 1848. She discovered several comets, and worked with her brother William Herschel as an astronomer.
Ejnar Hertzsprung October 8, 1873October 21, 1967. Known for the creation of the HertzsprungRussell Diagram, a classification system for stars that divides them by spectral type, the stage of their development, and their luminosity.
Anthony Hewish May 11, 1924. Discovered pulsars and received the Nobel prize of 1974 for this.
Jacqueline Hewitt September 4, 1958. American astrophysicist and first person to
discover Einstein rings, a deformation of the light from a source, such as a galaxy or star, into a ring through gravitational lensing of the source’s light by an object of extremely high mass , such as a galaxy or a black hole.
Hipparchus c.190c.120 BC. He developed a reliable method to predict solar eclipses, discovered and measured the procession of the earth, and compiled the first comprehensive star catalogue.
Fred Hoyle June 24, 1915August 20,2001. Coined the term ‘Big Bang’, a theory he rejected. He was noted primarily for the theory of stellar nucleosynthesis
Edwin Hubble November 20, 1889September 28, 1953. He is regarded as the most important astronomer of all time. He established Hubble’s Law, which says that that the universe is expanding because as stellar objects get farther and farther away from us, they increase more and more in velocity away. He also said that clouds of gas and dust called nebulas are really galaxies like our own beyond our galaxy.
John Huchra December 23, 1948October 8, 2010. Announced that based on the brightness and rotational speed of certain spiral galaxies that the universe was 9 billion years old, half the age most astronomers previously thought. He also co discovered the Great Wall, a structure measuring 600 million light years in length and 250 million light years in width. It is the second largest known structure in the universe.
Milton Humason August 19, 1891June 18, 1972. He helped Edwin Hubble establish Hubble’s Law. Human was once a mule driver who delivered supplies to Wilson Observatory. He discovered comet Human (C/ 1961R1), which has a very large perihelion distance. He missed discovering Pluto 14 years before Clyde Tombaugh discovered it.
Christian Huygens April 14, 1629July 8, 1695. He provided an explanation of Saturn’s rings.
Kaoru Ikeya 1943. Discoverer of a number of comets, including the bright comet C/ 1965 S1 (IkeyaSeki).
Karl Jansky October 22, 1905February 14, 1950. Founding figure in radio astronomy. In August of 1931, he first discovered radio waves from the Milky Way galaxy.
Lisa Kaltenegger March 4, 1977. Austrian astronomer with expertise in the modeling and characterization of exoplanets and the search for life.
Jacobus Kapteyn January 19, 1851June 18, 1922. Discoverer of galactic rotation.
Johannes Kepler December 27, 1571 November 15, 1630. He worked with the Danish
astronomer Tycho Brahe and later used his observational results to formulate this 3 laws of planetary motion. He paved the way for Isaac Newton to formulate the universal law of gravitation.
Daniel Kirkwood September 27, 1814June 11, 1895. Known for Kirkwood gaps, which are gaps in the orbits of the main belt asteroids, that correspond to the locations of orbital resonances with Jupiter.
Lubos Kohoutek January 29, 1935. Discoverer of minor planets and comets, including Comet Kohoutek, which was visible to the naked eye in 1973.
Chryssa Kouveliotou a Greek astrophysicist who studied in the Has worked on magnetars.
Gerard Kuiper December 7, 1905December 23, 1973. Considered by many the father of modern planetary science. Discovered the Kuiper belt, a circumstellar disk in the solar system beyond the known planets from 3050 astronomical units from the sun. It consists mainly of asteroids, or remnants of the solar system’s formation.
Leonid Kulik August 19, 1883April 14, 1942. Noted for his research into meteorites. He discovered the Tunguska blast site.
JosephLouis Lagrange January 25, 1736April 10, 1813. Known for the Lagrangian points, the positions in an orbital configuration of 2 large bodies where a small object affected only by gravity can maintain a stable position relative to the 2 large bodies.
PierreSimon Laplace March 23, 1749March 5, 1827. He restated and developed Immanual Kant’s earlier idea of the nebular hypothesis of the origin of the solar system and was one of the first scientists to postulate the existence of black holes and the idea of gravitational collapse.
William Lassell June 18, 1799October 8, 1880. In 1846, discovered Neptune’s largest moon Triton. In 1848, independently codiscovered Saturn’s moon Hyperion. Then in 1851, discovered Ariel and Umbriel, moons of Uranus.
Henrietta Swan Leavitt July 4, 1868December 12, 1921. American astronomer who discovered the relation between the luminosity and the period of Cepheid variable stars. This led to the ability to measure how far away distant galaxies are.
George Lemaitre July 17, 1894June 20, 1966. He proposed the theory of the expansion of the universe and also what became known as the Big Bang theory of the origin of the universe. He also formulated what is now known as Hubble’s Law in 1927, 2 years before Hubble did.
Urbain Le Verrier March 11, 1811September 23, 1877. French mathematician who specialized in celestial mechanics and using mathematics predicted the existence and orbit of the planet Neptune.
David Levy May 22, 1948. Discoverer of comets and minor planet, and codiscoverer of Comet ShoemakerLevy 9 in 1993, which collided with the planet Jupiter in July 1994.
Percival Lowell March 13, 1856November 12, 1916. Made telescopic observations of the planet Mars and fueled speculation that there were canals there. He founded Lowell Observatory which led to the discovery of Pluto 14 years after his death.
Geoffrey Marcy September 29, 1954. He is one of the pioneers in the discovery and characterization of planets around stars other than the sun.
John Mather August 7, 1946. Cosmologist and Nobel prize winner for his work on the
COBE (cosmic background explorer satellite) which confirmed electromagnetic radiation leftover from an early stage of the universe in the Big Bang cosmology.
Charles Messier June 26, 1730April 12, 1817. He is known for an astronomical catalogue of nebular and star clusters (110 Messier objects).
Rudolph Minkowski May 28, 1895January 4, 1976. He studied supernovas and divided them into type 1 and type 2 supernovas.
Maria Mitchell August 1, 1818June 28, 1889. Discovered a comet in 1847. She was the first professional American astronomer.
Antonin Mrkos January, 27, 1918May 29, 1996. Discoverer of several unusual comets, the most famous of them the bright comet of 1957d.
Isaac Newton December 25, 1642March 20, 1727. Using Kepler’s 3 laws of planetary motion and his law of universal gravitation, he used these to account for the trajectories of comets, procession of the equinoxes, and other phenomena. He removed all doubt about the heliocentric model of the solar system and demonstrated that the motion of celestial bodies could be accounted for by Kepler’s laws and his law of gravitation. He also predicted that the earth was shaped like an oblate spheroid.
Heinrich Olbers October 11, 1758March 2, 1840. Discovered the asteroids Pallas and Vesta, and came up with Olber’s Paradox, which states that the darkness of the night sky conflicts with the supposition of an infinite and eternal static universe (Why should the night sky be dark when it is full of stars?). He also discovered a comet.
Gerard O’Neill February 6, 1927April 27, 1992. He developed a plan to build human settlements in outer space, including a space habitat designed as the O’Neill cylinder.
Jan Oort April 28, 1900November 5, 1992. He did pioneering work in radio astronomy and is known for dark matter and the Oort Cloud. He overturned the idea that the Sun is at the center of the Milky Way Galaxy, and he determined that our galaxy rotates. In 1932, he postulated an invisible dark matter. He also discovered the main disk.
Ernest Opik October 22, 1893September 10, 1985. Determined that the white dwarf O2 Eridani has a density of 25,000 times the sun’s density. He also estimated the distance to the Andromeda galaxy using novel astronomical methods based on the observed rotational velocities of the galaxy, which depends on the total mass around which the stars are rotating, and on the assumption that the luminosity per unit mass was the same as our own galaxy.
Cecilia PayneGaposchkin May 10, 1900December 7, 1979. In her Ph.D. thesis in 1925, she explained the composition of stars in terms of the relative abundances of hydrogen and helium.
Arno Penzias April 26, 1933. Codiscoverer, along with Robert Wilson, of cosmic microwave background radiation, which helped establish the Big Bang theory of cosmology.
Roger Penrose August 8, 1931. Revolutionized the mathematical tools used to analyze the properties of spacetime.
Giuseppe Piazzi July 16, 1746July 22, 1826 Supervised thee compilation of the Palermo Catalogue of stars, containing 7,646 stars with unprecedented precision. Discovered the asteroid Ceres, the largest known asteroid.
Edward Pickering July 19, 1846February 3, 1919. Discovered the first spectroscopic binary stars.
Carolyn Porco March 6, 1953. Planetary scientist known for her work on voyager missions to Jupiter, Saturn, Uranus, and Neptune in the 1980’. She leads the imaging science team on the Cassini mission currently in orbit around Saturn. She is an expert on planetary rings and the moon of Saturn, Enceladus.
Ptolmey c. AD100c. 170. Wrote book called the Almagest proposing a geocentric (earth centered) model of the universe.
Grote Reber December 22, 1911December 20, 2002. Extended Karl Jansky’s pioneering work in radio astronomy and made the first sky survey in radio frequencies.
Martin Rees June 23, 1942. He is known for his confirmation of the Big Bang, discovery of neutron stars and black holes, his studies of the distribution of quasars which led to disproof of the steady state theory, and his important contributions to the origin of cosmic microwave background radiation.
Adam Riess December 16, 1969. Shared the 2011 Nobel prize in physics for providing evidence that the expansion of the universe is accelerating.
Edouard Roche October 17, 1820April 27, 1883. Famous for his theory, the Roche limit, that describes, for example, the planetary rings of Saturn were formed when a large moon came too close to the planet and was pulled apart by its gravitational forces. His other work is the Roche Lobe, which is the limits at which an object which is orbit around 2 other objects will be captured by one or the other, and the Roche Sphere approximates the gravitational sphere of influence of one astronomical body in the face of perturbations from another heavier body around which it orbits.
Ole Romer September 25, 1644September 19, 1710. In 1676, he made the first quantitative measurement of the speed of light.
Vera Rubin July 23, 1928December 25, 2016. She did pioneering work in galactic rotation rates and uncovered a discrepancy between the predicted angular motion of galaxies and the observed rates by studying galactic rotation curves. She also showed that stars and galaxies are immersed in the gravitational grip of dark matter.
Henry Norris Russell October 25, 1877February 18, 1957. With Ejar Herzsprung, developed the HR Diagram in 1910.
Martin Ryle September 27, 1918October 14, 1984. Developed ra revolutionary radio telescope system, aperture synthesis, to accurately locate and image weak radio sources, and was able to observe the most distant known galaxies at that time.
Carl Sagan November 9, 1934December 20, 1996. A science popularizer, especially in astronomy. He is best known for his research into extraterrestrial life, including experiments that demonstrated the production of amino acids from base chemicals by radiation.
Edwin Salpeter December 3, 1924November 26, 2008. He suggested that star could burn helium4 into carbon12 with the triplealpha process through an intermediate stare of beryllium6, which explained the carbon production in stars.
Allen Sandage June 18, 1926November 13, 2010. He determined the first reasonably accurate value of the Hubble Constant and of the age of the universe. He also discovered the first quasar.
Giovanni Schiaparelli March 14, 1835July 4, 1910. Made telescopic observations of Mars and saw ‘canal’ on its surface and this gave rise to the possibility of intelligent life there.
Martin Schmidt December 28, 1929. He coined the word quasar and measured their distances.
Karl Schwarzchild October 9, 1873May 11, 1916. His work led to derivation of the Scwartzchild Radius, the size of the event horizon of a non rotating black hole.
Martin Schwartzchild May 31, 1912April 10, 1997. He was one of the most prominent astrophysicists of the century. He was a leader in the theory of stellar evolution and the dynamics of elliptical galaxies.
Tsutomu Seki November 3, 1930. Japanese astronomer who discovered a number of comets and very many minor planets. Discovered the very bright comet C/1965S1 (IkeyaSeki).
Carl Seyfert February 11, 1911June 13, 1960. A type of galaxy is named after him, with a bright nucleus that emits light with emission line spectra with characteristic broadened emission lines.
Harlow Shapley November 2, 1885December 20, 1972. He determined the correct position of the Sun within the Milky Way galaxy using the parallax method. Also, he used RR Lyrae stars to correctly estimate the size of our galaxy. And he proposed what is now known as the habitable zone around a star where life can exist.
Ian Shelton born March 30, 1957 in Canada. He discovers the first supernova (SN1987A) seen with the naked eye in 383 years on February 24, 1987.
Carol Shoemaker June 24, 1929. Codiscoverer of Comet ShoemakerLevy 9. She once held the record for discovering the greatest number of comets.
Eugene Shoemaker April 28, 1928July 18,1997. He was one of the founders of planetary geology. He also discovered comet ShoemakerLevy, which hit the planet Jupiter if July 1994.
Willem de Sitter May 6, 1872November 20, 1934. Made many contributions to physical cosmology, especially the expanding universe (empty universe).
Vesto Slipher November 11, 1875November 8, 1969. He measured the radial velocities of galaxies and established an empirical basis for an expanding universe.
George Smoot February 20, 1945. Nobel laureate in 2006 for his work on the cosmic background explorer that led to the discovery of the black body form and anisotropy of the cosmic microwave background radiation.
Lyman spitzer June 26, 1914march 31,1997. Researcher who was a theoretical physicist and astronomer. He studied star formation, plasma physics, and in 1946, conceived the idea of a space telescope, which came into being as the Spitzer space telescope. He invented the stellarator plasma device which coffins hot plasma with magnetic fields in order to sustain a controlled nuclear fusion reaction. He was among the first to recognize star formation as an ongoing process.
Lewis Swift February 29, 1820January 5, 1913. Discoverer of a number of comets.
Jill TarterJanuary 16, 1944. Worked at the center for SETI trying to find signals from an extraterrestrial civilization.
Wilhelm Tempel December 4, 1821March 16, 1889. Prolific comet discoverer (21 in all), including comet 55P/TempelTuttle, the parent body of the Leonid meteor shower, and 9P/Tempel, the target of NASA probe Deep Impact in 2005.
Richard Terrile March 22, 1951. A voyager scientist who discovered several moons of Saturn, Uranus, and Neptune. He is a supporter of the simulation hypothesis, the idea that our reality is a computer generated virtual reality created by unknown programmers.
Kip ThorneJune 1, 1940. He has worked on gravitational waves, black hole cosmology, and wormholes and time travel.
Clyde TombaughFebruary 4, 1906January 17, 1997. He discovered the planet Pluto in 1930 and discovered the Kuiper belt.
Margaret turnbullshe is an authority on star systems which may have habitable planets, solar twins, and planetary habitability.
Horace TuttleMarch 17, 1837August 16, 1923. Comet discoverer
John Archibald WheelerJuly 9, 1911April 13, 2008. He is best known for linking the term ‘black hole’ to objects with gravitational collapse and coining the term ‘wormhole’.
Fred WhippleNovember 5, 1906August 30, 2004. He discovered some comets and asteroids, and come up with the dirt snowball cometary hypothesis.
Fritz ZwickyFebruary 14, 1898February 8, 1974. Hypothesized that supernovae were the transition of normal stars into neutron stars. He posited that galaxies could act as gravitational lenses in 1937, and it was not confirmed until 1979. He also inferred the existence of dark matter.
ROCKET SCIENTISTS
Miguel Alcubierre Moya (born March 28, 1964 in Mexico City) is a Mexican theoretical physicist.[2] Alcubierre is known for the proposed Alcubierre drive, a speculative warp drive by which a spacecraft could achieve fasterthanlight travel.
Nikolai Alekhin (Russian: Николай Алехин; 1913– 1964) was a Soviet Union rocket designer. The lunar crater Alekhin is named in his honour.
Charles E. Bartley (1921–1996) was an American scientist, known for developing the first elastomeric solid rocket propellant formula, at the Jet Propulsion Laboratory (now part of NASA) in Pasadena, California in the late 1940s.
Kristian von Bengtson (born August 1974) is a Danish architect, specializing in manned spaceflight, a resident of Copenhagen and married to animation director Karla von Bengtson. He is most notable for his involvement in founding Copenhagen Suborbitals. Kristian von Bengtson has participated in various space projects, simulated Mars habitation[2] and is a trained architect from School of Architecture in Copenhagen 2001 and also has a master’s degree in aerospace science from the International Space University ISU in Strasbourg, France (2006).
Allen Bond (born 1944) is an English mechanical and aerospace engineer, as well as Managing Director of Reaction Engines Ltd[1] and associated with Project Daedalus, Blue Streak missile, HOTOL, Reaction Engines Skylon and the Reaction Engines A2 hypersonic passenger aircraft. He was engaged in studies for the application of fusion to interplanetary space travel. He is the leading author of the report on the Project Daedalus interstellar, fusion powered starship concept, published by the British Interplanetary Society. In the 1980s, he was one of the creators of the HOTOL spaceplane project, along with Dr. Bob Parkinson of British Aerospace. Alan Bond brought a precooled jet engine design he had invented to the HOTOL project, and this became the Rolls Royce RB545 rocket engine.
Karel Jan Bossart (February 9, 1904 – August 3, 1975) was a pioneering rocket designer and creator of the Atlas ICBM. His achievements rank alongside those of Wernher von Braun and Sergei Korolev but as most of his work was for the United States Air Force and therefore was classified he remains relatively little known.
Atlas was first launched in June, 1957 but was never fully effective as an ICBM. As a launch vehicle it has formed the basis of the most successful and reliable expendable rockets in service. As a result, Bossart’s achievements include:
Launch of first US orbital manned missions, Launch of Mariner probes to Mars and Venus Launch of Pioneer 10 and Pioneer 11 to Jupiter and Saturn.
Edward Mounier Boxer (18221898) was an English inventor. Edward M. Boxer was a colonel of the Royal Artillery.
In 1855 he was appointed Superintendent of the Royal Laboratory of the Royal Arsenal at Woolwich.
He is known primarily two of his inventions:
• The 1865 “Boxer rocket”, an early two stage rocket, used for marine rescue line throwing
• His 1866 “Boxer primer”, very popular for centerfire ammunition
Yvonne Madelaine Brill (née Claeys; December 30, 1924 – March 27, 2013) was a Canadian American propulsion engineer best known for her development of rocket and jet propulsion technologies. During her career she was involved in a broad range of national space programs in the United States, including NASA and the International Maritime Satellite Organization.
Robert W. Bussard (August 11, 1928 – October 6, 2007) was an American physicist who worked primarily in nuclear fusion energy research. He was the recipient of the SchreiberSpence Achievement Award for STAIF2004. He was also a fellow of the International Academy of Astronautics and held a Ph.D. from Princeton University. Kiwi (RoverA) In June, 1955 Bussard moved to Los Alamos and joined the Nuclear Propulsion Division’s Project Rover designing nuclear thermal rocket engines. Bussard and R.D. DeLauer wrote two important monographs on nuclear propulsion, Nuclear Rocket Propulsion and Fundamentals of Nuclear Flight.
Bussard ramjet
In 1960, Bussard conceived of the Bussard ramjet, an interstellar space drive powered by hydrogen fusion using hydrogen collected with a magnetic field from the interstellar gas. Due to the presence of highenergy particles throughout space, much of the interstellar hydrogen exists in an ionized state (H II regions) that can be manipulated by magnetic or electric fields. Bussard proposed to “scoop” up ionized hydrogen and funnel it into a fusion reactor, using the exhaust from the reactor as a rocket engine. It appears the energy gain in the reactor must be extremely high for the ramjet to work at all; any hydrogen picked up by the scoop must be sped up to the same speed as the ship in order to provide thrust, and the energy required to do so increases with the ship’s speed.
Hydrogen itself does not fuse very well (unlike deuterium, which is rare in the interstellar medium), and so cannot be used directly to produce energy, a fact which accounts for the billionyear scale of stellar lifetimes. This problem was solved, in principle, according to Dr. Bussard by use of the stellar CNO cycle in which carbon is used as a catalyst to burn hydrogen via the strong nuclear reaction. In the Star Trek universe, a variation called the Bussard Hydrogen Collector or Bussard Ramscoop appears as part of the matter/antimatter propulsion system that allows Starfleet ships to travel faster than the speed of light. The ramscoops attach to the front of the warp nacelles, and when the ship’s internal supply of deuterium runs low, they collect interstellar hydrogen and convert it to deuterium and antideuterium for use as the primary fuel in a starship’s warp drive.
Vladimir Nikolayevich Chelomey 30 June 1914 – 8 December 1984) was a Soviet mechanics scientist, aviation and missile engineer. He invented the very first Soviet pulse jet engine and was responsible for the development of the world’s first antiship cruise missiles and ICBM complexes like the UR100, UR200, UR500 and UR700.
Boris Evseyevich Chertok 1 March 1912 – 14 December 2011) was a prominent Soviet and Russian rocket designer, responsible for control systems of a number of ballistic missiles and spacecraft. He was the author of a fourvolume book Rockets and People, the definitive source of information about the history of the Soviet space program.
Arthur Valentine Cleave (14 February 1917 – 16 September 1977) was a distinguished British rocket engineer. He co authored a paper which discussed the possibilities and problems of nuclear rocket engines in 1948. After the Second World War he developed de Havilland’s Sprite and Spectre rocket engines. He moved to Rolls Royce in 1957 and in 1960 he became general manager and chief engineer of the Rolls Royce’s rocket departments, where he was responsible for the engines which powered the Blue Streak missile and Black Arrow launch vehicle. While the ELDO vehicle was ultimately unsuccessful and abandoned, the Blue Streak vehicle and its engines worked perfectly on every launch, and Cleaver was awarded the OBE for his part in developing them.
Early life
He was born at Conway in Wales to Percy and Mildred Cleaver. From the age of 11 he became fascinated by space. For three years from 1931 he attended Acton Technical College. He joined the British Interplanetary Society (BIS) in 1937, aged 20. RollsRoyce RZ.2, which he was responsible for Rolls Royce. In 1956 he handed in his notice at de Havilland and became Chief Rocket Propulsion Engineer of Rolls Royce’s new rocket engine division. Under his guidance the RZ.2 rocket engine was developed, an advanced engine for its time. For the work on this engine he was awarded the OBE. He worked with Rocketdyne.
Sir William Congreve, 2nd Baronet KCH FRS (20 May 1772 – 16 May 1828)
was an English inventor and rocket artillery pioneer distinguished for his development and deployment of Congreve rockets, and a Tory Member of Parliament (MP).
Gaetano Arturo Crocco (26 October 1877 – 19 January 1968) was an Italian scientist and aeronautics pioneer, the founder of the Italian Rocket Society, and went on to become Italy’s leading space scientist. He was born in Naples.
In 1927, Crocco begun working with solidpropellant rockets and, in 1929, designed and built the first liquid propellant rocket motors in Italy. He began work with monopropellants (fuel and oxidizer combined in one chemical liquid) in 1932, making him one of the first researchers in this field. in 1956, he suggested exploiting the Mars and Venus gravitational fields as propelling forces to cut dramatically the travelling time of a space capsule. The importance of his intuition, now a scientific theory known as ‘gravitational slingshot’ or ‘gravity assist’ or ‘swing by’, was such that the NASA recommended the study of his theories and especially the swingby maneuvers suggested by Crocco to all the contracting firms working on interplanetary flight and its perspectives. Basing his calculations on Hohmann’s orbit, the scifi writer Arthur C. Clarke had stated once that an Earth to Mars flight with a minimum fuel consumption would
require at least 259 days. Then another 425 days should elapse on the Red Planet to realign the planets so as to
travel back again in 259 days. Crocco deemed this period too long and drew his own calculations exploiting Mars gravity pull to fly over the planet without landing. Mars gravity would deflect the spaceship’s trajectory towards the Earth cutting the flight’s overall length to less than a year, the only objection being the poor quality of data gathered passing over Mars at an altitude of more than a million miles. But, Crocco added, should the spaceship be redirected towards Venus and not the Earth, it would fly over Mars at a much closer range: observation by the astronauts would be much more satisfactory, and moreover they could observe Venus as well, still keeping the trip’s time under a year. He calculated 113 days from Earth to Mars, 154 to reach Venus from Mars and 98 days from Venus back to Earth and affirmed that the first occasion for this ‘Crocco Grand Tour’ would be occurring in 1971. Gravity assist manoeuvres as envisaged by him are used extensively in all interplanetary missions today.
Sir Alwyn Douglas Crow KBE FInstP (10 May 1894 – 5 February 1965) was a British scientist involved in research into ballistics, projectiles and missiles from 1916 to 1953. At Fort Halstead he developed the Unrotated Projectile an antiaircraft weapon for the Royal Navy, used in the early period of World War II when the supply of antiaircraft guns was limited. His obituary in The Times called him a Rocket Projectile Pioneer.
Konrad Dannenberg (August 5, 1912 – February 16, 2009) was a German American rocket pioneer and member of the German rocket team brought to the United States after World War II. He was at Peenemünde on 3 October 1942 to witness the launch of the first manmade object to reach outer space, a V2 rocket. This was the first man made vehicle to ever reach space which most experts agree is over 50 miles in altitude. In 1960, Dannenberg joined NASA’s newly established Marshall Space Flight Center as Deputy Manager of the Saturn program. He received the NASA Exceptional Service Medal in 1973 for successfully initiating development of the largest rocket ever built, the Saturn V, which took the first human beings to the moon. When Arthur Rudolph came back from the Army’s development of the Pershing missile system, von Braun assigned the management of the Saturn system to him. Dannenberg then started to work on Saturnbased space stations, which were eventually replaced by the Space Shuttlebased ISS.
Franklin Ramón Chang Díaz (born April 5, 1950) is a Costa RicanAmerican mechanical engineer, physicist and former NASA astronaut. After leaving NASA, Chang Díaz set up the Ad Astra Rocket Company, which became dedicated to the development of advanced plasma rocket propulsion technology. Years of research and development have produced the Variable Specific Impulse Magnetoplasma Rocket (VASIMR), an electrical propulsion device for use in space. With a flexible mode of operation, the rocket can achieve very high exhaust speeds, and even has the theoretical capability to take a manned rocket to Mars in 39 days.
Mikhail Borisovich Dobriyan, (Russian: Добриян, Михаил Борисович, (26 June 1947 – 16 November
2013) was a Soviet and Russian aerospace engineer and a former director of the Space Research Institute of the Russian Academy of Sciences in Tarusa. He was one of the leading figures in the programs of the International Astrophysical Observatory GRANAT and Vega program. Mikhail Dobriyan was a head of Tarussky District and an honorary citizen of city of Tarusa.
MajorGeneral Dr. Walter Robert Dornberger (6 September 1895 – 27 June 1980) was a German Army artillery officer whose career spanned World War I and World War II. He was a leader of Nazi Germany’s V2 rocket program and other projects at the Peenemünde Army Research Center.
Leonid Stepanovich Dushkin (August 15, 1910 in the Spirove settlement of the Tver region – April 4, 1990), was a major pioneer of Soviet rocket engine technology. He graduated from Moscow State University with a degree in mathematics and mechanics. In October 1932, he joined Fridrikh Tsander’s brigade of GIRD, the Moscow rocket research group. He assisted in the creation of their first rocket engine OR2, and after Tsander’s death, he oversaw the creation of engine “10” which powered the first Soviet liquidfuel rocket, GIRDX. Dushkin’s engines were among the first to be regeneratively cooled, and he also experimented with uncooled engines of hightemperature ceramic. The 12K engines were of both types, and powered the Aviavnito rocket. After the arrest of Valentin Glushko, Dushkin took over the development of rocket engines for the rocket enhanced fighter plane RP318. He became the leader of the department of liquid propellent rocket engines in NII3 beginning in January 1938. Starting with Glushko’s engines (ORM65 and RD1), he began a series of important engineering transformations, moving the fuel injectors to a head at one end of a cylindrical chamber, typical of modern design. The RDA150, RDA300 used nitric acid as an oxydizer, RDK150 used liquid oxygen. The 1100 kgf thrust engine, D1A1100 was developed for the rocketpowered interceptor BI1. It was also regeneratively cooled, using the kerosine to cool the chamber, and the nitric acid to cool the nozzle. Starting with that engine, Aleksei Mihailovich Isaev began the evolution of his engines, which continued the evolution of engines toward the spacerocket engines of the 1950s.
Freeman dyson– december 15, 1923.Space exploration—A direct search for life in Europa’s ocean would today be prohibitively expensive. Impacts on Europa give us an easier way to look for evidence of life there. Every time a major impact occurs on Europa, a vast quantity of water is splashed from the ocean into the space around Jupiter. Some of the water evaporates, and some condenses into snow. Creatures living in the water far enough from the impact have a chance of being splashed intact into space and quickly freezedried. Therefore, an easy way to look for evidence of life in Europa’s ocean is to look for freeze dried fish in the ring of space debris orbiting Jupiter. Freeze dried fish orbiting Jupiter is a fanciful notion, but nature in the biological realm has a tendency to be fanciful. Nature is usually more imaginative than we are. […] To have the best chance of success, we should keep our eyes open for all possibilities.
Robert Lull Forward(August 15, 1932 – September 21, 2002) was an American physicist and science fiction writer. His literary work was noted for its scientific credibility and use of ideas developed from his career as an aerospace engineer. Much of his research focused on the leading edges of speculative physics but was always grounded in what he believed humans could accomplish. He worked on such projects as space tethers and space fountains, solar sails (including Starwisp), antimatter propulsion, and other spacecraft propulsion technologies, and did further research on more esoteric possibilities such as time travel and negative matter. He was issued a patent for the statite, and contributed to a concept to drain the Van Allen Belts.
Valentin Petrovich Glushko 2 September 1908 – 10 January 1989), was a Soviet engineer, and designer of rocket engines during the Soviet/American Space Race.
Conrad Haas (1509–1576) was an Austrian or Transylvanian Saxon military engineer for the Kingdom of Hungary and Principality of Transilvania. He is a pioneer of rocket propulsion.
Roy Healy (1915–1968) was an American rocket scientist. He was a member of the American Rocket Society.
Clarence Nichols Hickman (August 16, 1889 – May 7, 1981) was a physicist who worked on rockets with Robert Goddard. He is known for developing the bazooka manportable recoilless antitank rocket launcher weapon, and the American Piano Company Model B player piano. He is also known as the “Father of Scientific Archery”.
Aleksei Mikhailovich Isaev (October 24, 1908, Saint Petersburg– June 10, 1971, Moscow) was a Russian rocket engineer. walled copper combustion chambers backed by steel support, antioscillation baffle to prevent chugging, and the flat injector plate with mixingswirling injectors. The latter was an enormous simplification of the “plumbing nightmare” of the V2 engine, because it avoided the need for separate fuel lines to each sprayer. Staged combustion (Замкнутая схема) was first proposed by Alexey Isaev in 1949. Although his inventions influenced the design of Glushko’s large engines, Isaev was better known for building efficient small rockets. He designed engines for the Soviet antimissile and antiaircraft rockets, and in 1951, his engine powered the R11 Zemlya shortrange missile, later named the Scud. He designed a series of coursecorrection engines for Soviet planetary probes, including the KDU414 used in Venera 1, Mars 1 up to Venera 8, the KTDU425 used in later planetary probes, KTDU5 used in the Soviet lunar landers Luna 4 to Luna 13. Isaev was a corresponding member of the USSR Academy of Sciences.
A.M. Isayev Chemical Engineering Design Bureau is named after him. The crater Isaev on the far side of the Moon is named after him.
Hideo Itokawa 1912 – February 21, 1999) was a pioneer of Japanese rocketry, popularly known as “Dr. Rocket,” and described in the media as the father of Japan’s space development.
Oleg Genrikhovich Ivanovsky January 18, 1922 – September 18, 2014) was a Soviet engineer, and pioneer of spacecraft construction. Ivanovsky graduated from the Moscow Power Engineering Institute in 1953. DesignerGeneral Sergei Korolev recruited him into the Soviet space program. Ivanovsky rose to chief designer at OKB1, Korolev’s design bureau. Among other things he was deputy principal designer of the first and second Sputniks,principal designer of Vostok manned spaceships, and creator of space probes. Ivanovsky personally
helped Yuri Gagarin mount the gantry and climb into Vostok 1 and helped rebolt the hatch after Gagarin complained that it had not been closed and sealed correctly. He was said to be the last person to shake Gagarin’s hand before the Vostok 1 flight. Ivanovsky was the Recipient of the Lenin Prize (1960) and USSR State Prize (1977).
Daniel Jubb (born 1984 in Manchester, England) is a British rocket scientist. In a 17 November 2008 article from the British newspaper The Times, he was named “one of the world’s leading rocket scientists”, by the Royal Air Force Wing Commander Andy Green. Having been interested in rockets since childhood, Jubb had obtained corporate financing and flew many amateur rockets, all by the time he was 14 years old. In 1995, and along with his grandfather Sid Guy, he co founded The Falcon Project, a company that designs and develops rocket engines for commercial and military applications. At that time, Jubb obtained permission from the UK Ministry of Defence to launch rockets from the missile test platform of the Otterburn Army Training Estate in Northumberland and after his rockets reached the maximum allowable launch height of 20,000 feet he wanted to go higher. The operations of The Falcon Project
Boris Katorgin 13 October 1934 in Solnechnogorsk) is a Russian scientist who is known for his development of commercially successful rocket engine systems. Katorgin is mainly known for his work on cryogenic liquid propellant rocket engines. He was the CEO and chief designer of NPO Energomash during the development of the RD180 engine, which has been exported to the United States for driving Atlas III and Atlas V rockets. He was also involved in the development of the earlier and twice as powerful RD170 engine. As of 2000, when the first RD180powered Atlas III rocket flew, the engine was considered to be 15 to 20 percent more fuel efficient than competing designs. Katorgin has also contributed to the study of nuclear pulse propulsion, chemical lasers and superconducting systems for power transmission. In 2012, along with Valery Kostuk and Rodney John Allam, Katorgin received the Global Energy Prize for his research and development relating to highefficiency and reliable cryogenic fuelpowered rocket propellant engines.
Rudy Kennedy (October 27, 1927 – November 10, 2008) was a British rocket scientist, Holocaust survivor, and a protester for Jewish causes. He spent a substantial period of his youth in German concentration camps of Auschwitz, MittelbauDora, and BergenBelsen. After liberation, he worked as a rocket scientist and led the campaign for compensation for the survivors of the German policy of “extermination through labour.
LieutenantGeneral Kerim Aliyevich Kerimov (1917–2003) was an Azerbaijani Soviet/Russian aerospace engineer and a renowned rocket scientist, one of the founders of the Soviet space industry, and for many years a central figure in the Soviet space program. Despite his prominent role, his identity was kept a secret from the public for most of his career. He was one of the lead architects behind the string of Soviet successes that stunned the world from the late 1950s – from the launch of the first satellite, the Sputnik 1 in 1957, and the first human spaceflight, Yuri Gagarin’s 108minute trip around the globe aboard the Vostok 1 in 1961, to the first fully automated space docking, of Cosmos 186 and Cosmos 188 in 1967, and the first space stations, the Salyut and Mir series from 1971 to 1991.
• Sergei Pavlovich Korolev 12 January [O.S. 30 December 1906] 1907 – 14 January 1966) worked as the lead Soviet rocket engineer and spacecraft designer during the Space Race between the United States and the Soviet Union in the 1950s and 1960s. He is considered by many as the father of practical astronautics. He was involved in the development of the R7 Booster Rocket, Sputnik, and launching Laika and the first human being into space.
Semyon Ariyevich Kosberg (Семен Ариевич Косберг in Russian) (October 1(14), 1903, Slutsk – January 3, 1965, Voronezh) was a Jewish Soviet engineer, expert in the field of aircraft and rocket engines, Doctor of Technical Sciences (1959), Hero of Socialist Labor (1961).
Nikolai Dmitriyevich Kuznetsov was a Chief Designer of the Soviet Design Bureau OKB276 which deals with the development, manufacture and distribution of equipment, especially aircraft engines, turbines and gearboxes.
Geoffrey Alan Landis (May 28, 1955) is an American scientist, working for the National Aeronautics and Space Administration (NASA) on planetary exploration, interstellar propulsion, solar power and photovoltaics. He holds nine patents, primarily in the field of improvements to solar cells and photovoltaic devices and has given presentations and commentary on the possibilities for interstellar travel and construction of bases on the Moon, Mars, and Venus. NASA Institute for Advanced Concepts—Landis was a fellow of the NASA Institute for Advanced Concepts (“NIAC”), where he worked on a project investigating the use of laser and particlebeam pushed sails for propulsion for interstellar flight. In 2002 Landis addressed the annual convention of the American Association for the Advancement of Science on the possibilities and challenges of interstellar travel in what was described as the “first serious discussion of how mankind will one day set sail to the nearest star”. Dr. Landis said, “This is the first meeting to really consider interstellar travel by humans. It is historic. We’re going to the stars. There really isn’t a choice in the long term.” He went on to describe a star ship with a diamond sail, a few nanometres thick, powered by solar energy, which could achieve “10 per cent of the speed of light”. He was selected again as a NASA Innovative Advanced Concepts fellow in 2012, with an investigation of a Landsailing rover for Venus exploration, and in 2015 was the science lead on a NIAC study to design a mission to Neptune’s moon Triton.
Derek Frank Lawden (15 September 1919 – 15 February 2008) was a New Zealand mathematician of English descent. After doing mathematics at Cambridge University he served in the Royal Artillery and then lectured at the Royal Military College of Science and the College of Advanced Technology Birmingham, where he worked on rocket trajectories and space flight. In 1956 he moved to University of Canterbury as professor. In the 1960s he got a DSc from Cambridge, was appointed FRSNZ and won the Hector Medal. He return to the UK to University of Aston in 1967.
Willy Otto Oskar Ley (October 2, 1906 – June 24, 1969) was a German American science writer, spaceflight advocate, and historian of science who helped to popularize rocketry, spaceflight, and natural history in both Germany and the United States. The crater Ley on the far side of the Moon is named in his honor.
Lovell Lawrence, Jr. (1915–1971) was an American rocket scientist who developed the first engine to break the sound barrier while working with Reaction Motors, Inc.
Peter Madsen born 12 January 1971, is an artist, submarine builder, aerospace engineer, entrepreneur and cofounder of Copenhagen Suborbitals; a private non profit spaceflight organization. CEO and founder of RML Spacelab ApS
Frank Joseph Malina (October 2, 1912 – November 9, 1981) was an American aeronautical engineer and painter, especially known for becoming both a pioneer in the art world and the realm of scientific engineering.
Manoug Manougian is an Armenian scientist, professor, and considered the father of the Lebanese space program.
Dr. Gregory L. Matloff he did pioneering work in solar sail technology used by NASA for extrasolar probes and
technology to divert earth threatening asteroids. He was appointed an advisor to the Project Starshot mission to the star Alpha Centauri in April 2016. He has co authored the book, The Starlight Handbook. He also helped establish interstellar propulsion studies as a sub division of applied physics.
 Salim Mehmood,is a Pakistani rocket scientist and a nuclear engineer. He is the former chairman of Space and
 Upper Atmosphere Research Commission (SUPARCO). He has served as chief scientist at the Defence Science and
 technology Organization. Currently, he is the chief Scientific and Technological Advisor at the Ministry of
 Communications of Pakistan. Marc Millis He is an aerospace engineer who has researched possibilities for creating
 space propulsion breakthroughs. He has worked with other researchers across the United States to create NASA’s
 Breakthrough Propulsion Physics Project and managed this from 19962001. He now has returned to conducting
 research.
Mary Sherman Morgan (November 4, 1921 – August 4, 2004) was a U.S. rocket fuel scientist credited with the invention of the liquid fuel Hydyne in 1957, which powered the JupiterC rocket that boosted the United States’ first satellite, Explorer 1. During the development program for the reentry vehicle of the Jupiter missile, also under development, Wernher von Braun’s team used modified Redstone missiles, dubbed the Jupiter C, to accelerate test nose cones to the necessary speed. In order to improve the performance of the first stage, they awarded a contract to North American Aviation’s Rocketdyne Division to come up with a more powerful fuel. Morgan worked in the group of Dr. Jacob Silverman at North American Aviation’s Rocketdyne Division. Due to her expertise and experience with new rocket propellants, Morgan was named the technical lead on the contract. Morgan’s work resulted in a new propellant,
Hydyne. The first Hydynepowered Redstone R&D flight took place on 29 November 1956, and Hydyne subsequently powered three Jupiter C nose cone test flights. In 1957, the Soviet Union and the United States had set a goal of placing satellites into Earth orbit as part of a worldwide scientific celebration known as the International Geophysical Year. In this endeavor the United States effort was called Project Vanguard. The Soviet Union successfully launched the Sputnik satellite on October 4, 1957, an event followed soon after by a very public and disastrous explosion of a Vanguard rocket. Political pressure forced U.S. politicians to allow a former German rocket scientist, Wernher von Braun, to prepare his Jupiter C rocket for an orbital flight. In the renamed launcher (now called Juno I) the propellant succeeded in launching America’s first satellite, Explorer I, into orbit on January 31, 1958. After the Jupiter C and Juno I programs (there six launch attempts in the latter), the U.S. switched to more powerful fuels. As HydyneLOX (liquid oxygen) was the fuel combination used for the Redstone rocket, Morgan whimsically suggested naming her new fuel formulation Bagel, since the rocket’s propellant combination would then be called Bagel and LOX. Her suggested name for the new fuel was not accepted, and Hydyne was chosen instead by the U.S. Army. The standard Redstone was fueled with a 75% ethyl alcohol solution, but the Jupiter C first stage had used Hydyne fuel, a blend of 60% unsymmetrical dimethylhydrazine (UDMH) and 40% diethylenetriamine (DETA). This was a more powerful fuel than ethyl alcohol, but it was also more toxic. The fuel was used with the Rocketdyne Redstone rocket only once— to launch America’s first satellite Explorer I, after which it was discontinued in favor of higher performing fuels.
Tom Mueller is an American rocket engineer and rocket engine designer. He is a founding employee of SpaceX (Space Exploration Technologies Corp.), a space transport services company headquartered in Hawthorne, California. He is best known for his engineering work on the TR106, the Dragon spacecraft propulsion, and Merlin Rocket Engines. He is considered one of the world’s leading spacecraft propulsion experts and holds several United States patents for propulsion technology. The Dragon spacecraft being launched on a Falcon 9 v1.0 rocket powered by Merlin engines engineered by Tom Mueller. For 15 years, Mueller worked for TRW Inc., a conglomerate corporation involved in aerospace, automotive, credit reporting, and electronics. He managed the propulsion and combustion products department where he was responsible for liquid rocket engine development. He worked as a lead engineer during the development of the TR106, a 650,000 lbf (2,900 kN) thrust hydrogen engine that was one of the most powerful engines ever at the time it was constructed. During his time at TRW, Mueller felt that his ideas were being lost in a diverse corporation and as a hobby he began to build his own engines. He would attach them to airframes and launch them in the Mojave Desert along with other members of the Reaction Research Society. In late 2001, Mueller began developing a liquidfueled rocket engine in his garage and later moved his project to a friend’s warehouse in 2002. His design was the largest amateur liquidfuel rocket engine, weighing 80 lb (36 kg) and producing 13,000 lbf (58 kN) of thrust. His work caught the attention of Elon Musk, PayPal co founder and CEO of Tesla Motors, and in 2002 Mueller joined Musk as a founding employee of SpaceX. Mueller is currently the CTO of Propulsion Development at SpaceX, responsible for all propulsion development, including the Dragon spacecraft propulsion systems and Merlin rocket engine family that powers the Falcon 9 launch vehicle to orbit. The Merlin is the highest performing hydrocarbon engine made in the United States and the first hydrocarbon booster engine made in the United States in 40 years. Mueller developed the Merlin 1A and Kestrel engines for the Falcon 1, the first liquid fueled orbital rocket launched by a private company as well as leading the team that developed the Merlin 1C, Merlin 1D and MVac engines for the Falcon 9, the first to launch into orbit and recover a spacecraft. The Dragon was the first spacecraft launched by a private company to dock at the International Space Station, with its technology being used on projects for manned missions to Mars. Outside his work at SpaceX, he was a commencement speaker for Loyola graduate students in 2013, the year after SpaceX became the first private company to send a cargo payload to the International Space Station. He was also the feature of an appropriately titled article called “Rocket Man,” published by LMU Magazine in 2011. In 2014, Mueller was nominated for the Wyld Award, presented by the American Institute of Aeronautics and Astronautics (AIAA) for outstanding achievement in the development or application of rocket propulsion systems. Mueller is currently working on development of the Raptor rocket engine family that will power the Interplanetary Transport System on its journey to Mars and beyond.
Elon Reeve Musk June 28, 1971 (age 46) In 2001, Musk conceptualized “Mars Oasis”; a project to land a miniature experimental greenhouse on Mars, containing food crops growing on Martian regolith, in an attempt to regain public interest in space exploration. In October 2001, Musk travelled to Moscow with Jim Cantrell (an aerospace supplies fixer), and Adeo Ressi (his best friend from college), to buy refurbished Dnepr Intercontinental ballistic missiles (ICBMs) that could send the envisioned payloads into space. The group met with companies such as NPO Lavochkin and Kosmotras; however, according to Cantrell, Musk was seen as a novice and was consequently spat on by one of the Russian chief designers, and the group returned to the United States emptyhanded. In February 2002, the group returned to Russia to look for three ICBMs, bringing along Mike Griffin, who had worked for the CIA’s venture capital arm, InQTel; NASA’s Jet Propulsion Laboratory; and was just leaving Orbital Sciences, a maker of satellites and spacecraft. The group met again with Kosmotras, and were offered one rocket for US$8 million, however, this was seen by Musk as too expensive; Musk consequently stormed out of the meeting. On the flight back from Moscow, Musk realized that he could start a company that could build the affordable rockets he needed. According to early Tesla and SpaceX investor Steve Jurvetson, Musk calculated that the raw materials for building a rocket actually were only 3 percent of the sales price of a rocket at the time. It was concluded that theoretically, by applying vertical integration and the modular approach from software engineering, SpaceX could cut launch price by a factor of ten and still enjoy a 70percent gross margin. Ultimately, Musk ended up founding SpaceX with the long term goal of creating a “true spacefaring civilization”.
With US$100 million of his early fortune, Musk founded Space Exploration Technologies, or SpaceX, in May 2002. Musk is chief executive officer (CEO) and chief technology officer (CTO) of the Hawthorne, California based company. SpaceX develops and manufactures space launch vehicles with a focus on advancing the state of rocket technology. The company’s first two launch vehicles are the Falcon 1 and Falcon 9 rockets (a nod to Star Wars’ Millennium Falcon), and its first spacecraft is the Dragon (a nod to Puff the Magic Dragon). In seven Musk and President Barack Obama at the Falcon 9 launch site in 2010 years, SpaceX designed the family of Falcon launch vehicles and the Dragon multipurpose spacecraft. In September 2008, SpaceX’s Falcon 1 rocket became the first privately funded liquidfueled vehicle to put a satellite into Earth orbit. On May 25, 2012, the SpaceX Dragon vehicle berthed with the ISS, making history as the first commercial company to launch and berth a vehicle to the International Space Station. In 2006, SpaceX was awarded a contract from NASA to continue the development and test of the SpaceX Falcon 9 launch vehicle and Dragon spacecraft in order to transport cargo to the International Space Station, followed by a US$1.6 billion NASA Commercial Resupply Services program contract on December 23, 2008, for 12 flights of its Falcon 9 rocket and Dragon spacecraft to the Space Station, replacing the US Space Shuttle after it retired in 2011. Astronaut transport to the ISS is currently handled solely by the Soyuz, but SpaceX is one of two companies awarded a contract by NASA as part of the Commercial Crew Development program, which is intended to develop a US astronaut transport capability by 2018. On 22 December 2015, SpaceX successfully landed the first stage of its Falcon rocket back at the launch pad. This was the first time in history such a feat had been achieved by an orbital rocket and is a significant step towards rocket reusability lowering the costs of access to space. This first stage recovery was replicated several times in 2016 by landing on an Autonomous spaceport drone ship, an ocean based recovery platform. SpaceX is both the largest private producer of rocket engines in the world, and holder of the record for highest thrusttoweight ratio for a rocket engine. SpaceX has produced more than 100 operational Merlin 1D engines, currently the world’s most powerful engine for its weight. The relatively immense power to weight ratio allows each Merlin 1D engine to vertically lift the weight of 40 average family cars. In combination, the 9 Merlin engines in the Falcon 9 first stage produces anywhere from 5.8 to 6.7 MN (1.3 to 1.5 million pounds) of thrust, depending on altitude. Musk was influenced by Isaac Asimov’s Foundation series and views space exploration as an important step in preserving and expanding the consciousness of human life. Musk said that multiplanetary life may serve as a hedge against threats to the survival of the human species. An asteroid or a super volcano could destroy us, and we face risks the dinosaurs never saw: an engineered virus, inadvertent creation of a micro black hole, catastrophic global warming or some asyetunknown technology could spell the end of us. Humankind evolved over millions of years, but in the last sixty years atomic weaponry created the potential to extinguish ourselves. Sooner or later, we must expand life beyond this green and blue ball—or go extinct. Musk’s goal is to reduce the cost of human spaceflight by a factor of 10. In a 2011 interview, he said he hopes to send humans to Mars’ surface within 10–20 years. In Ashlee Vance’s biography, Musk stated that he wants to establish a Mars colony by 2040, with a population of 80,000. Musk stated that, since Mars’ atmosphere lacks oxygen, all transportation would have to be electric (electric cars, electric trains, Hyperloop, electric aircraft). Space X intends to launch a Dragon spacecraft on a Falcon Heavy in 2018 to softland on Mars – this is intended to be the first of a regular cargo mission supply run to Mars building up to later crewed flights. Musk stated in June 2016 that the first unmanned flight of the larger Mars Colonial Transporter (MCT) spacecraft is aimed for departure to the red planet in 2022, to be followed by the first manned MCT Mars flight departing in 2024. In September 2016, Musk revealed details of his plan to explore and colonize Mars. By 2016, Musk’s private trust holds 54% of SpaceX stock, equivalent to 78% of voting shares.
Katuru Narayana is an Indian rocket scientist and a former director of Satish Dhawan Space Centre, one of the two launch centres of the Indian Space Research Organisation. He held the post from 1999 to 2005 after which he served as the cochairman of the Mission Readiness Review Committee for two Indian space programs, Polar Satellite Launch Vehicle and Geosynchronous Satellite Launch Vehicle. He is a recipient of an honorary doctorate from Sri Venkateswara University. The Government of India awarded him the fourth highest civilian honour of the Padma Shri, in 2002, for his contributions to science and engineering.
Hermann Julius Oberth 25 June 1894 – 28 December 1989) was an Austro Hungarianborn German physicist and engineer. He is considered one of the founding fathers of rocketry and astronautics, along with the French Robert Esnault Pelterie, the Russian Konstantin Tsiolkovsky and the American Robert Goddard.
Gerard Kitchen O’Neill (February 6, 1927 – April 27, 1992) was an American physicist and space activist. As a faculty member of Princeton University, he invented a device called the particle storage ring for highenergy physics experiments. Later, he invented a magnetic launcher called the mass driver. In the 1970s, he developed a plan to build human settlements in outer space, including a space habitat design known as the O’Neill cylinder. He founded the Space Studies Institute, an organization devoted to funding research into space manufacturing and colonization.
O’Neill saw great potential in the United States space program, especially the Apollo missions. He applied to the Astronaut Corps after NASA opened it up to civilian scientists in 1966. Later, when asked why he wanted to go on the Moon missions, he said, “to be alive now and not take part in it seemed terribly myopic”. He was put through NASA’s rigorous mental and physical examinations. During this time NASA envisioned an ambitious scientific exploration of the Moon. he met Brian O’Leary, also a scientist astronaut candidate, who became his good friend. O’Leary was selected for Astronaut Group 6 but O’Neill was not. O’Neill became interested in the idea of space colonization in 1969 while he was teaching freshman physics at Princeton University. His students were growing cynical about the benefits of science to humanity because of the controversy surrounding the Vietnam War. To give them something relevant to study, he began using examples from the Apollo program as applications of elementary physics. O’Neill posed the question during an extra seminar he gave to a few of his students: “Is the surface of a planet really the right place for an expanding technological civilization?” His students’ research convinced him that the answer was no.
O’Neill was inspired by the papers written by his students. He began to work out the details of a program to build self supporting space habitats in free space. Among the details was how to provide the inhabitants of a space colony with an Earthlike environment. His students had designed giant pressurized structures, spun up to approximate Earth gravity by centrifugal force. With the population of the colony living on the inner surface of a sphere or cylinder, these structures resembled “insideout planets”. He found that pairing counterrotating cylinders would eliminate the need to spin them using rockets. This configuration has since been known as the O’Neill cylinder. Looking for an outlet for his ideas, O’Neill wrote a paper titled “The Colonization of Space”, and for four years attempted to have it published. He submitted it to several journals and magazines, including Scientific American and Science, only to have it rejected by the reviewers. During this time O’Neill gave lectures on space colonization at Hampshire College, Princeton, and other schools. Many students and staff attending the lectures became enthusiastic about the possibility of living in space. Another outlet for O’Neill to explore his ideas was with his children; on walks in the forest they speculated about life in a space colony. His paper finally appeared in the September 1974 issue of Physics Today. In it, he argued that building space colonies would solve several important problems: It is important to realize the enormous power of the spacecolonization technique. If we begin to use it soon enough, and if we employ it wisely, at least five of the most serious problems now facing the world can be solved without recourse to repression: bringing every human being up to a living standard now enjoyed only by the most fortunate; protecting the biosphere from damage caused by transportation and industrial pollution; finding high quality living space for a world
population that is doubling every 35 years; finding clean, practical energy sources; preventing overload of Earth’s heat balance. — Gerard K. O’Neill, “The Colonization of Space” He even explored the possibilities of flying gliders inside a space colony, finding that the enormous volume could support atmospheric thermals. He calculated that humanity could expand on this manmade frontier to 20,000 times its population.[28] The initial colonies would be built at the EarthMoon L4 and L5 Lagrange points. L4 and L5 are stable points in the Solar System where a spacecraft can maintain its position without expending energy. The paper was well received, but many who would begin work on the project had already been introduced to his ideas before it was even published.[21] The paper received a few critical responses. Some questioned the practicality of lifting tens of thousands of people into orbit and his estimates for the production output of initial colonies. While he was waiting for his paper to be published, O’Neill organized a small two day conference in May 1974 at Princeton to discuss the possibility of colonizing outer space. The conference, titled First Conference on Space Colonization, was funded by Stewart Brand’s Point Foundation and Princeton University. Among those who attended were Eric Drexler (at the time a freshman at MIT), scientistastronaut Joe Allen (from Astronaut Group 6), Freeman Dyson, and science reporter Walter Sullivan. Representatives from NASA also attended and brought estimates of launch costs expected on the planned Space Shuttle. O’Neill thought of the attendees as “a band of daring radicals”. Sullivan’s article on the conference was published on the front page of The New York Times on May 13, 1974. As media coverage grew, O’Neill was inundated with letters from people who were excited about living in space. To stay in touch with them, O’Neill began keeping a mailing list and started sending out updates on his progress. A few months later he heard Peter Glaser speak about solar power satellites at NASA’s Goddard Space Flight Center. O’Neill realized that, by building these satellites, his space colonies could quickly recover the cost of their construction. According to O’Neill, “the profound difference between this and everything else done in space is the potential of generating large amounts of new wealth”. O’Neill held a much larger conference the following May titled Princeton University Conference on Space Manufacturing.[37] At this conference more than two dozen speakers presented papers, including Keith and Carolyn Henson from Tucson, Arizona. After the conference Carolyn Henson arranged a meeting between O’Neill and Arizona Congressman Morris Udall. Udall wrote a letter of support, which he asked the Hensons to publicize, for O’Neill’s work. The Hensons included his letter in the first issue of the L5 Society newsletter, sent to everyone on O’Neill’s mailing list and those who had signed up at the conference. In June 1975, O’Neill led a tenweek study of permanent space habitats at NASA Ames. During the study he was called away to testify on July 23 to the House Subcommittee on Space Science and Applications. On January 19, 1976, he also appeared before the Senate Subcommittee on Aerospace Technology and National Needs. In a presentation titled Solar Power from Satellites, he laid out his case for an Apollostyle program for building power plants in space. He returned to Ames in June 1976 and 1977 to lead studies on space manufacturing. In these studies, NASA developed detailed plans to establish bases on the Moon where spacesuited workers would mine the mineral resources needed to build space colonies and solar power satellites. Although NASA was supporting his work with grants of up to $500,000 per year, O’Neill became frustrated by the bureaucracy and politics inherent in government funded research. He thought that small privately funded groups could develop space technology faster than government agencies. In 1977, O’Neill and his wife Tasha founded the Space Studies Institute, a nonprofit organization, at Princeton University. SSI received initial funding of almost $100,000 from private donors, and in early 1978 began to support basic research into technologies needed for space manufacturing and settlement. Kolm (left) and O’Neill (center) with mass driver One of SSI’s first grants funded the development of the mass driver, a device first proposed by O’Neill in 1974. Mass drivers are based on the coilgun design, adapted to accelerate a nonmagnetic object. One application O’Neill proposed for mass drivers was to throw baseball sized chunks of ore mined from the surface of the Moon into space. Once in space, the ore could be used as raw material for building space colonies and solar power satellites. He took a sabbatical from Princeton to work on mass drivers at MIT. There he served as the Hunsaker Visiting Professor of Aerospace during the 1976– 77 academic year. At MIT, he, Henry H. Kolm, and a group of student volunteers built their first mass driver prototype. The eightfoot (2.5 m) long prototype could apply 33 g (320 m/s2) of acceleration to an object inserted into it. With financial assistance from SSI, later prototypes improved this to 1,800 g (18,000 m/s2), enough acceleration that a mass driver only 520 feet (160 m) long could launch material off the surface of the Moon. In 1977, O’Neill saw the peak of interest in space colonization, along with the publication of his first book, The High Frontier. He and his wife were flying between meetings, interviews, and hearings. On October 9, the CBS program 60 Minutes ran a segment about space colonies. Later they aired responses from the viewers, which included one from Senator William Proxmire, chairman of the Senate Subcommittee responsible for NASA’s budget. His response was, “it’s the best argument yet for chopping NASA’s funding to the bone …. I say not a penny for this nutty fantasy”. He successfully eliminated spending on space colonization research from the budget. In
1978, Paul Werbos wrote for the L5 newsletter, “no one expects Congress to commit us to O’Neill’s concept of large scale space habitats; people in NASA are almost paranoid about the public relations aspects of the idea”. When it became clear that a government funded colonization effort was politically impossible, popular support for O’Neill’s ideas started to evaporate. Other pressures on O’Neill’s colonization plan were the high cost of access to Earth orbit and the declining cost of energy. Building solar power stations in space was economically attractive when energy prices spiked during the 1979 oil crisis. When prices dropped in the early 1980s, funding for space solar power research dried up.[56] His plan had also been based on NASA’s estimates for the flight rate
and launch cost of the Space Shuttle, numbers that turned out to have been wildly optimistic. His 1977 book quoted a Space Shuttle launch cost of $10 million, but in 1981 the subsidized price given to commercial customers started at $38 million. Eventual accounting of the full cost of a launch in 1985 raised this as high as $180 million per flight. O’Neill was appointed by United States President Ronald Reagan to the National Commission on Space in 1985. The commission, led by former NASA administrator Thomas Paine, proposed that the government commit to opening the inner Solar System for human settlement within 50 years. Their report was released in May 1986, four months after the Space Shuttle Challenger broke up on ascent. O’Neill’s popular science book The High Frontier: Human Colonies in Space (1977) combined fictional accounts of space settlers with an explanation of his plan to build space colonies. Its publication established him as the spokesman for the space colonization movement. It won the Phi Beta Kappa Award in Science that year, and prompted Swarthmore College to grant him an honorary doctorate. The High Frontier has been translated into five languages and remained in print as of 2008. His 1981 book 2081: A Hopeful View of the Human Future was an exercise in futurology. O’Neill narrated it as a visitor to Earth from a space colony beyond Pluto. The book explored the effects of technologies he called “drivers of change” on the coming century. Some technologies he described were space colonies, solar power satellites, antiaging drugs, hydrogen propelled cars, climate control, and underground magnetic trains. He left the social structure of the 1980s intact, assuming that humanity would remain unchanged even as it expanded into the Solar System. Reviews of 2081 were mixed. New York Times reviewer John Noble Wilford found the book “imaginationstirring”, but Charles Nicol thought the technologies described were unacceptably farfetched. In his book The Technology Edge, published in 1983, O’Neill wrote about economic competition with Japan. He argued that the United States had to develop six industries to compete: microengineering, robotics, genetic engineering, magnetic flight, family aircraft, and space science.[51] He also thought that industrial development was suffering from shortsighted executives, self interested unions, high taxes, and poor education of Americans. According to reviewer Henry Weil, O’Neill’s detailed explanations of emerging technologies differentiated the book from others on the subject. O’Neill founded Geostar Corporation to develop a satellite position determination system for which he was granted a patent in 1982. The system, primarily intended to track aircraft, was called Radio Determination Satellite Service (RDSS). In April 1983 Geostar applied to the FCC for a license to broadcast from three satellites, which would cover the entire United States. Geostar launched GSTAR2 into geosynchronous orbit in 1986. Its transmitter package permanently failed two months later, so Geostar began tests of RDSS by transmitting from other satellites. With his health failing, O’Neill became less involved with the company at the same time it started to run into trouble. In February 1991 Geostar filed for bankruptcy and its licenses were sold to Motorola for the Iridium satellite constellation project. Although the system was eventually replaced by GPS, O’Neill made significant advances in the field of position determination. O’Neill founded O’Neill Communications in Princeton in 1986. He introduced his Local Area Wireless Networking, or LAWN, system at the PC Expo in New York in 1989. The LAWN system allowed two computers to exchange messages over a range of a couple hundred feet at a cost of about $500 per node. O’Neill Communications went out of business in 1993; the LAWN technology was sold to Omnispread Communications. As of 2008, Omnispread continued to sell a variant of O’Neill’s LAWN system.[70] On November 18, 1991, O’Neill filed a patent application for a vactrain system. He called the company he wanted to form VSE International, for velocity, silence, and efficiency. However, the concept itself he called Magnetic Flight. The vehicles, instead of running on a pair of tracks, would be elevated using electromagnetic force by a single track within a tube (permanent magnets in the track, with variable magnets on the vehicle), and propelled by electromagnetic forces through tunnels. He estimated the trains could reach speeds of up to 2,500 mph (4,000 km/ h) — about five times faster than a jet airliner — if the air was evacuated from the tunnels.To obtain such speeds, the vehicle would accelerate for the first half of the trip, and then decelerate for the second half of the trip. The acceleration was planned to be a maximum of about one half of the force of gravity. O’Neill planned to build a network of stations connected by these tunnels, but he died two years before his first patent on it was granted.
Dr Geoffrey Keith Charles Pardoe OBE FREng FRAeS FBIS (2 November 1928 – 3 January 1996) was the Project Manager for the Blue Streak ballistic missile programme. He was also an advocate for British advanced science and technology, and involvement in space exploration, deploring (repeated) government negligence and its aborted technology programmes.
Dr Robert Charles Parkinson MBE (born 15 July 1941) is a British aerospace engineer that worked on many projects including HOTOL which he cooriginated with Alan Bond. He was the president of the British Interplanetary Society from 2009 – 2012.
John Whiteside “Jack” Parsons (born Marvel Whiteside Parsons; October 2, 1914 – June 17, 1952) was an American rocket engineer and rocket propulsion researcher, chemist, and Thelemite occultist. Associated with the California Institute of Technology (Caltech), Parsons was one of the principal founders of both the Jet Propulsion Laboratory (JPL) and the Aerojet Engineering Corporation. He invented the first rocket engine to use a castable, composite rocket propellant, and pioneered the advancement of both liquidfuel and solidfuel rockets.
Pedro Eleodoro Paulet Mostajo (July 2, 1874 – January 30, 1945) was a Peruvian inventor who allegedly in 1895 was the first person to build a liquid fuel rocket engine and, in 1900, the first person to build a modern rocket propulsion system. German V2 inventor Wernher von Braun considered Paulet one of the “fathers of aeronautics.” The National Air & Space Museum in Washington, D.C., has a small plaque honoring the memory of Paulet.
Jordi PuigSuari is a professor and aerospace technology developer. He is the coinventor of the CubeSat standard, and the cofounder of Tyvak Nano Satellite Systems.
Jesco Hans Heinrich Max Freiherr von Puttkamer (September 22, 1933 – December 27, 2012) was a GermanAmerican aerospace engineer and senior NASA manager from Leipzig.
Johann Schmidlap of Schorndorf was a 16th century Bavarian fireworks maker and rocket pioneer.
were then moved to a location near Garlock in the Mojave Desert in California. Jubb runs The Falcon Project from a home office in his parents’ house and the company supplies the MOD, United States military, and plans to build satellite launch vehicles. In a short documentary produced in 1998 for Channel 4 titled Raw Talent: The Rocket Scientist, Jubb stated that he built his first rocket at age five, “from a McDonald’s straw, a lightbulb holder and some household ingredients”. Although many media claims have been made about the altitudes reached by Jubb’s rockets, none have appeared on the list of altitude records held by the United Kingdom Rocketry Association. In November 2005, Jubb joined the Bloodhound SSC project. The Bloodhound is a jet and rocket powered car that was designed to break the land speed record by traveling at approximately 1,000 miles per hour (1,609 km/h). Jubb and The Falcon Project designed, built, and repeatedly tested their hybrid rocket engine that will produce an estimated 25,000 lbs of thrust, suitable for either Bloodhound SSC or Virgin Galactic’s SpaceShip Two. In addition, The Falcon Project Ltd completed and tested a full scale monopropellant thruster for subsonic testing of the vehicle. On 28 November 2010 Neil Armstrong visited the Bloodhound SSC headquarters and chatted with the team, including Jubb. This 3 October 2012 report was televised on the Bloodhound SSC hybrid rocket fabricated by The Falcon Project Ltd with Daniel Jubb as director, which was successfully tested in public at Newquay, GB. Due to escalating costs caused by control system delays, the hybrid rocket for Bloodhound will instead be developed by Nammo. On 10 June 2015, Jubb visited Stokesley School and spoke with Year 10 students extensively about Rocket Science and assisted them in fitting their own rockets with motors, which was a great success. Jubb has also been noted for his prominent moustache which earned him recognition from The Chap magazine.
Qian Xuesen or HsueShen Tsien 11 December 1911 – 31 October 2009) was a
Chinese engineer who contributed to aerodynamics and rocket science. Recruited from MIT, he joined Theodore von Karman’s group at Caltech, including the founding of the Jet Propulsion Laboratory.[1] Later he returned to China as Qian Xuesen and made important contributions to China’s missile and space program.
Simon “Si” Ramo (May 7, 1913 – June 27, 2016) was an American engineer, businessman, and author. He led development of microwave and missile technology and is sometimes known as the father of the intercontinental ballistic missile (ICBM). He also developed General Electric’s electron microscope. He has been partly responsible for the creation of two Fortune 500 companies, Ramo Wooldridge (TRW after 1958) and BunkerRamo (now part of Honeywell).
Tecwyn Roberts (10 October 1925 – 27 December 1988) was a Welshborn American spaceflight engineer who in the 1960s played important roles in designing the Mission Control Center at NASA’s Johnson Space Center in Houston, Texas and creating NASA’s worldwide tracking and communications network.
Milton William Rosen (July 25, 1915 – December 30, 2014) was a United States Navy engineer and project manager in the US space program between the end of World War II and the early days of the Apollo Program. He led development of the Viking and Vanguard rockets, and was influential in the critical decisions early in NASA’s history that led to the definition of the Saturn rockets, which were central to the eventual
success of the American Moon landing program. He died of prostate cancer in 2014.
Eugen Sänger (22 September 1905 – 10 February 1964) was an Austrian aerospace engineer best known for his contributions to lifting body and ramjet technology.
Helmut W. Schulz (1912 – 28 January 2006) was a German chemical engineer and professor at Columbia University known for his many works in disparate fields like nuclear physics, rocketry and wastetoenergy processes. He developed the process for separating uranium isotopes.
John Lanfear ScottScott (22 June 1934 – 12 December 2015) was a British mechanical and aerospace engineer. After graduating from the University of Birmingham, he joined Armstrong Siddeley Motors in 1955, becoming a hydrodynamicist at their Rocket Department. He worked there on Black Arrow, making important contributions to the fuel pump system. Later he helped to form, and worked at, Reaction Engines Limited until he retired in 2011. ScottScott married Pauline W. A. Cullen in 1955; they had two daughters and a son. He was the Chairman of the Coventry Branch, Rolls Royce Heritage Trust from November 2000 until May 2014.
Kazimierz Siemienowicz (Latin: Casimirus Siemienowicz, Lithuanian: Kazimieras Simonavičius, Polish: Kazimierz Siemienowicz, born c. 1600 – c. 1651), was a Polish–Lithuanian general of artillery, gunsmith, military engineer, and pioneer of rocketry. Born in the Grand Duchy of Lithuania, he served the armies of the Polish–Lithuanian Commonwealth and of Frederick Henry, Prince of Orange, a ruler of the Netherlands. No portrait or detailed biography of him has survived and much of his life is a subject of dispute.
Colonel Leslie Alfred Skinner LOM (April 21, 1900 – November 2, 1978) was an American rocket engineer. He played a leading role in the development of several rocket propelled weapons during World War II, notably the first shoulder fired missile system, the Bazooka.
Richard G. Smith was director of NASA’s John F. Kennedy Space Center from September 26, 1979 to August 2, 1986. Born in Durham, N.C., in 1929, Smith was educated in Alabama schools. After graduation from Decatur High School, he attended Florence State College and Auburn University. He received a bachelor’s degree in electrical engineering from Auburn in 1951. Smith became a member of the rocket research and development team at Redstone Arsenal, Alabama, in June 1951. He transferred to NASA in July 1960 when the Development Operations Division of the Army Ballistic Missile Agency became the nucleus for the establishment of the George C. Marshall Space Flight Center. Smith served in positions of increasing responsibility at the Marshall Center. He held various assignments in the former Guidance and Control Laboratory and in the Systems Engineering Office prior to being appointed deputy manager and later manager of the Saturn Program. In January 1974 Smith became director of science and engineering and served in that position until he was named deputy director of the Marshall Center in 1974. On August 15, 1978, Smith accepted a oneyear assignment as deputy associate administrator for Space Transportation Systems at NASA Headquarters, Washington, D.C. He served as director of the Skylab Task Force appointed by the NASA administrator to represent NASA preceding and following the reentry of Skylab. Smith was a member of the NASA Executive Development Education Panel, and he also served a threeyear term as a member of the Auburn Alumni Engineering Council. For his contributions to the Apollo Lunar Landing Program and the Skylab Program he received the NASA Medal for Exceptional Service in 1969 and the NASA Medal for Distinguished Service in 1973. In January 1980 he received NASA’s Outstanding Leadership Medal for his management of the Skylab Reentry Program. In September 1980 he was awarded the rank of meritorious executive in the Senior Executive Service. In June 1981, he was awarded an honorary doctorate of science degree by Florida Institute of Technology. He was also awarded an honorary doctorate of science degree by his Alma Mater, Auburn University, on December 9, 1983. Smith’s administration covered the completion of the Space Shuttle buildup, the launch of 25 shuttle missions and the beginning of the planning effort for the Space Station. Smith retired on Aug. 2, 1986.
Stephen Hector TaylorSmith (4 February 1891 – 15 February 1951) often known as Stephen Smith, was a pioneering Indian aerospace engineer who developed techniques in delivering mail by rocket. Unlike Friedrich Schmiedl, whom the Austrian Authorities banned from further experimenting, Smith was encouraged in his experiments by Indian Officials. In the tenyear span of his experiments (19341944), Smith made some 270 launches, including at least 80 rocket mail flights.
Johndale C. Solem (born 1941) is an American theoretical physicist and Fellow of Los Alamos National Laboratory. Solem has authored or co authored over 185 technical papers in many different scientific fields. He is known for his work on avoiding comet or asteroid collisions with Earth and on interstellar spacecraft propulsion.
Nuclear explosive propulsion for interplanetary space travel
Solem’s research on interplanetary travel culminated in his MEDUSA concept, a nuclear explosive propelled spacecraft for interplanetary space travel (1994b). Gregory Matloff said this was “a surprising [propulsion] concept which might greatly reduce spacecraft mass.” The concept inspired research and elaboration by the aerospace community. At the behest of NASA’s Breakthrough Propulsion Physics Project, Solem investigated whether a nuclear external pulsed plasma propelled (EPPP) interstellar probe could reach Alpha Centauri in 40 years, the average length of a scientist’s career. No scheme could be found, even involving elaborate staging, that could accelerate such a vehicle much beyond 1% the speed of light.
Grigori Aleksandrovich Tokaev October 13, 1909, died 23 November 2003) was a rocket scientist and long standing critic of Stalin’s USSR.
Konstantin Eduardovich Tsiolkovsky 17 September [O.S. 5 September] 1857 – 19 September 1935) was a Russian and Soviet rocket scientist and pioneer of the astronautic theory. Along with the French Robert EsnaultPelterie, the German Hermann Oberth and the American Robert H. Goddard, he is considered to be one of the founding fathers of modern rocketry and astronautics. His works later inspired leading Soviet rocket engineers such as Sergei Korolev and Valentin Glushko and contributed to the success of the Soviet space program. Tsiolkovsky spent most of his life in a log house on the outskirts of Kaluga, about 200 km (120 mi) southwest of
Moscow. A recluse by nature, his unusual habits made him seem bizarre to his fellow townsfolk. He was born in Izhevskoye (now in Spassky District, Ryazan Oblast), in the Russian Empire, to a middle class family. His father, Edward Tsiolkovsky (in Polish: Ciołkowski), was a Polishborn Russian Orthodox; his mother, Maria Ivanovna Yumasheva belonged to Russian nobility and was of mixed Volga Tatar and Russian origin. His father was successively a forester, teacher, and minor government official. At the age of 10, Konstantin caught scarlet fever and became hard of hearing. When he was 13, his mother died. He was not admitted to elementary schools because of his hearing problem, so he was self taught.[6] As a reclusive home schooled child, he passed much of his time by reading books and became interested in mathematics and physics. As a teenager, he began to contemplate the possibility of space travel. After falling behind in his studies, Tsiolkovsky spent three years attending a Moscow library where Russian cosmism proponent Nikolai Fyodorov worked. He later came to believe that colonizing space would lead to the perfection of the human race, with immortality and a carefree existence.
Additionally, inspired by the fiction of Jules Verne, Tsiolkovsky theorized many aspects of space travel and rocket propulsion. He is considered the father of spaceflight and the first person to conceive the space elevator, becoming inspired in 1895 by the newly constructed Eiffel Tower in Paris. Despite the youth’s growing knowledge of physics, his father was concerned that he would not be able to provide for himself financially as an adult and brought him back home at the age of 19 after learning that he was overworking himself and going hungry. Afterwards, Tsiolkovsky passed the teacher’s exam and went to work at a school in Borovsk near Moscow. He also met and married his wife Varvara Sokolova during this time. Despite being stuck in Kaluga, a small town far from major learning centers, Tsiolkovsky managed to make scientific discoveries on his own. The first two decades of the 20th century were marred by personal tragedy. Tsiolkovsky’s son Ignaty committed suicide in 1902, and in 1908 many of his accumulated papers were lost in a flood. In 1911, his daughter Lyubov was arrested for engaging in revolutionary activities. Tsiolkovsky stated that he developed the theory of rocketry only as a supplement to philosophical research on the subject. He wrote more than 400 works including approximately 90 published pieces on space travel and
related subjects. Among his works are designs for rockets with steering thrusters, multistage boosters, space stations, airlocks for exiting a spaceship into the vacuum of space, and closed cycle biological systems to provide food and oxygen for space colonies. Tsiolkovsky’s first scientific study dates back to 1880– 1881. He wrote a paper called “Theory of Gases,” in which he outlined the basis of the kinetic theory of gases, but after submitting it to the Russian Physico Chemical Society (RPCS), he was informed that his discoveries had already been made 25 years earlier. Undaunted, he pressed ahead with his second work, “The Mechanics of the Animal Organism”. It received favorable feedback, and Tsiolkovsky was made a member of the Society. Tsiolkovsky’s main works after 1884 dealt with four major areas: the scientific rationale for the allmetal balloon (airship), streamlined airplanes and trains, hovercraft, and rockets for interplanetary travel. In 1892, he was transferred to a new teaching post in Kaluga where he continued to experiment. During this period, Tsiolkovsky began working on a problem that would occupy much of his time during the coming years: an attempt to build an allmetal dirigible that could be expanded or shrunk in size. Tsiolkovsky developed the first aerodynamics laboratory in Russia in his apartment. In 1897, he built the first Russian wind tunnel with an open test section and developed a method of experimentation using it. In 1900, with a grant from the Academy of Sciences, he made a survey using models of the simplest shapes and determined the drag coefficients of the sphere, flat plates, cylinders, cones, and other bodies. Tsiolkovsky’s work in the field of aerodynamics was a source of ideas for Russian scientist Nikolay Zhukovsky, the father of modern aerodynamics and hydrodynamics. Tsiolkovsky described the airflow around bodies of different geometric shapes, but because the RPCS did not provide any financial support for this project, he was forced to pay for it largely out of his own pocket. Tsiolkovsky studied the mechanics of powered flying machines, which were designated “dirigibles” (the word “airship” had not yet been invented). Tsiolkovsky first proposed the idea of an allmetal dirigible and built a model of it. The first printed work on the airship was “A Controllable Metallic Balloon” (1892), in which he gave the scientific and technical rationale for the design of an airship with a metal sheath. Progressive for his time, Tsiolkovsky was not supported on the airship project, and the author was refused a grant to build the model. An appeal to the General Aviation Staff of the Russian army also had no success. In 1892, he turned to the new and unexplored field of heavierthan air aircraft. Tsiolkovsky’s idea was to build an airplane with a metal frame. In the article “An Airplane or a Birdlike (Aircraft) Flying Machine” (1894) are descriptions and drawings of a monoplane, which in its appearance and aerodynamics anticipated the design of aircraft that would be constructed 15 to 18 years later. In an Aviation Airplane, the wings have a thick profile with a rounded front edge and the fuselage is faired. But work on the airplane, as well as on the airship, did not receive recognition from the official representatives of Russian science, and Tsiolkovsky’s further research had neither monetary nor moral support. In 1914, he displayed his models of allmetal dirigibles at the Aeronautics Congress in St. Petersburg but met with a lukewarm response. Disappointed at this, Tsiolkovsky gave up on space and aeronautical problems with the onset of World War I and instead turned his attention to the problem of alleviating poverty. This occupied his time during the war years until the Russian Revolution in 1917. Starting in 1896, Tsiolkovsky systematically studied the theory of motion of rocket apparatus. Thoughts on the use of the rocket principle in the cosmos were expressed by him as early as 1883, and a rigorous theory of rocket propulsion was developed in 1896. Tsiolkovsky derived the formula, which he called the “formula of aviation”, establishing the relationship between:
• change in therocket’s speed(δV)
• exhaust velocity of the engine(ve)
• initial (M0) and final (M1) mass of the rocket δV=veln(M0/M1)
After writing out this equation, Tsiolkovsky recorded the date: 10 May 1897. In the same year, the formula for the motion of a body of variable mass was published in the thesis of the Russian mathematician I. V. Meshchersky (“Dynamics of a Point of Variable Mass,” I. V. Meshchersky, St. Petersburg, 1897). His most important work, published in 1903, was Exploration of Outer Space by Means of Rocket Devices. Tsiolkovsky calculated, using the Tsiolkovsky equation,:1 that the horizontal speed required for a minimal orbit around the Earth is 8,000 m/s (5 miles per second) and that this could be achieved by means of a multistage rocket fueled by liquid oxygen and liquid hydrogen. In the article “Exploration of Outer Space by Means of Rocket Devices”, it was proved for the first time that a rocket could perform space flight. In this article and its subsequent sequels (1911 and 1914), he developed some ideas of missiles and considered the use of liquid rocket engines. The outward appearance of Tsiolkovsky’s spacecraft design, published in 1903, was a basis for modern spaceship design. The design had a hull divided into 3 main sections. The pilot and copilot were in the first section, the second and third sections held the liquid oxygen and liquid hydrogen needed to fuel the spacecraft. However, the result of the first publication was not what Tsiolkovsky expected. No foreign scientists appreciated his research, which today is a major scientific discipline. In 1911 he published the second part of the work “Exploration of Outer Space by Means of Rocket Devices”. Here Tsiolkovsky evaluated the work needed to overcome the force of gravity, determined the speed needed to propel the device into the solar system (“escape velocity”), and examined calculation of flight time. The publication of this article made a splash in the scientific world, Tsiolkovsky found many friends among his fellow scientists. In 1926–1929, Tsiolkovsky solved the practical problem regarding the role played by rocket fuel in getting to escape velocity and leaving the Earth. He showed that the final speed of the rocket depends on the rate of gas flowing from it and on how the weight of the fuel relates to the weight of the empty rocket. Tsiolkovsky conceived a number of ideas that have been later used in rockets. They include: gas rudders (graphite) for controlling a rocket’s flight and changing the trajectory of its center of mass, the use of components of the fuel to cool the outer shell of the spacecraft (during re entry to Earth) and the walls of the combustion chamber and nozzle, a pump system for feeding the fuel components, the optimal descent trajectory of the spacecraft while returning from space, etc. In the field of rocket propellants, Tsiolkovsky studied a large number of different oxidizers and combustible fuels and recommended specific pairings: liquid oxygen and hydrogen, and oxygen with hydrocarbons. Tsiolkovsky did much fruitful work on the creation of the theory of jet aircraft, and invented his chart Gas Turbine Engine. In 1927 he published the theory and design of a train on an air cushion. He first proposed a “bottom of the retractable body” chassis. However, space flight and the airship were the main problems to which he devoted his life. Tsiolkovsky had been developing the idea of the hovercraft since 1921, publishing a fundamental paper on it in 1927, entitled “Air Resistance and the Express Train” (Russian: Сопротивление воздуха и скорый по́езд). In 1929, Tsiolkovsky proposed the construction of multistage rockets in his book Space Rocket Trains (Russian: Космические ракетные поезда). Tsiolkovsky championed the idea of the diversity of life in the universe and was the first theorist and advocate of human spaceflight. Tsiolkovsky never built a rocket; he apparently did not expect many of his theories to ever be implemented. Hearing problems did not prevent the scientist from having a good understanding of music, as outlined in his work “The Origin of Music and Its Essence.” Although Tsiolkovsky supported the Bolshevik Revolution, he did not particularly flourish under a communist system. Eager to promote science and technology, the new Soviet government elected him a member of the Socialist Academy in 1918. He worked as a high school mathematics teacher until retiring in 1920 at the age of 63. In 1921 he received a lifetime pension. Only late in his lifetime was Tsiolkovsky honored for his pioneering work. In particular, his support of eugenics made him politically unpopular. However, from the mid 1920s onwards the importance of his other work was acknowledged, and he was honoured for it and the Soviet state provided financial backing for his research. He was initially popularized in Soviet Russia in 19311932 mainly by two writers: Iakov Perel’man and Nikolai Rynin. Tsiolkovsky died in Kaluga on 19 September 1935 after undergoing an operation for stomach cancer. He bequeathed his life’s work to the Soviet state. Although many called his ideas impractical, Tsiolkovsky influenced later rocket scientists throughout Europe, like Wernher von Braun. Russian search teams at Peenemünde found a German translation of a book by Tsiolkovsky of which “almost every page…was embellished by von Braun’s comments and notes.” Leading Soviet rocketengine designer Valentin Glushko and rocket designer Sergey Korolev studied Tsiolkovsky’s works as youths, and both sought to turn Tsiolkovsky’s theories into reality. In particular, Korolev saw traveling to Mars as the more important priority, until in 1964 he decided to compete with the American Project Apollo for the moon. Tsiolkovsky wrote a book called The Will of the Universe. The Unknown Intelligence in 1928 in which he propounded a philosophy of panpsychism. He believed humans would eventually colonize the Milky Way galaxy. His thought preceded the Space Age by several decades, and some of what he foresaw in his imagination has come into being since his death. Tsiolkovsky also did not believe in traditional religious cosmology, but instead (and to the chagrin of the Soviet authorities) he believed in a cosmic being that governed humans as “marionettes, mechanical puppets, machines, movie characters”, thereby adhering to a mechanical view of the universe, which he believed would be controlled in the millennia to come through the power of human science and industry.
Air Commodore Władysław Józef ولوادیسیو—January 1980), usually referred to as W. J. M. Turowicz, was a Polish Pakistani aviator, military scientist and aeronautical engineer. Turowicz was the administrator of Pakistan’s Space and Upper Atmosphere Research Commission (SUPARCO) from 1967 to 1970. He was one of forty five Polish officers and airmen who joined RPAF on contract in the early fifties. After completion of his initial contract, Turowicz opted to stay on in Pakistan and continued to serve in PAF and later, SUPARCO. Turowicz made significant contributions to Pakistan’s missile/rocket program as a chief aeronautical engineer. In Pakistan, he remains highly respected as a scientist and noted aeronautical engineer.
Bob Twiggs is a consulting professor emeritus at Stanford University who is responsible, along with Jordi PuigSuari of California Polytechnic State University, for coinventing the CubeSat reference design for miniaturised satellites which became an Industry Standard for design and deployment of the satellites.
Stanisław Marcin Ulam 13 April 1909 – 13 May 1984) was a PolishAmerican mathematician. He participated in America’s Manhattan Project, originated the Teller–Ulam design of thermonuclear weapons, discovered the concept of cellular automaton, invented the Monte Carlo method of computation, and suggested nuclear pulse propulsion. In pure and applied mathematics, he proved some theorems and proposed several conjectures. Starting in 1955, Ulam and Frederick Reines considered nuclear propulsion of aircraft and rockets. This is an attractive possibility, because the nuclear energy per unit mass of fuel is a million times greater than that available from chemicals. From 1955 to 1972, their ideas were pursued during Project Rover, which explored the use of nuclear reactors to power rockets. In response to a question by Senator John O. Pastore at a congressional committee hearing on “Outer Space Propulsion by Nuclear Energy”, on January 22, 1958, Ulam replied that “the future as a whole of mankind is to some extent involved inexorably now with going outside the globe.” Ulam and C. J. Everett also proposed, in contrast to Rover’s continuous heating of rocket exhaust, to harness small nuclear explosions for propulsion. Project Orion was a study of this idea. It began in 1958 and ended in 1965, after the Partial Nuclear Test Ban Treaty of 1963 banned nuclear weapons tests in the atmosphere and in space. Work on this project was spearheaded by physicist Freeman Dyson, who commented on the decision to end Orion in his article, “Death of a Project”. Bradbury appointed Ulam and John H. Manley as research advisors to the laboratory director in 1957. These newly created positions were on the same administrative level as division leaders, and Ulam held his until he retired from Los Alamos. In this capacity, he was able to influence and guide programs in many divisions: theoretical, physics, chemistry, metallurgy, weapons, health, Rover, and others. In addition to these activities, Ulam continued to publish technical reports and research papers. One of these introduced the Fermi–Ulam model, an extension of Fermi’s theory of the acceleration of cosmic rays. Another, with Paul Stein and Mary Tsingou, titled “Quadratic Transformations”, was an early investigation of chaos theory and is considered the first published use of the phrase “chaotic behavior”.
Richard Antony Varvill (born 23 September 1961) is a British engineer, and the Chief Designer (Technical Director) at Reaction Engines Limited.
Wernher von braun(March 23, 1912 – June 16, 1977) was a German, later American, aerospace engineer[3] and space architect credited with inventing the V2 rocket for Nazi Germany and the Saturn V for the United States. He was the leading figure in the development of rocket technology in Germany and the father of rocket technology and space science in the United States.
Theodore von Kármán 11 May 1881 – 6 May 1963) was a HungarianAmerican mathematician, aerospace engineer, and physicist who was active primarily in the fields of aeronautics and astronautics. He is responsible for many key advances in aerodynamics, notably his work on supersonic and hypersonic airflow characterization. He is regarded as the outstanding aerodynamic theoretician of the twentieth century.
Mikhail Kuzmich Yangel (Russian: Михаил Кузьмич Янгель; November 7, 1911 – October 25, 1971), was a leading missile designer in the Soviet Union.
Friedrich Zander 11 August [O.S. 23 August] 1887 – 28 March 1933), was a Baltic German pioneer of rocketry and spaceflight in the Russian Empire and the Soviet Union. He designed the first liquidfueled rocket to be launched in the Soviet Union, GIRDX, and made many important theoretical contributions to the road to space.
Zhang Qingwei is a Chinese politician, business executive, and aerospace engineer. He is the Communist Party Secretary of Heilongjiang, former Governor of Hebei, and former chairman of the Commission for Science, Technology and Industry for National Defense (COSTIND). Prior to his government career he was president of China Aerospace Science and Technology Corporation (CASC) and chairman of Comac, an aerospace manufacturer.
Aleksandr Borisovich Zheleznyakov January 28, 1957 is a specialist in design and production of rocket and space systems. He is also a writer and journalist.
Robert Zubrin (born April 9, 1952) is an American aerospace engineer and author, best known for his advocacy of the manned exploration of Mars. He and his colleague at Martin Marietta, David Baker, were the driving force behind Mars Direct, a proposal intended to produce significant reductions in the cost and complexity of such a mission. The key idea was to use the Martian atmosphere to produce oxygen, water, and rocket propellant for the surface stay and return journey. A modified version of the plan was subsequently adopted by NASA as their “design reference mission”. He questions the delay and costtobenefit ratio of first establishing a base or outpost on an asteroid or another Project Apollo like return to the Moon, as neither would be able to provide all of its own oxygen, water, or energy; these resources are producible on Mars, and he expects people would be there thereafter.
Disappointed with the lack of interest from government in Mars exploration and after the success of his book The Case for Mars, as well as leadership experience at the National Space Society, Zubrin established the Mars Society in 1998. This is an international organization advocating a manned Mars mission as a goal, by private funding if possible. Robert Zubrin was born April 9, 1952. Zubrin holds a B.A. in Mathematics from the University of Rochester (1974), a M.S. in Nuclear Engineering (1984), a M.S. in Aeronautics and Astronautics (1986), and a Ph.D. in Nuclear Engineering (1992) — all from the University of Washington. He has developed a number of concepts for space propulsion and exploration, and is the author of over 200 technical and non technical papers and five books. He was a member of Lockheed Martin’s scenario development team charged with developing strategies for space exploration. He was also “a senior engineer with the Martin Marietta Astronautics company, working as one of its leaders in development of advanced concepts for interplanetary missions”. He is also President of both the Mars Society and Pioneer Astronautics, a private company that does research and development on innovative aerospace technologies. Zubrin is the co inventor on a U.S. design patent and a U.S. utility patent on a hybrid rocket/airplane, and on a U.S. utility patent on an oxygen supply system (see links below). He was awarded his first patent at age 20 in 1972 for Three Player Chess. His inventions also include the nuclear salt water rocket and coinventor (with Dana Andrews) of the magnetic sail. Zubrin is fellow at Center for Security Policy.
Famous Inventors
Archimedes (287 BCE – c. 212 BCE) Archimedes of Syracuse was an ancient Greek mathematician, physicist, engineer, inventor, and astronomer. Amongst other things he calculated pi and developed the Archimedes screw for lifting up water from mines or wells.
Cai Lun (50–121 CE), Chinese inventor of paper. Cai Lun was a Chinese political administrator credited with inventing modern paper and inventing the papermaking process. His invention included the use of raw materials such as bark, hemp, silk and fishing net. The sheets of fibre were suspended in water before removing for drying.
Leonardo Da Vinci (1452–1519) Italian artist, scientist and polymath. Da Vinci invented a huge range of machines and drew models that proved workable 3500 years later. These included prototype parachutes, tanks, flying machines and singlespan bridges. More practical inventions included an optical lens grinder and various hydraulic machines.
Galileo (1564–1642) Italian scientist. Galileo developed a powerful telescope and confirmed revolutionary theories about the nature of the world. Also developed an improved compass.
Sir Isaac Newton (1642–1726) English scientist. Newton invented the reflecting telescope. This greatly improved the capacity of telescopes and reduced optical distortion. Newton was also a great physicist and astronomer.
Thomas Savery (c. 1650–1715) English inventor. Savery patented one of the first steam engines which was pioneered for use in pumping water from mines. This original Savery steam engine was basic, but it was used as a starting point in later developments of the steam engine.
Thomas Newcomen (1664–1729) English inventor who created the first practical steam engine for pumping water from mines. He worked with Savery’s initial design, but significantly improved it, using atmospheric pressure which was safer and more effective for use in mines to remove water.
Jethro Tull (1674–1741) English agricultural entrepreneur. Tull invented the seed drill and horsedrawn hoe. The seed drill improved the efficiency of farming and led to increased yields. It was an important invention in the agricultural revolution which increased yields prior to the industrial revolution.
Abraham Darby (1678–1717) English Quaker, inventor and businessman. Darby developed a process for producing large quantities of pig iron from coke. Coke smelted iron was a crucial raw material in the industrial revolution.
John Harrison (1693–1776) English carpenter and clockmaker. He invented a device for measuring longitude at sea. This was a crucial invention to improve the safety of navigating the oceans.
Benjamin Franklin (1705–1790) American polymath who discovered electricity and invented the Franklin stove, the lightning rod and bifocals. Franklin was also an American statesman and an influential figure in the development of modern America.
William Cullen (1710–1790) Scottish physician and chemist. He is credited with inventing the basis for the first artificial refrigerator, although it took others to make his designs suitable for practical use.
John Wilkinson (1728–1808) English industrialist. John ‘Iron Mad’ Wilkinson developed the manufacture and use of cast iron. These precisionmade cast iron cylinders were important in steam engines.
Sir Richard Arkwright (1732–1792) English entrepreneur and ‘father of the industrial revolution.’ Arkwright was a leading pioneer of the spinning industry. He invented the spinning frame and was successful in using this in massscale factory production.
James Watt (1736–1819) Scottish inventor of the steam engine, which was suitable for use in trains. His invention of a separate condensing chamber greatly improved the efficiency of steam. It enabled the steam engine to be used for a greater range of purpose than just pumping water.
Alessandro Volta (1745–1827), Italian physicist, credited with inventing the battery. Volta invented the first electrochemical battery cell. It used zinc, copper and an electrolyte, such as sulphuric acid and water.
Sir Humphrey Davy (1778–1829) English inventor of the Davy lamp. The lamp could be used by miners in areas where methane gas existed because the design prevented a flame escaping the fine gauze.
Charles Babbage (1791–1871) English mathematician and inventor. Babbage created the first mechanical computer, which proved to be the prototype for future computers. Considered to be the ‘Father of Computers,’ despite not finishing a working model.
Michael Faraday (1791–1867) English scientist who helped convert electricity into a format that could be easily used. Faraday discovered benzene and also invented an early form of the Bunsen burner.
Samuel Morse (1791–1872) American inventor Morse used principles of Jackson’s electromagnet to develop a single telegraph wire. He also invented Morse code, a method of communicating via telegraph.
William Henry Fox Talbot (1800–1877) British Victorian pioneer of photography. He invented the first negative, which could make several prints. He is known for inventing the calotype process (using Silver Chloride) of taking photographs.
Louis Braille (1809–1852) French inventor. Louis Braille was blinded in a childhood accident. He developed the Braille system of reading for the blind. He also developed a musical Braille, for reading music scores.
Kirkpatrick Macmillan (1812–1878) Scottish inventor of the pedal bicycle. Kirkpatrick’s contribution was to make a rear wheel driven bicycle through the use of a chain, giving the basic design for the bicycle as we know it today.
James Clerk Maxwell (1831–1879) Scottish physicist and inventor. Maxwell invented the first process for producing colour photography. Maxwell was also considered one of the greatest physicists of the millennium.
Karl Benz (1844–1929), German inventor and businessman. Benz developed the petrolpowered car. In 1879, Benz received his first patent for a petrolpowered internal combustion engine, which made an automobile car practical. Benz also became a successful manufacturer.
Thomas Edison (1847–1931) American inventor who filed over 1,000 patents. He developed and innovated a wide range of products from the electric light bulb to the phonograph and motion picture camera. One of the greatest inventors of all time.
Alexander Bell (1847–1922) Scottish scientist credited with inventing the first practical telephone. Also worked on optical telecommunications, aeronautics and hydrofoils.
Nikola Tesla (1856–1943) American Physicist who invented fluorescent lighting, the Tesla coil, the induction motor, 3 phase electricity and AC electricity.
Rudolf Diesel (1858–1913), German inventor of the Diesel engine. Diesel sought to build an engine which had much greater efficiency. This led him to develop a dieselpowered combustion engine.
Édouard Michelin (1859–1940), French inventor of a pneumatic tire. John Dunlop invented the first practical pneumatic tyre in 1887. Michelin improved on this initial design to develop his own version in 1889.
Marie Curie (1867–1934) Polish born French chemist and physicist. Curie discovered Radium and helped make use of radiation and Xrays.
The Wright Brothers (1871–1948) American inventors who successfully designed, built and flew the first powered aircraft in 1903.
Alexander Fleming (1881–1955), Scottish scientist. Fleming discovered the antibiotic penicillin by accident from the mould Penicillium notatum in 1928.
John Logie Baird (1888–1946) Scottish inventor who invented the television and the first recording device.
Enrico Fermi (1901–1954) Italian scientist who developed the nuclear reactor. Fermi made important discoveries in induced radioactivity. He is considered the inventor of the nuclear reactor.
J. Robert Oppenheimer (1904–1967), United States – Atomic bomb. Oppenheimer was in charge of the Manhattan project which led to the creation of the first atomic bomb, later dropped in Japan. He later campaigned against his own invention.
Alan Turing (1912–1954) English 20th century mathematician, pioneer of computer science. He developed the Turing machine, capable of automating processes. It could be adapted to simulate the logic of any computer algorithm.
Robert Noyce (1927–1990) American 20thcentury electrical engineer. Along with Jack Kilby, he invented the microchip or integrated circuit. He filed for a patent in 1959. The microchip fueled the computer revolution.
James Dyson (1947– ) British entrepreneur. He developed the bagless vacuum cleaner using Dual Cyclone action. His Dyson company has also invented revolutionary hand dryers.
Tim BernersLee (1955– ) British computer scientist. Tim BernersLee is credited with inventing the World Wide Web, which enabled the internet to display websites viewable on internet browsers. He developed the http:// protocol for the internet and made the world wide web freely available.
Steve Jobs (1955–2011) American entrepreneur and developer. Jobs helped revolutionise personal computer devices with the iPod, iPad, Macbook and iPhone. He is credited with inventing the new wave of handheld personal computer devices.
Biologists
Hippocrates (c.460 BC
c.370 BC) Nationality: Greek Known for: The Father of Western Medicine Wrote On the Physician, a guide outlining how a physician should treat their patients. Also authored the Hippocratic Oath, which doctors still use today as part of their practice.

Aristotle (384 BC322
BC) Nationality: Greek Known for: Classified organisms into a “Ladder of Life” Aristotle was the first to categorize animal life based on their characteristics. He separated them into two categories: “animals with blood” and “animals without blood.” Many of his theories lasted all the way until the 19th century.

Galen (c.129c.200216)
Nationality: Greek Known for: First to introduce medicinal experimentation

Biologists of the Middle Ages (15001700)
Andreas Vesalius
(15141564) Nationality: Brabantian

Anton van
Leeuwenhoek (16321723) Nationality: Dutch Known for: The Father of Microbiology

Robert Hooke
(16351703) Nationality: English Known for: Coined the term “cell”

Biologists of the 1700s
Joseph Priestley
(17331804) Nationality: English Known for: Believed to have discovered oxygen Priestley is one of the men believed to have discovered oxygen. He also invented soda water by dissolving heavy gas in water. He won a medal in 1773 from the Royal Society for this discovery. He was also the first to observe photosynthesis.

Antoine Lavoisier
(17431794) Nationality: French Known for: Observing metabolism

Edward Jenner
(17491823) Nationality: English Known for: Created the first effective vaccine for smallpox Developed the first experimental vaccine which was used to treat smallpox. He also coined the term “vaccination” and is often referred to as the “father of immunology.” Jenner also helped establish what is now the Royal Society of Medicine.

Biologists of the 1800s
Alexander Von
Humboldt (17691859) known for humboltian science. He helped establish the field of biogeography, which is the study of ecosystems and species throughout geological time and space Humboldtian science is also named for him, which is the belief that the most modern and accurate resources should be used for collecting data. 
Claude Bernard
(18131878) Nationality: French Known for: Blind experimental method for objective results By suggesting using blind experiments to conduct studies, Bernard helped researchers get more objective results to their experiments. He also did studies on the pancreas gland, the liver, and parts of the body’s nervous system.

Gregor Mendel
(18221884) Nationality: German Known for: Plant hybridizations and genetics Mendel worked with plants, peas, and honeybees to test his theories regarding genetics. He is credited with being the founder of the science of genetics and discovering a set of laws about genetic patterns, now called the Mendelian inheritance.

Louis Pasteur
(18221895) Nationality: French Known for: Created the process of pasteurization for treating milk and wine Performed experiments that supported the germ theory of disease, which stated that diseases are caused by microorganisms. He also cofounded the field of microbiology and created vaccines for anthrax and rabies.

Joseph Lister (18271912)
Nationality: British
Known for: Using antiseptics for cleaning and sterilizing wounds
As a professor of surgery. Lister introduced the idea of sterilizing surgical instruments with carbolic acid to help prevent infection. He came to be known as the “father of antisepsis” due to his work. He also developed better methods for mastectomies and repairing kneecaps.
Biologists of the 1900s
Ernst Mayr (19042005)
Nationality: German Known for: The Darwin of the 20th Century In an attempt to solve the “species problem” of Darwin’s work, Mayr published Systematics and the Origin of Species to explain his ideas regarding evolutionary biology. His work and findings influenced future theories, such as the theory of punctuated equilibrium.

Erwin Chargaff
(19052002) Nationality: Austrian Known for: Chargaff’s rules regarding DNA structure Chargaff is known mainly for discovering two rules related to the DNA structure and its double helix formation. He found that certain substances within the DNA structure are equal to other substances. He also found that the DNA composition varies from one species to another.

Rachel Carson
(19071964) Nationality: American Known for: Warning the public about the dangers of pesticides Marine biologist whose work helped lead to the creation of the Environmental Protection Agency. Carson published several books about sea life in her early career, but later helped change governmental policies regarding the use of certain pesticides.

biochemists
 John Jacob Abel, (18571938) American biochemist and pharmacologist. He founded and chaired the first department of pharmacology in the United States at the University of Michigan.
 John Abelson, (b. 1938) American biologist with expertise in biophysics, biochemistry, and genetics. He was a professor at the California Institute of Technology (Caltech).
 Gary Ackers, (19392011) American Professor of Biochemistry and Molecular Biophysics at Washington University in St. Louis.
 Julius Adler, (b. 1930) American Professor of biochemistry and genetics at the University of Wisconsin–Madison.
 David Agard, American Professor of Biochemistry and Biophysics at the University of California, San Francisco. Member of the National Academy of Sciences.
 Natalie Ahn, Professor of Chemistry and Biochemistry at the University of Colorado at Boulder.
 Bruce Alberts, (born 1938) American biochemist known for his work in science public policy and as an original author of Molecular Biology of the Cell. Alberts, noted particularly for his study of the protein complexes which enable chromosome replication when living cells divide.
 Denis Alexander, (b. 1945), Emeritus Director of the Faraday Institute for Science and Religion at St Edmund’s College, Cambridge. Open Scholar at Oxford, where he studied Biochemistry. He studied for a PhD in Neurochemistry at the Institute of Psychiatry.
 Richard Amasino, Professor of biochemistry and genetics at the University of WisconsinMadison. Member of the National Academy of Sciences and was awarded the McKnight Foundation Individual Research Award in Plant Biology in 1986.
 Bruce Ames, (b. 1928) Professor of Biochemistry and Molecular Biology at the University of California, Berkeley. Awarded the National Medal of Science and is the inventor of the Ames test.
 John E. Amoore, British, Biochemist who postulated the stereochemical theory of olfaction in 1952.
 Rudolph John Anderson, (18791961) American biochemist, graduated with a Ph.D. from Cornell University Medical College.
 Thomas F. Anderson, (19111991) American biophysical chemist and geneticist. Elected to the National Academy of Sciences in 1964.
 Mortimer Louis Anson, (19011968), American biochemist famous for the advancement in the field of Protein Chemistry.
 Judy Armitage, British professor of molecular and cellular biochemistry at the University of Oxford.
 Gilbert Ashwell, (19162014), American biochemist known for isolating the first cell receptor.
 Isaac Asimov, (19201992), Russianborn American science fiction writer and professor of biochemistry at Boston University
 William Astbury, (18981961), British, pioneer in applying Xray crystallography to biological molecules such as proteins
 Milo Aukerman, (b. 1963) American biochemist best known for being the lead singer of the punk band the Descendents.
 Werner Emmanuel Bachmann (19011951), American chemist, studied physical organic chemistry and organic synthesis. Considered a pioneer in steroid synthesis.
 David Baker (born 1962) American biochemist and computational biologist who studies methods to predict and design the threedimensional structures of proteins. He is a Professor of Biochemistry at the University of Washington.
 Tania A. Baker, American biochemist, Professor of Biology at the Massachusetts Institute of Technology and member of the National Academy of Science.
 Clinton Ballou (b. 1923), Professor Emeritus of biochemistry at the University of California, Berkeley. He served as an editorial board of the Journal of Biological Chemistry. Member of the National Academy of Sciences.
 Horace Barker (19072000), American biochemist and microbiologist. Awarded his Ph.D. from Stanford University in 1933.
 David Bartel, Professor of Biology at the Massachusetts Institute of Technology, Member of the Whitehead Institute.
 Paul Baskis, American biochemist.
 Bonnie Bassler (b. 1962), American molecular biologist and Professor at Princeton University.
 Philip A. Beachy (b. 1958), Ernest and Amelia Gallo Professor at Stanford University School of Medicine.
 Jon Beckwith (b. 1935), American microbiologist and geneticist. Professor of the Department of Microbiology and Molecular Genetics at Harvard Medical School.
 Lorena S. Beese, Professor of Biochemistry at Duke University.
 Michael Behe (b. 1952), American biochemist, author, and intelligent design (ID) advocate. Professor of biochemistry at Lehigh University in Pennsylvania and as a senior fellow of the Discovery Institute‘s Center for Science and Culture.
 Helmut Beinert (19132007), German bornAmerican professor in the Biochemistry Department at the University of Wisconsin–Madison.
 Marlene Belfort (b. 1945), American biochemist and professor at the Wadsworth Center at the New York State Department of Health.
 Boris Pavlovich Belousov (1893–1970), USSR, chemist/biophysicist, BelousovZhabotinsky reaction.
 Paul Berg (born 1926) American biochemist who was awarded the Nobel Prize in Chemistry in 1980.
 Helen M. Berman, Board of Governors Professor of Chemistry and Chemical Biology at Rutgers University.
 Klaus Biemann (b. 1926), Professor Emeritus of chemistry at the Massachusetts Institute of Technology.
 Ethel Ronzoni Bishop (18901975), American biochemist and physiologist. Awarded her Ph.D. from the University of Wisconsin in 1923.
 Pamela J. Bjorkman (b. 1956), American biochemist and Max Delbrück Professor of Biology at the California Institute of Technology.
 Konrad Emil Bloch (19122000), GermanAmerican, 1964 Nobel Prize in Physiology or Medicine.
 Elkan Blout (19192006), Professor of biochemistry at Harvard University. Awarded the National Medal of Science in 1990.
 Aaron Bodansky (18871960), Russianborn American biochemist specializing in the area calcium metabolism. Earned his Ph.D. from Cornell University in 1921.
 Paul D. Boyer (born 1918), American, studies on ATP synthase, won the Nobel Prize in Chemistry in 1997.
 Harold C. Bradley (18781976), Professor in biochemistry at the University of Wisconsin.
 Roscoe Brady (b. 1923), American biochemist, Earned his M.D. from Harvard Medical School in 1947. Member of the National Academy of Sciences.
 Kenneth Breslauer, Linus C. Pauling professor of Chemistry and Chemical Biology at Rutgers University.
 Anne Briscoe (19182014), American biochemist and activist. Earned her Ph.D. from Yale University in 1949.
 Bernard Brodie (19071989), Leading researcher in the field of pharmacology. Awarded the Distinguished Service Award of the Department of Health, Education and Welfare in 1958 and the National Medal of Science in 1968.
 Adrian John Brown (18521920), British, pioneer in enzyme kinetics
 Patrick O. Brown (b. 1954), Professor in the Department of Biochemistry at Stanford University.
 Thomas Bruice, Professor of chemistry and biochemistry at University of California, Santa Barbara. Member of the National Academy of Sciences.
 John Buchanan, Professor of biochemistry at the Massachusetts Institute of Technology. Earned his Ph.D. from Harvard University in 1943.
 Eduard Buchner (18601917), German, 1907 Nobel Prize in Chemistry see fermentation (biochemistry)
 Dean Burk (19041988), American, codiscoverer of biotin.
 Robert H. Burris (19142010), Professor in the Biochemistry Department at the University of WisconsinMadison. Member of the National Academy of Sciences. Was awarded the National Medal of Science in 1979.
 David S. Cafiso, (b. 1952) American biochemist and a Professor of Chemistry at the University of Virginia.
 T. Colin Campbell, (b. 1934) Professor Emeritus of Nutritional Biochemistry at Cornell University.
 David E. Cane, (b. 1944) Professor of Chemistry and Professor of Biochemistry at Brown University. Earned his PhD at Harvard University in 1971.
 Lewis C. Cantley, (b. 1949) Professor in the Departments of Systems Biology and Medicine at Harvard Medical School.
 John Carbon, Professor Emeritus of molecular and cellular biology at the University of California, Santa Barbara.
 H. E. Carter, (19102007) American biochemist, Earned PhD in 1934 in organic chemistry from the University of Illinois.
 Thomas Cech, (b. 1947) President of Howard Hughes Medical Institute and was awarded the 1989 Nobel prize in chemistry along with Sidney Altman.
 Howard Cedar, (b. 1943) Israeli American biochemist, awarded the Israel Prize in Biology in 1999.
 Michael Chamberlin (b. 1937) Professor Emeritus of biochemistry and molecular biology at University of California, Berkeley. Member of the United States National Academy of Sciences.
 Britton Chance, (19132010), Professor Emeritus of Biochemistry and Biophysics. Has a PhD in Physical Chemistry and also a PhD in Biology/Physiology. Also earned a Gold Metal in sailing from the 1952 Summer Olympics.
 Christopher Chang, (b. 1974) Professor of chemistry at the University of California, Berkeley.
 Michelle Chang, (b. 1977)
 Emmett Chappelle, (b. 1925) Biochemist inducted into the National Inventors Hall of Fame for his work on Bioluminescence.
 Erwin Chargaff, (19052002) Austrian biochemist known for Chargaff’s rules.
 Martha Chase, (19272003) American geneticist, earned her PhD from the University of Southern California.
 Zhijian James Chen, Chinese American biochemist and Professor in the Department of Molecular Biology at University of Texas Southwestern Medical Center.
 Gilbert Chu, Professor of Medicine and Biochemistry at the Stanford Medical School.
 Paul Chun, Professor emeritus at the University of Florida.
 George M. Church, (b. 1954) Professor of Genetics at Harvard Medical School and Professor of Health Sciences and Technology at Harvard University and MIT.
 Steven Clarke, (b. 1949)
 W. Wallace Cleland, (19302013)
 G. Marius Clore, (b. 1955) American biochemist, chemist and biophysicist, National Institutes of Health Distinguished Investigator and Member of the United States National Academy of Science. Foundational work in threedimensional protein and nucleic acid structure determination by nuclear magnetic resonance spectroscopy.
 Philip Cohen, (born 1945)
 Edwin Joseph Cohn, (18921953)
 Mildred Cohn, (19132009)
 Robert Corey, (18971971), American, codiscoverer of the alpha helix and beta sheet
 Carl Ferdinand Cori, (18961984), American, 1947 Nobel Prize in Physiology or Medicine, glycogen research.
 Gerty Cori, (18961957), American, 1947 Nobel Prize in Physiology or Medicine, glycogen research.
 Shirley Corriher, (b. 1935)
 Peter Coveney, UK, Computational molecular biology specialist.
 Nicholas R. Cozzarelli, (19382006)
 Gerald Crabtree, (b. 1946)
 Elizabeth A. Craig,
 Margaret Crane,
 Robert K. Crane, (19192010), American, discovered sodiumglucose cotransport.
 Francis Crick, (19162004), British, discovered the double helical structure of DNA.
 Lourdes J. Cruz,
 Pedro Cuatrecasas, (b. 1936)
 Richard D. Cummings,
 David Cushman, (19392000)
 Valerie Daggett
 John Call Dalton (18251889)
 John W. Daly (19332008)
 Marie Maynard Daly (19212003)
 Carl Peter Henrik Dam (18951976), Danish, 1943 Nobel Prize in Physiology or Medicine
 Robert B. Darnell (b. 1957),
 Marguerite Davis (b. 1887),
 Ronald W. Davis (b. 1941),
 Margaret Oakley Dayhoff (19251983),
 Michael W. Deem
 William DeGrado
 Hector DeLuca
 Pierre De Meyts (1944), Belgian physician and biochemist, 2002 Christophe Plantin Prize, Belgium
 Willey Glover Denis (18791929),
 Herbert C. Dessauer (19212013),
 Revaz Dogonadze (19311985), Georgian, Coauthor of the quantummechanical model of Enzyme Catalysis
 Edward Adelbert Doisy (18931986),
 Ford Doolittle (b. 1942),
 Jonathan Dordick (b. 1959),
 Ralph Dorfman (19111985)
 Jennifer Doudna,
 Alexander Dounce (19091997),
 Gideon Dreyfuss,
 Jack Cecil Drummond FRS (18911952), isolation of Vitamin A, wartime advisor on nutrition
 Christian de Duve, (19172013), Britishborn Belgian, 1974 Nobel Prize for Physiology or Medicine
 Richard H. Ebright, American molecular biologist and Professor of Chemistry and Chemical Biology at Rutgers University.
 John Tileston Edsall (19022002)
 Konstantin Efetov, (b. 1958) Ukrainian biochemist.
 Gertrude B. Elion (19181999), American biochemist and pharmacologist. Recipient of the Nobel Prize in Physiology or Medicine and is a member of the National Inventors Hall of Fame.
 Terry Elton, American biochemist, earned his PhD in Biochemistry from Washington State University.
 Conrad Elvehjem (19011962), American biochemist specializing in nutrition.
 Gladys Anderson Emerson (19031984), American historian, biochemist and nutritionist.
 Akira Endo, statins
 Donald Engelman, cancer research
 Earl Evans (19101999),
 Richard D. Feinman (b. 1940) Professor of biochemistry and medical researcher at SUNY Downstate Medical Center.
 David Sidney Feingold (b. 1922) American biochemist
 John D. Ferry, (born 1912)
 Edmond H. Fischer (b. 1920) Swiss American biochemist awarded the Nobel Prize in Physiology or Medicine.
 Louis B. Flexner (19021996), American biochemist.
 Otto Folin (18671934)
 Karl August Folkers (19061997), American biochemist awarded the National Medal of Science.
 Bent Formby
 Sidney W. Fox (19121998)
 Heinz FraenkelConrat (19101999), German/US, virus research.
 Rosalind Franklin, (19201958), Xray crystallographer who helped determine the structure of DNA
 Perry A. Frey (b. 1935) Professor emeritus of biochemistry at the University of Wisconsin–Madison.
 Irwin Fridovich (b. 1929) American biochemist.
 Joseph S. Fruton, (19122007)
 Kazimierz Funk, (18841967), Polish, see Vitamin
 Robert F. Furchgott (19162009), American biochemist awarded the Nobel Prize in Physiology or Medicine.
 Elmer L. Gaden
 Alberto Granado, (19222011) Argentine–Cuban biochemist, doctor, writer, and scientist. Best known for being friends with Che Guevara.
 Merrill Garnett, (b. 1931) Biochemist and cancer researcher.
 Michael H. Gelb, (b. 1957)
 Susan Gerbi, (b. 1944) Professor of Biochemistry and a professor of biology at Brown University.
 Jonathan Gershenzon
 William John Gies, (18721956)
 Walter Gilbert, (b. 1932) Biochemist, awarded the Nobel Prize in Chemistry.
 Martin Glennie, (born 1956) British, developed anticancer therapeutic chiLOB7/4.
 Edward D. Goldberg, (19212008)
 Joseph L. Goldstein, (b. 1940) Biochemist awarded the Nobel Prize in Physiology or Medicine.
 Eugene Goldwasser, (19222010)
 Michael M. Gottesman, (b. 1946) American biochemist.
 Sam Granick, (19091977) American biochemist and member of the United States National Academy of Sciences.
 David E. Green, (19101983) pioneer in the study of enzymes, particularly those involved in oxidative phosphorylation.
 Lewis Joel Greene, (b. 1934) American Brazilian biochemist
 Walter Greiling, (19001986), German, worked in the field of agricultural microbiology.
 Mark Griep, (b. 1959), Professor of chemistry at the University of NebraskaLincoln.
 Frederick Griffith, (18791941), British, discovered that DNA carried hereditary information.
 Charles Grisham, Professor of chemistry at the University of Virginia.
 KunLiang Guan, (b. 1963)
 F. Peter Guengerich, Professor of biochemistry and the director of the Center in Molecular Toxicology at Vanderbilt University.
 Irwin Gunsalus, (19122008) American biochemist who discovered lipoic acid.
 John Scott Haldane, (18601936), British, physiologist.
 Dorothy Hodgkin, (19101994), British, founder of protein crystallography and Nobel Prize winner
 Frederick Gowland Hopkins, (18611947), British, Nobel Prizewinner for the discovery of vitamins
 Arthur Harden, (18651940), British, awarded a Nobel prize for studies on the enzymes of fermentation
 Wayne L. Hubbell, (born 1943), American, biochemistpioneer of sitedirected spin labeling
 Max Henius, (18591935) DanishAmerican Biochemist who specialized in the fermentation processes.
 Harvey Itano (19202010)
 Zheng Ji, (19002010), Reputed to be the world’s oldest professor and the founder of modern nutrition science in China.
 Tracy L. Johnson, Biochemist, Cell and Molecular Biologist, HHMI Professor
 Herman Kalckar, (19081991), Danish, early work on cellular respiration, nucleotide metabolism and galactose metabolism.
 Sir Bernard Katz (19112003), Germanborn, 1970 Nobel Prize in physiology or medicine for work on nerve biochemistry and the pineal gland.
 Stuart Alan Kauffman, (born 1939), Professor of Biochemistry and Biophysics
 John Kendrew, (19171997), British. Nobel Prize in Chemistry in 1962 for determining the first crystal structure of a protein, myoglobin.
 Sir Ernest Kennaway, (18811958), British. Early work on carcinogenic effects of hydrocarbons
 Aila Keto, (born 1943) President of the Rainforest Conservation Society in Queensland, Australia, now known as the Australia Rainforest Conservation Society. Studied biochemistry at the University of Queensland.
 Antony Kidman, (19382014), Australian biochemist earned his Ph.D on an American Cancer Society Scholarship from the University of Hawaii. Best known for being the father of Academy Awardwinning actress Nicole Kidman.
 Charles Glen King (18961988) was an American biochemist who was a pioneer in the field of nutrition research.
 Arthur Kornberg, (19182007) American biochemist, won the Nobel Prize in 1959 for discovery of DNA polymerase.
 Sir Hans Kornberg, (born 1928), British. Microbial biochemistry
 Roger D. Kornberg, American biochemist, won the Nobel Prize in 2006 for studies on RNA polymerase.
 Thomas B. Kornberg, American biochemist
 Ernst T. Krebs, Jr. (19111996). Promoter of the ineffective cancer cures laetrile and pangamic acid
 Sir Hans Adolf Krebs, (19001981), German, 1953 Nobel Prize in Physiology or Medicine see Krebs cycle
 Marc Lacroix (biochemist), (b. 1963), Belgian.
 David Lester (19161990), American biochemist who did extensive studies of alcoholism and was a professor at Rutgers University.
 Phoebus Levene, (18691940), Russian, discovered that DNA was composed of nucleobases and phosphate.
 Choh Hao Li (19131987) Known for discovering and synthesizing the human pituitary growth hormone.
 John James Rickard Macleod, (18761935), Scottish biochemist and physiologist, 1923 Nobel Prize in Physiology or Medicine, discovery of Insulin.
 Thaddeus Mann, (19081993), British reproductive biologist.
 Harden M. McConnell, (born 1927) American biochemist
 Maude Menten, (18791960) Canadian, early work on enzyme kinetics.
 Friedrich Miescher, (18441895) first scientist to isolate DNA
 Peter D. Mitchell, (19201992) British, 1978 Nobel Prize in Chemistry
 Leonor Michaelis, (18751949) German, early work on enzyme kinetics.
 César Milstein, (19272002), Argentine biochemist in the field of antibody research. Shared the Nobel Prize in Physiology or Medicine in 1984 with Niels K. Jerne and Georges Köhler.
 Jacques Monod, (19101976), French, 1965 Nobel Prize in Physiology or Medicine
 Kary Mullis, (born 1944), American, 1993 Nobel Prize in Chemistry see Polymerase chain reaction
 Elmer Verner McCollum (18791967) codiscovered Vitamins A and D and their benefits
 David Nachmansohn, (18991983), German, responsible for elucidating the role of phosphocreatine in energy production in the muscles.
 Joseph Needham, (19001995), British, studied the history of Chinese science
 Carl Neuberg, (18771956), German, pioneer in the study of metabolism.
 Marshall Warren Nirenberg, (born 1927), American, winner of the 1968 Nobel Prize in Physiology or Medicine
 Paul Nurse, (born 1949), British, awarded a Nobel prize for studies on the control of the cell cycle
 Eva J. Neer, (19372000), American Scientist, awarded the American Heart Association’s Basic Research Prize 1997, also the FASEB Excellence in Science Award in 1998 for research on Gproteins cell biology
 Frank Olson, (19101953), American, nonconsenting subject of CIA MKULTRA
 Alexander Oparin, (18941980) Soviet biochemist notable for his untested theories about the origin of life.
 Mary Jane Osborn (born 1927), American lipopolysaccharide researcher
 Jakub Karol Parnas, (18841949), Polish – Soviet, major contributor to the discovery of glycolysis
 Linus Pauling, (19011994) American, 1954 Nobel Prize in Chemistry
 Louis Pasteur, (18221895), French, Pioneer in microbiology and stereochemistry
 Max Perutz, (19142002), British, Nobel Prize in Chemistry in 1962 for solving the crystal structure of hemoglobin
 Samuel Victor Perry (19182009), British, pioneer in muscle research
 David Andrew Phoenix, (Born 1966), British, Structurefunction relationships of amphiphilic peptides
 Judah Hirsch Quastel, (18991987), BritishCanadian, neurochemistry, soil metabolism, cell metabolism, and cancer.
 R. Rajalakshmi (19262007), Indian nutritionist and biochemist
 David Rittenberg, (19061970), US, pioneer in the use of radioactive tracers in molecules
 Jane S. Richardson, (1941 ), US, developer of the ribbon diagram
 Frederick Sanger (19182013), two Nobel prizes for DNA sequencing and protein sequencing.
 Rudolph Schoenheimer (18981941), German/US, pioneer of radioactive tagging of molecules
 Anatoly Sharpenak, (18951969), Russian, biochemist.
 Alexander Shulgin, (Born 1925), Russian/American pharmacologist, popularized MDMA in America, and work with various psychoactive drugs
 Karl Slotta, (18951987), German/US, biochemist pioneer in study of progesterone and antivenom.
 Olav Aasmund Smidsrød (b. 1936) Norwegian biochemist
 Donald F. Steiner, (19302014), American biochemist who made ground breaking discoveries in the treatment of diabetes
 Audrey Stevens, (19322010), codiscoverer of RNA polymerase
 Amanda Swart, South African biochemist known for her research on rooibos
 Arne Tiselius, (1902–1971), Nobel laureate, developed protein electrophoresis.
 Angela Vincent, (born ?), British, Autoimmune and genetic disorders.
 Frederic Vester, (19252003), German, Author and ecologist.
 John Craig Venter, (born 1946), American, Human Genome Project.
 John E. Walker, (b. 1941), British biochemist. Awarded
 Selman Waksman, (18881973), Russian, biochemist.
 Christopher T. Walsh, Professor of biological chemistry and pharmacology at Harvard Medical School.
 James C. Wang, (b. 1938), Chineseborn American biochemist and biologist. Professor of biochemistry and molecular biology at Harvard University. Known for the discovery of topoisomerases.
 Xiaodong Wang, (b. 1963), Chineseborn American biochemist best known for his work with cytochrome c. Member of United States National Academy of Sciences and the Howard Hughes Medical Institute.
 Lewis W. Wannamaker, (19241983), American biochemist and was a member of the Institute of Medicine of the National Academy of Sciences.
 Arieh Warshel, (b. 1940), IsraeliAmerican biochemist and biophysicist. Awarded the Nobel Prize in Chemistry in 2013.
 James D. Watson, (born 1928), American, discovered the double helical structure of DNA
 Samuel Weiss, Canadian neurobiologist. Studied Biochemistry at McGill University.
 Karl Günther Weitzel, (19151984) Founder of the first university degree program of biochemistry in Germany.
 Harold Dadford West, (19041974), American biochemist known for the first to synthesize threonine.
 William T. Wickner, (b. 1946), Professor of Biochemistry at Dartmouth Medical School.
 Maurice Wilkins, (19162004), British, discovered the double helical structure of DNA
 Allan Charles Wilson, (19341991), Professor of Biochemistry at the University of California, Berkeley, a pioneer in the use of molecular approaches to understand evolutionary change and reconstruct phylogenies, and a revolutionary contributor to the study of human evolution.
 Friedrich Wöhler, (18101882), German, chemist.
 Felisa WolfeSimon, American microbial geobiologist and biogeochemist. Member of the NASA Astrobiology Institute.
 Richard Wolfenden, (b. 1935), Professor of chemistry, biochemistry and biophysics at the University of North Carolina at Chapel Hill.
Robert woodward— synthesized vitamin b12, cholesterol, chlorophyl, and many more
molecules
Hang Yin, (b. 1976), Professor at the Department of Chemistry and Biochemistry and the BioFrontiers Institute at
the University of Colorado Boulder.
 Donald Zilversmit, (19192010), Dutchborn American nutritional biochemist. Professor at Cornell University and member of the National Academy of Sciences.
geneticists
 Dagfinn Aarskog (1928–2014), Norwegian pediatrician and geneticist, described Aarskog–Scott syndrome
 Jon Aase (born 1936), US dysmorphologist, described Aase syndrome, expert on fetal alcohol syndrome
 John Abelson (born c. 1939), US biochemist, studies of machinery and mechanism of RNA splicing
 Susan L. Ackerman, US neurogeneticist, genes controlling brain development and neuron survival
 Jerry Adams (born 1940), US molecular biologist in Australia, hematopoietic genetics and cancer
 Bruce Alberts (born 1938), US biochemist, phage worker, studied DNA replication and cell division
 William Allan (1881–1943), US country doctor, pioneered human genetics
 C. David Allis (born 1951), US biologist with a fascination for chromatin
 Robin C. Allshire (born 1960), UKbased Irish Molecular Biologist/Geneticist expert in formation of heterochromatin and centromeres
 CarlHenry Alström (1907–1993), Swedish psychiatrist, described genetic disease: Alström syndrome
 Sidney Altman (born 1939), CanadianUS biophysicist who won Nobel Prize for catalytic functions of RNA
 Cecil A. Alport (1880–1959), UK internist, identified Alport syndrome (hereditary nephritis and deafness)
 David Altshuler (born c. 1965), US endocrinologist and geneticist, the genetics of type 2 diabetes
 Bruce Ames (born 1928), US molecular geneticist, created Ames test to screen chemicals for mutagenicity
 D. Bernard Amos (1923–2003), UKUS immunologist who studied the genetics of individuality
 Edgar Anderson (1897–1969), eminent US botanical geneticist
 E. G. (“Andy”) Anderson, US Drosophila and maize geneticist
 William French Anderson (born 1936), US worker in gene therapy
 Corino Andrade (1906–2005), Portuguese neurologist and clinical geneticist
 Tim Anson (1901–1968), US molecular biologist, proposed protein folding a reversible twostate reaction
 Stylianos E. Antonarakis (born 1951), USGreek medical geneticist, genotypic and phenotypic variation
 Werner Arber (born 1929), Swiss microbiologist, Nobel Prize for discovery of restriction endonucleases
 Enrico Arpaia (born 1949), Canadian molecular geneticist, TaySachs, Zap70, Purine Nucleoside Phosphorylase
 Michael Ashburner (born 1942), British Drosophila geneticist and polymath
 William Astbury (1898–1961), UK molecular biologist, Xray crystallography of proteins and DNA
 Giuseppe Attardi, ItalianUS molecular biologist, genetics of human mitochondrial function
 Charlotte Auerbach (1899–1994), Germanborn British pioneer in mutagenesis
 Oswald Avery (1877–1955), Canadianborn US codiscoverer that DNA is the genetic material
 Richard Axel (born 1946) US physicianscientist, Nobel Prize for genetic analysis of olfactory system
 E. B. Babcock (1877–1954), US plant geneticist, pioneered genetic analysis of genus Crepis
 ÉdouardGérard Balbiani (1823–1899), French embryologist who found chromosome puffs now called Balbiani rings
 David Baltimore (born 1938), US biologist, Nobel Prize for the discovery of reverse transcriptase
 Guido Barbujani (born 1955), Italian population geneticist and evolutionary biologist
 Cornelia Bargmann, US, molecular neurogeneticist studying the C. elegans brain
 David P. Bartel (B.A. 1982), US geneticist, discovered many microRNAs regulating gene expression
 William Bateson (1861–1926), British geneticist who coined the term “genetics”
 E. Baur (1875–1933), German geneticist, botanist, discovered inheritance of plasmids
 George Beadle (1903–1989), US Neurospora geneticist and Nobel Prizewinner
 Peter Emil Becker (1908–2000), German human geneticist, described Becker’s muscular dystrophy
 Jon Beckwith, US microbiologist and geneticist, isolated first gene from a bacterial chromosome
 Peter Beighton (born 1934) UK/South Africa medical geneticist
 Julia Bell (1879–1979), English geneticist who documented inheritance of many diseases
 John Belling (1866–1933), English cytogeneticist who developed staining technique for chromosomes
 Baruj Benacerraf (1920–2011), VenezuelanUS immunologist who won Nobel Prize for human leukocyte antigen system
 Kurt Benirschke (born 1924), GermanUS pathologist, comparative cytogenetics, twinning in armadillos
 Seymour Benzer (born 1921), US molecular biologist and pioneer of neurogenetics
 Dorothea Bennett (1929–1990) US geneticist, Pioneer of developmental genetics
 Paul Berg (born 1926), US biochemist and Nobel Prizewinner for basic research on nucleic acids
 J. D. Bernal (1901–1971), Irish physicist and pioneer Xray crystallographer
 James Birchler, Drosophila and Maize geneticists and cytogenticist.
 J. Michael Bishop (born 1936), US microbial immunogeneticist, Nobel Prizewinner for oncogenes
 Elizabeth Blackburn (born 1948), AustraloUS biologist, Lasker Award and Nobel Prize for telomeres and telomerase
 Günter Blobel (born 1936), GermanUS biologist, Nobel Prize for protein targeting (address tags on proteins)
 David Blow (1931–2004), British biophysicist who helped develop Xray crystallography of proteins
 Baruch Blumberg (Barry Blumberg) (1925–2011), US physician and Nobel Prizewinner on hepatitis B
 Julia Bodmer (1934–2001), British geneticist, key figure in discovery and definition of the HLA system
 Walter Bodmer (born 1936), GermanUK human population geneticist, immunogeneticist, cancer research
 James Bonner (1910–1996), farranging US molecular biologist, into histones, chromatin, nucleic acids
 David Botstein (born 1942), Swissborn US molecular geneticist, brother of Leon Botstein
 Theodor Boveri (1862–1915), German biologist and cytogeneticist
 Peter Bowen (1932–1988), Canadian medical geneticist
 Herb Boyer (born 1936), US, created transgenic bacteria inserting human insulin gene into E. coli
 Paul D. Boyer (born 1918), US biochemist and Nobel Prizewinner
 Jean Brachet (1909–1998), Belgian biochemist, made key contributions to fathoming roles of RNA
 Roscoe Brady US physicianscientist at NIH, studies of genetic neurological metabolic disorders
 Sydney Brenner (born 1927), British molecular biologist and Nobel Prizewinner
 Calvin Bridges (1889–1938), US geneticist, nondisjunction proof that chromosomes contain genes
 R. A. Brink (1897–1984), CanadianUS plant geneticist and breeder, studied paramutation, transposons
 Roy Britten (1919–2012) US molecular and evolutionary biologist, discovered and studied junk DNA
 John Brookfield, Drosophila population geneticist.
 Michael Stuart Brown (born 1941) US geneticist and Nobel Prizewinner on cholesterol metabolism
 Manuel Buchwald (born 1940), Peruvianborn Canadian medical geneticist and molecular geneticist
 Linda Buck (born 1947) US biologist, Nobel Prize for postdoc work (with Axel) cloning olfactory receptors
 James Bull, US molecular biologist and phage worker, evolution of sex determining mechanisms
 Luther Burbank (1849–1926), US botanist, horticulturist, pioneer in agricultural science
 Macfarlane Burnet (1899–1985), Australian biologist, Nobel Prize for immunological tolerance
 Cyril Burt (1883–1971), British educational psychologist, did debated mental and behavioral twin study
 John Cairns (born 1922), UK physicianscientist, showed bacterial DNA one molecule with replicating fork
 Allan Campbell, US microbiologist and geneticist, pioneering work on phage lambda
 Howard Cann, US pediatrician and geneticist, human population genetics at Stanford and CEPH in Paris
 Antonio Cao (born 1929), Italian pediatrician and medical geneticist, expert on the thalassemias
 Mario Capecchi (born 1937), Italianborn US molecular geneticist, coinvented the knockout mouse, Nobel Prize in Medicine, 2007
 Elof Axel Carlson, US geneticist and eminent historian of science
Bruce C. Carlton (born 1935) US microbial genetics, genetics of Bacilli, role of plasmids in insectical proteins
 Hampton L. Carson (1914–2004), US population geneticist, studied cytogenetics and evolution of Drosophila
 Tom Caskey (born c. 1938), US internist, human geneticist and entrepreneur; biochemical diseases
 Torbjörn Caspersson (1910–1997), Swedish cytogeneticist, revealed human chromosome banding
 William B. Castle (1897–1990), US hematologist, work on hereditary spherocytosis, sickle cell anemia
 William E. Castle (1867–1962), US geneticist, inspired T.H. Morgan, father of William B. Castle
 David Catcheside (1907–1994) UK plant geneticist, expert on genetic recombination, active in Australia
 Bruce Cattanach (born 1932), eminent UK mouse geneticist, Xinactivation and sex determination in mice
 Luigi Luca CavalliSforza (born 1922), distinguished Italian population geneticist at Stanford University
 Thomas Cech (born 1947), US biochemist who won Nobel Prize for catalytic functions of RNA
 Aravinda Chakravarti (born 1954), Indianborn bioinformatician studying genetic factors in common diseases
 JeanPierre Changeux (born 1936), French molecular neurobiologist, studied allosteric proteins
 Erwin Chargaff (1905–2002), Austrianborn US biochemist, Chargaff’s rules led to the double helix
 Brian Charlesworth (born 1945), British evolutionary biologist, husband of Deborah Charlesworth
 Deborah Charlesworth, British evolutionary biologist, wife of Brian Charlesworth
 Martha Chase (1927–2003), US biologist, with Hersey proved genetic material is DNA, not protein
 Sergei Chetverikov (1880–1959), Russian population geneticist
 Barton Childs (1916–2010), US pediatrician, biochemical geneticist, philosopher of medical genetics
 George M. Church (born 1954), US molecular geneticist, did first direct genomic sequencing with Gilbert
 Aaron Ciechanover (born 1947), Israeli biologist, won Nobel Prize for ubiquitinmediated protein degradation
 Bryan Clarke (1932–2014), British population geneticist, studied apostatic selection and molecular evolution
 Cyril Clarke (1907–2000), British medical geneticist, discovered how to prevent Rh disease in newborns
 Jens Clausen (1891–1969), DanishUS botanist, geneticist, and ecologist
 Edward H. Coe, Jr. (born 1926), influential US maize (corn) geneticist
 Stanley Cohen (born 1922), US neurobiologist, Nobel Prize for cell growth factors
 Francis Collins (born 1950), US medical geneticist, gene cloner, director of Human Genome Institute
 James J. Collins (born 1965), US bioengineer, pioneered synthetic biology and systems biology
 Robert Corey (1897–1971), US biochemist, αhelix, βsheet and atomic models for proteins
 Carl Correns (1864–1933), German botanist and geneticist, one of the rediscoverers of Mendel in 1900
 Lewis L. Coriell (1911–2001), US pioneer in culturing human cells
 Diane W. Cox, Canadian medical geneticist and expert on Wilson’s disease
 Harriet Creighton (1909–2004), US botanist who with McClintock first saw chromosomal crossover
 Francis Crick (1916–2004), English molecular biologist, neuroscientist, codiscoverer of the double helix
 James F. Crow (19162012), US population geneticist and renowned teacher of genetics
 Lucien Cuénot (1866–1951), French biologist, proved Mendel‘s rules apply to animals as well as plants
 A. Jamie Cuticchia (born 1966), US geneticist, into human genome informatics
 David M. Danks (1931–2003), Australian pediatrician and medical geneticist, expert on Menkes disease
 C. D. Darlington (1903–1981), British biologist and geneticist, elucidated chromosomal crossover
 Charles Darwin (1809–1882), English naturalist and author of Origin of the Species
 Kay Davies, English geneticist, expert on muscular dystrophy
 Jean Dausset (1916–2009) French immunogeneticist and Nobel Prizewinner for the HLA system
 Martin Dawson (1896–1945), CanadianUS researcher, confirmed and named genetic transformation
 Margaret Dayhoff (1925–1983), US pioneer in bioinformatics of protein sequences and evolution
 Albert de la Chapelle (born 1933), eminent Finnish medical geneticist, genetic predisposition to cancer
 Max Delbrück (1906–1981), GermanUS scientist, Nobel Prize for genetic structure of viruses
 Charles DeLisi, US biophysicist, led the initiative that planned and launched the Human Genome Project
 Félix d’Herelle (1873–1949), CanadianFrench microbiologist, discovered phages, invented phage therapy
 Hugo de Vries (1848–1935), Dutch botanist and one of the rediscoverers of Mendel‘s laws in 1900
 Carrie Derrick (1862–1941), Canadian geneticist, Canada’s first female professor
 M. Demerec (1895–1966), CroatianUS geneticist, directed Cold Spring Harbor Laboratory
 Theodosius Dobzhansky (1900–1975), noted UkrainianUS geneticist and evolutionary biologist
 John Doebley, (born 1952), US geneticist, studies genes that drive development and evolution of plants
 Peter Doherty (born 1940), Australian, won Nobel Prize for immune recognition of antigens
 Albert Dorfman (1916–1982), US biochemical geneticist, discovered cause of Hurler’s syndrome
 Gabriel Dover, British evolutionary geneticist
 NT Dubinin (1907–1998), Russian biologist and geneticist
 Bernard Dutrillaux (born 1940), French cytogeneticist, chromosome banding, comparative cytogenetics
 Christian de Duve (1917–2013), Belgian cytologist, Nobel Prize for cell organelles (peroxisomes, lysosomes)
 Richard H. Ebright (born 1959), US bacterial geneticist, molecular mechanisms of transcription and transcriptional regulation
 A.W.F. Edwards (born 1935), British statistician, geneticist, developed methods of phylogenetic analysis
 John Edwards (1928–2007), British medical geneticist and cytogeneticist who first described trisomy 18
 Hans Eiberg (born 1945), Danish geneticist, discovered the mutation causing blue eyes
 Eugene “Gene” J. Eisen (born 1938), American geneticist, experimental validation of the theory of genetic correlations; first to conduct a longterm selection experiment with transgenic mice
 Jeff Ellis (born 1953), Australian scientist
 R. A. Emerson (1873–1947), American plant geneticist, the main pioneer of corn genetics
 Sterling Emerson (1900–1988), American, biochemical genetics, recombination, son of R. A. Emerson
 Alan Emery (born 1928), British neuromuscular geneticist, Emery–Dreifuss muscular dystrophy
 Boris Ephrussi (1901–1979), Russianborn French geneticist, created way to transplant chromosomes
 Robert C. Elston (born 1932), Britishborn American biostatistical genetics and genetic epidemiologist
 Charlie Epstein, American medical geneticist, editor, developed mouse model for Down syndrome, wounded by the Unabomber
 Herbert McLean Evans (1882–1971), US anatomist, reported in 1918 humans had 48 chromosomes
 Martin Evans, British scientist, discovered embryonic stem cells and developed knockout mouse
 Warren Ewens, AustralianUS mathematical population geneticist, Ewens’s sampling formula
 Alexander Cyril Fabergé (1912–1988), Russianborn AngloAmerican geneticist, grandson of Carl Fabergé
 Arturo Falaschi (1933–2010), Italian geneticist, researched the origin of DNA replication
 D. S. Falconer (1913–2004), Scottish quantitative geneticist, wrote textbook to the subject
 Darrel R. Falk
 Stanley Falkow, US microbial geneticist, molecular mechanisms of bacterial pathogenesis
 Harold Falls (1909–2006), US ophthalmologic geneticist, helped found first genetics clinic in US
 William C. Farabee (1865–1925), US anthropologist, brachydactyly is evidence of Mendelism in humans
 Nina Fedoroff (born c. 1945), US plant geneticist, cloning of transposable elements, plant stress response
 Malcolm FergusonSmith (born 1931) UK cytogeneticist, Klinefelter syndrome, chromosome flow cytometry
 Philip J. Fialkow (1934–1996), US internist, educator, research in medical genetics and cancer genetics
 Giorgio Filippi (1935–1996), Italian medical geneticist, researched diseases linked to X chromosome
 J. R. S. Fincham (1926–2005), British microbial (Neurospora) and biochemical geneticist
 Gerald Fink (born 1941), US molecular geneticist, preeminent figure in the field of yeast genetics
 Andrew Fire (born 1959), US geneticist, Nobel Prize with Mello for discovery of RNA interference
 Robert L. Fischer (born 1950), A US geneticist, contributed to the understanding of genomic imprinting and epigenetics
 R. A. Fisher (1890–1962), British stellar statistician, evolutionary biologist, and geneticist
 Ed Fischer (born 1920), SwissUS biochemist, Nobel Prize for phosphorylation as switch activating proteins
 Eugen Fischer (1874–1967), German physician, anthropologist, eugenicist, influenced Nazi racial hygiene
 Ivar Asbjørn Følling (1888–1973), Norwegian biochemist and physician who discovered phenylketonuria (PKU)
 E. B. Ford (1901–1988), British ecological geneticist, specializing in butterflies and moths
 Charles Ford (1912–1999), British pioneer in the golden age of mammalian cytogenetics
 Heinz FraenkelConrat (1910–1999), Germanborn US biochemist who studied tobacco mosaic virus
 Rosalind Franklin (1920–1958), British crystallographer whose data led to discovery of double helix
 Clarke Fraser (born 1920), Canada’s first medical geneticist, student of congenital malformations
 Elaine Fuchs (born c. 1951), US cell biologist, molecular mechanisms of skin diseases, reverse genetics
 Walter Fuhrmann (1924–1995), German medical geneticist, at Giessen University
 Douglas J. Futuyma (born 1942), US evolutionary and ecological biologist
 Fred Gage, US neuroscientist, studies of neurogenesis and neuroplasticity of the adult brain
 Joseph G. Gall (born 1932), distinguished US cell biologist, chromosomes, created in situ hybridization
 André Gallais, French specialist in quantitative genetics and breeding methods theory
 Francis Galton (1822–1911), British geneticist, eugenicist, statistician
 George Gamow (1904–1968), Ukrainianborn American polymath, proposed genetic code concept
 Eldon J. Gardner (1909–1989), US professor of genetics in Utah, described Gardner’s syndrome
 Alan Garen (born c. 1924), US, early molecular geneticist, nonsense triplets terminating transcription
 Archibald Garrod (1857–1936), English physician, pioneered inborn errors, founded biochemical genetics
 Stan Gartler (born 1923), US human geneticist, G6PD as Xlinked marker, clonality of cancer, HeLa cells contaminating cell lines
 Lihadh AlGazali, Iraqi geneticist, research on congenital disorders in the United Arab Emirates
 Luigi Gedda (1902–2000), Italian geneticist best known for his fascination with twin studies
 Walter Gehring (1939–2014), Swiss, developmental genetics of Drosophila, discovered homeobox
 Park S. Gerald (1921–1993), US medical geneticist, research on hemoglobins and chromosomes
 James L. German, US medical geneticist and cytogeneticist, pioneer on Bloom syndrome
 Walter Gilbert (born 1932), US biochemist and molecular biologist, Nobel Prizewinner, entrepreneur
 H. Bentley Glass (1906–2005) US geneticist, provocative science theorizer, writer, science policy maker
 Salome GluecksohnWaelsch (born 1907), Germanborn US cofounder of developmental genetics
 Richard Goldschmidt (1878–1958), GermanAmerican, integrated genetics, development, and evolution
 Joseph L. Goldstein (born 1940), US medical geneticist, Nobel Prizewinner on cholesterol
 Richard M. Goodman (1932–1989), USIsraeli clinical geneticist, pioneered Jewish genetic diseases
 Robert J. Gorlin (1923–2006) US oral pathologist, clinical geneticist, craniofacial syndrome expert
 Irving I. Gottesman (1930–2016) US behavioral geneticist, used twin studies to analyze schizophrenia
 Carol W. Greider (born 1961), US molecular biologist, Lasker Award and Nobel Prize for telomeres and telomerase
 Frederick Griffith (1879–1941), British medical officer who found transforming principle now called DNA
 Clifford Grobstein (1916–1998), US scientist, bridged classical embryology and developmental biology
 Jean de Grouchy (1926–2003), French pioneer of clinical cytogenetics and karyotype–phenotype correlation
 Hans Grüneberg (1907–1982), British mouse geneticist and blood cell biologist
 PierreHenri Gouyon (born 1953), French biologist specializing in genetics and bioethics
 Elliot S. Goldstein American geneticist at Arizona State University
 Ernst Hadorn (1902–1976), Swiss pioneer in developmental genetics, mentor of Walter Gehring
 JBS Haldane (1892–1964), brilliant British human geneticist and cofounder of population genetics
 Ben Hall, US geneticist, DNA:RNA hybridization, yeast production of genetically engineered proteins
 Judy Hall (born 1939), dual American and Canadian charismatic clinical geneticist and dysmorphologist
 Dean Hamer (born 1951) US geneticist, postulated gay gene and God gene for religious experience
 John Hamerton (1929–2006), AngloCanadian cytogeneticist, prenatal diagnostician, bioethicist
 W. D. Hamilton (1936–2000), British evolutionary biologist and eminent evolutionary theorist
 Phil Hanawalt, US geneticist, discovered DNA repair replication
 Anita Harding (1952–1995), UK neurologist, first mitochondrial DNA mutation in disease
 G. H. Hardy (1877–1947), British mathematician, formulated basic law of population genetics
 Henry Harpending (born 1944), US anthropologist and human population geneticist
 Harry Harris (1919–94), British biochemical geneticist par excellence
 Henry Harris (1925–2014), Australianborn cell biologist, work on cancer and human genetics
 Lee Hartwell (born 1939), US yeast geneticist, Nobel Prize, “start” gene and checkpoints in the cell cycle
 Mogens Hauge (1922–1988), Danish medical geneticist and twin researcher
 Donald Hawthorne (1926–2003), US, major contributor to yeast genetics, centromerelinked gene maps
 William Hayes (1918–1994), Australian physician, microbiologist and geneticist, bacterial conjugation
 Robert Haynes (1931–1998), Canadian geneticist and biophysicist, work on DNA repair and mutagenesis
 Frederick Hecht (born 1930), US clinical geneticist, cytogeneticist, coined term fragile site
 Michael Heidelberger (1888–1991) US pioneer of modern immunology, won two Lasker Awards
 Martin Heisenberg (born 1940), German geneticist, neurobiologist, genetic study of brain of Drosophila
 Charles Roy Henderson, (1911–1989), US animal geneticist, basis for genetic evaluation of livestock, developed statistical methods used in animal breeding
 Al Hershey (1908–1997), US bacterial geneticist, Nobel Prize largely for Hershey–Chase experiment
 Ira Herskowitz (1946–2003), US phage and yeast geneticist, genetic regulatory circuits and mechanisms
 Len Herzenberg (1931–2013), US human geneticist, immunologist, cell biologist and cell sorter
 Avram Hershko (born 1937), Israeli biologist, Nobel Prize for ubiquitinmediated protein degradation
 Kurt Hirschhorn (born 1926), Vienneseborn American pediatrician, medical geneticist, cytogeneticist; described Wolf–Hirschhorn syndrome
 Mahlon Hoagland (1921–2009), US physician and biochemist, codiscovered tRNA with Paul Zamecnik
 Dorothy Hodgkin (1910–1994), British founder of protein crystallography and Nobel Prize winner
 Robert W. Holley (1922–1993), US biochemist, structure of transfer RNA, Nobel Prize
 Leroy Hood (born 1938), US molecular biotechnologist, created DNA and protein sequencers and synthesizers
 Norman Horowitz (1915–2005), US geneticist, one geneone enzyme, chemical evolution, space biology
 H. Robert Horvitz (born 1947), US cell biologist, Nobel Prize for programmed cell death
 David E. Housman, US molecular biologist, genetic basis of trinucleotide repeat diseases and cancer
 Martha M. Howe, US phage geneticist, notable contributions to the study of phage Mu
 T. C. Hsu (1917–2003), distinguished ChineseAmerican cell biologist, geneticist, cytogeneticist
 Thomas J. Hudson (born 1961), Canadian genome scientist, maps of human and mouse genomes
 David Hungerford (1927–1993), US codiscoverer of Philadelphia chromosome in CML
 Tim Hunt (born 1943), UK biochemist, Nobel Prize for discovery of cyclins in cell cycle control
 Charles Leonard Huskins (1897–1953), Englishborn Canadian cytogeneticist at McGill University and University of Wisconsin–Madison
 Harvey Itano (1920–2010), American biochemist and pioneer in the study of sickle cell disease
 François Jacob (1920–2013), French biologist, won Nobel Prize for bacterial gene control
 Patricia A. Jacobs (born 1934), Scottish human geneticist and cytogeneticist
 Albert Jacquard (1925–2013), French geneticist, essayist, humanist, activist
 Rudolf Jaenisch (born 1942), German cell biologist, created transgenic mice, leader in therapeutic cloning
 Richard Jefferson (born 1956) US molecular plant biologist in Australia, reporter gene system GUS
 Alec Jeffreys (born 1950), British geneticist, developed DNA fingerprinting and DNA profiling techniques
 Niels Kaj Jerne (1911–1994), Danish, greatest theoretician in modern immunology, Nobel Prize
 Elizabeth W. Jones (1939–2008) US yeast geneticist, first to complete the University of Washington graduate genetics program.
 Wilhelm Johannsen (1857–1927), Danish botanist who in 1909 coined the word “gene”
 Jonathan D. G. Jones, British plant molecular biologist
 Steve Jones (born 1944), British evolutionary geneticist and malacologist
 Christian Jung (born 1956), German plant geneticist and molecular biologist
 Dronamraju Krishna Rao (born 1937), Indian born Geneticis, founder of Foundation of Genetic Research
 Elvin Kabat (1914–2000) US immunochemist, a founder of modern immunology, antibodycombining sites
 Henrik Kacser (1918–1995), Romanianborn UK biochemist and geneticist, worked on metabolic control
 Axel Kahn (born 1944), French scientist and geneticist, known for work on genetically modified plants
 Patricia Verne Kailis (born 1933)
 Franz Josef Kallmann (1897–1965), GermanUS psychiatrist, pioneer in genetics of psychiatric diseases
 Gopinath Kartha (1927–1984), Indian biophysicist, codiscovered triplehelix structure of collagen
 Berwind P. Kaufmann (1897–1975), US botanist, did research in basic plant and animal cytogenetics
 John Kendrew (1917–1997), UK crystallographer, won Nobel Prize for structure of myoglobin
 Cynthia Kenyon (born c. 1955), US molecular biologist, genetics of aging in the worm C. elegans
 Warwick Estevam Kerr (born 1922) Brazilian expert in the genetics and sex determination of bees
 Bernard Kettlewell (1907–1979), UK physician, lepidopterist, ecological geneticist, peppered moth
 Seymour Kety (1915–2000), US neuroscientist, essential involvement of genetic factors in schizophrenia
 Gobind Khorana (1922–2011), IndianUS molecular biologist, synthesized nucleic acids, Nobel Prize
 Motoo Kimura (1924–1994), influential Japanese mathematical biologist in theoretical population genetics
 MaryClaire King (born 1946), US human geneticist and social activist, identified breast cancer genes
 David Klein, (1908–1993), Swiss ophthalmologist and human geneticist
 Harold Klinger (1929–2004), US pioneer on human chromosomes, founded journal Cytogenetics
 Aaron Klug (born 1926), Lithuania/S Africa/UK, Nobel Prize for developing electron crystallography
 Al Knudson (born 1922), US pediatric oncologist, geneticist, formulated two hit hypothesis of cancer
 Georges J. F. Köhler (1946–1995), German, Nobel Prize for hybridomas making monoclonal antibodies
 Arthur Kornberg (born 1918), US biochemist, Nobel Prize on DNA synthesis, father of Roger Kornberg
 Roger Kornberg (born 1947), US biologist, Nobel Prize on eukaryotic transcription
 Hans Kornberg (born 1928), GermanUK biologist, studies of carbohydrate transport
 Ed Krebs (1918–2009), US biochemist, Nobel Prize for phosphorylation as switch activating proteins
 Eric Kremer, US molecular biologist, found trinucleotide repeat in fragile X, research now in gene therapy
 Henry Kunkel (1916–1983), US immunologist, created starch gel electrophoresis to separate proteins
 Bruce Lahn (born 1969), Chineseborn geneticist specializing in evolutionary changes of the human brain
 JeanBaptiste Lamarck (1744–1829), French naturalist, evolutionist, “inheritance of acquired traits”
 Eric Lander (born 1957), American molecular geneticist, major contributor to Human Genome Project
 Karl Landsteiner (1868–1943), AustrianAmerican pathologist, won Nobel Prize for blood group discoveries
 André Langaney, French evolutionary geneticist
 Derald Langham (1913–1991), American agricultural geneticist, the “father of sesame”
 Sam Latt (1938–1988), US pioneer in molecular cytogenetics, fluorescent DNA chromosome probes
 Philip Leder (born 1934), US geneticist, method to decode genetic code, transgenic animals to study cancer
 Esther Lederberg (1922–2006), US microbiologist and bacterial genetics pioneer
 Joshua Lederberg (born 1925), US molecular biologist, Nobel Prize, headed Rockefeller University
 Jérôme Lejeune (1926–1994), French pediatrician, geneticist, discovered trisomy 21 in Down syndrome
 Richard Lenski (born 1956), US biologist and phage worker, did longterm E. coli evolution experiment
 Fritz Lenz (1887–1976), German geneticist and eugenicist, ideas influenced Nazi racial hygiene policies
 Widukind Lenz (1919–1995), eminent German medical geneticist who recognized thalidomide syndrome
 Leonard Lerman, US molecular biologist, phage worker, mentor of Nobel Prizewinner Sidney Altman
 I. Michael Lerner (1910–1977), RussianUS contributor to population, quantitative and evolutionary genetics
 Albert Levan (1905–1998), Swedist geneticist, coauthored report that humans have 46 chromosomes
 Cyrus Levinthal (1922–1990), US molecular geneticist, DNA replication, mRNA, molecular graphics
 Edward B. Lewis (1918–2004), American founder of developmental genetics and Nobel Prizewinner
 Richard Lewontin (born 1929), American evolutionary biologist, geneticist and social commentator
 C. C. Li (1912–2003), eminent Chinese American population geneticist and human geneticist
 WenHsiung Li (born 1942), TaiwaneseAmerican, molecular evolution, population genetics, genomics
 David Linder (1923–1999), US pathologist and geneticist, used G6PD as Xlinked clonal tumor marker
 Susan Lindquist, US molecular biologist studying effects of protein folding and heatshock proteins
 Jan Lindsten (born 1935), eminent Swedish medical geneticist, secretary general of the Nobel Assembly
 Fritz Lipmann (1899–1986), GermanAmerican biochemist, Nobel Prize for codiscovery of coenzyme A
 C. C. Little (1888–1971), US pioneer mouse geneticist, founded Jackson Laboratory in Bar Harbor, Maine
 Richard Losick, US molecular biologist, RNA polymerase, gene transcription, bacterial development
 Herbert Lubs (born c. 1928), US internist, medical geneticist, described “marker X” (fragile X chromosome)
 Salvador Luria (1912–1991), ItalianAmerican molecular biologist, Nobel Prize for bacteriophage genetics
 Jay Lush (1896–1982), American animal geneticist who pioneered modern scientific animal breeding
 Michael Lynch, US quantitative geneticist studying evolution, population genetics, and genomics
 Mary F. Lyon (born 1925), English mouse geneticist, noted Xinactivation and proposed Lyon hypothesis
 David T. Lykken (1928–2006), American psychologist and behavioral geneticist known for twin studies
 Trofim Lysenko (1898–1976), Soviet scientist, led vicious political campaign against genetics in US
 Ellen Magenis (19252014), US medical geneticist and cytogeneticist, Smith–Magenis syndrome
 Phyllis McAlpine (1941–1998), Canadian human geneticist and gene mapper
 Maclyn McCarty (1911–2005), American codiscoverer that DNA is the genetic material
 Barbara McClintock (1902–1992), American cytogeneticist, Nobel Prize for genetic transposition
 William McGinnis, US molecular geneticist, found homeobox (Hox) genes responsible for basic body plan
 Victor A. McKusick (born 1921), US internist and clinical geneticist, organized human genetic knowledge
 Colin MacLeod (1909–1972), CanadianAmerican codiscoverer that DNA is the genetic material
 Tak Wah Mak (born 1946), ChineseCanadian molecular biologist, codiscovered human T cell receptor genes
 Gustave Malécot (1911–1998), French mathematician who influenced population genetics
 Tom Maniatis (born 1943), US molecular biologist, gene cloning, regulation of gene expression
 Clement Markert (1917–1999), eminent US biologist, discovered isozymes
 Joan Marks, American social worker, principal architect of the profession of genetic counselor
 Marco Marra
 Richard E. Marshall (born 1933), American paediatrician, Greig’s syndrome I, Marshall–Smith syndrome
 John Maynard Smith (1920–2004), British evolutionary biologist and population geneticist
 Ernst Mayr (1904–2005), leading Germanborn American evolutionary biologist
 Peter Medawar (1915–1987), Brazilianborn English scientist, Nobel Prize for immunological tolerance
 Craig C. Mello (born 1960), American geneticist, Nobel Prize for discovery of RNA interference
 Gregor Mendel (1822–1884), Bohemian monk who discovered laws of Mendelian inheritance
 Josef Mengele (1911–1979), German SS officer and a PhD in genetics
 Carole Meredith, American geneticist who pioneered DNA typing to differentiate between grape varieties
 Matthew Meselson (born 1930), US molecular geneticist, work on DNA replication, recombination, repair
 Peter Michaelis, German plant geneticist, focused on cytoplasmic inheritance
 Ivan Vladimirovich Michurin (1855–1935), Russian plant geneticist, scientific agricultural selection
 Friedrich Miescher (1844–1895), Swiss biologist, found weak acid in white blood cells now called DNA
 Margareta Mikkelsen (1923–2004), eminent Germanborn Danish human geneticist and cytogeneticist
 Lois K. Miller (d. 1999, age 54), entomologist and molecular geneticist, studied insect viruses
 O. J. Miller, US physician, human and mammalian genetics and chromosome structure and function
 César Milstein (1927–2002) ArgentineUK, Nobel Prize for hybridomas making monoclonal antibodies
 Aubrey Milunsky (born c. 1936), S. AfricanUS physician, medical geneticist, writer, prenatal diagnosis
 Alfred Mirsky (1900—1974), US pioneer in molecular biology, hemoglobin structure, constancy of DNA
 Felix Mitelman (born 1940), Swedish cancer geneticist and cytogeneticist, catalog of chromosomes in cancer
 Jan Mohr (1921–2009), eminent NorwegianDanish pioneer in human gene mapping
 Jacques Monod (1910–1976), French molecular biologist, Nobel Prizewinner
 Lilian Vaughan Morgan (1870–1952), wife of T. H. Morgan and a fine geneticist in her own right
 T. H. Morgan (1866–1945), head of the “fly room,” first geneticist to win the Nobel Prize
 Newton E. Morton (born 1929), population geneticist and genetic epidemiologist
 Arno Motulsky (19232018), GermanUS hematologist who influenced medical genetics and founded pharmacogenetics
 Arthur Mourant (1904–1994), British hematologist, first to examine worldwide blood group distributions
 H. J. Muller (1890–1967) American Drosophila geneticist, Nobel Prize for producing mutations by Xrays
 Hans J. MüllerEberhard (1927–1998), GermanUS immunogeneticist, immunoglobulins and complement
 Kary Mullis (born 1944), American biochemist, Nobel Prize for the polymerase chain reaction (PCR)
 Walter E. Nance (born 1933), US internist and geneticist, research on twins and genetics of deafness
 Daniel Nathans (1928–1999), US microbiologist, Nobel Prize for restriction endonucleases
 James V. Neel (1915–2000), distinguished human geneticist, founded first genetics clinic in the US
 Fred Neidhardt, US microbiologist, pioneer in molecular physiology and proteomics of E. coli
 Oliver Nelson (born 1920), US maize geneticist, profound impact on agriculture and basic genetics
 Walter NelsonRees, US cytogeneticist, confirmed HeLa cells contamination of other cell lines
 Eugene W. Nester, US microbial geneticist, genetics of Agrobacterium (crown gall formation)
 Carl Neuberg, early pioneer of the study of metabolism.
 Hans Neurath (1909–2002), AustrianUS protein chemist, helped set stage for proteomics
 Marshall W. Nirenberg (1927–2010), US geneticist, biochemist and Nobel Prizewinner
 Eva Nogales, Spanish biophysicist studying eukaryotic transcription and translation initiation complexes
 Edward Novitski (1918–2006), eminent US Drosophila geneticist, pioneer in chromosome mechanics
 Paul Nurse (born 1949), UK biochemist, Nobel Prize for work on CDK, a key regulator of the cell cycle
 Christiane NüssleinVolhard (born 1942), German developmental biologist and Nobel Prizewinner
 William Nyhan (born 1926), US pediatrician and biochemical geneticist, described LeschNyhan syndrome
 Severo Ochoa (1905–1993), SpanishAmerican biochemist, Nobel Prize for work on the synthesis of RNA
 Susumu Ohno (1928–2000), JapaneseUS biologist, evolutionary cytogenetics and molecular evolution
 Tomoko Ohta, Japanese scientist in molecular evolution, the nearly neutral theory of evolution
 Pete Oliver (1898–1991), American geneticist, switched from Drosophila to human genetics
 Jane M. Olson (1952–2004), American genetic epidemiologist and biostatistician
 Maynard Olson, American geneticist, pioneered map of yeast genome and Human Genome Project
 John Opitz (born 1935), GermanAmerican medical geneticist, expert on dysmorphology and syndromes
 Harry Ostrer, American medical geneticist, studies origins of Jewish peoples
 Ray Owen (born 1915), US geneticist, immunologist, found cattle blood groups and chimeric twin calves
 Svante Pääbo (born 1955), Swedish molecular anthropologist in Leipzig studying Neanderthal genome
 David Page, US physician and geneticist who mapped, cloned and sequenced the human Y chromosome
 Theophilus Painter (1889–1969), US zoologist, studied fruit fly and human testis chromosomes
 Arthur Pardee (born 1921), American scientist who discovered restriction point in the cell cycle
 Klaus Patau (1908–1975), GermanAmerican cytogeneticist, described trisomy 13
 John Thomas Patterson (1878–1960), American embryologist and geneticist who studied isolating mechanisms
 Andrew H. Paterson, US geneticist, research leader in plant genomics
 Linus Pauling (1901–1994), eminent American chemist, won Nobel Prizes for chemical bonds and peace
 Crodowaldo Pavan (1919–2009), Brazilian biologist, fly geneticist, and influential scientist in Brazil
 Rose Payne (1909–1999), US transplant geneticist, key to discovery and development of HLA system
 Raymond Pearl (1879–1940), American biologist, biostatistician, rejected eugenics
 Karl Pearson (1857–1936), British statistician, made key contributions to genetic analysis
 LS Penrose (1898–1972), British psychiatrist, human geneticist, pioneered genetics of mental retardation
 Max Perutz (1914–2002), AustrianBritish molecular biologist, Nobel Prize for structure of hemoglobin
 Massimo Pigliucci (born 1964), ItalianUS plant ecological and evolutionary geneticist. Winner of the Dobzhansky Prize.
 Alfred Ploetz (1860–1940), German physician, biologist, eugenicist, introduced racial hygiene to Germany
 Paul Polani (1914–2006), Triesteborn UK pediatrician, major catalyst of medical genetics in Britain
 Charles Pomerat (1905–1951), American cell biologist, pioneered the field of tissue culture
 Guido Pontecorvo (1907–1999), Italianborn Scottish geneticist and pioneer molecular biologist
 George R. Price (1922–1975), brilliant but troubled US population geneticist and theoretical biologist
 Peter Propping (1942–2016), German human geneticist, studies of epilepsy
 Mark Ptashne (born c. 1940), US molecular biologist, studies of genetic switch, phage lambda
 Ted Puck (1916–2005), US physicist, work in mammalian and human cell culture, genetics, cytogenetics
 RC Punnett (1875–1967), early English geneticist, discovered linkage with William Bateson, stimulated GH Hardy
 Lluis QuintanaMurci (born 1970), Spanish human population geneticist, heads part of Genographic Project
 Michèle Ramsay, South African geneticist, singlegene disorders, epigenetics, complex diseases
 Robert Race (1907–1984), British expert on blood groups, along with wife Ruth Sanger
 Sheldon C. Reed (1910–2003), American pioneer in genetic counseling and behavioral genetics
 G. N. Ramachandran (1922–2001) Indian biophysicist, codiscovered triplehelix structure of collagen
 David Reich, US, human population genetics and genomics, did humans and chimps interbreed?
 Theodore Reich (1938–2003), CanadianAmerican psychiatrist, a founder of modern psychiatric genetics
 Alexander Rich (1925–2015), US biologist, biophysicist, discovered ZDNA and tRNA 3dimensional structure
 Rollin C. Richmond, US, evolutionary and pharmacogenetic studies of Drosophila, university administrator
 Neil Risch, American human and population geneticist, studied torsion dystonia
 Otto Renner (1883–1960), German plant geneticist, established maternal plastid inheritance
 Marcus Rhoades (1903–1991), great maize (corn) geneticist and cytogeneticist
 David L. Rimoin (1936–2012), Canadian–US medical geneticist, studied skeletal dysplasias
 Richard Roberts (born 1943), British molecular biologist, Nobel Prize for introns and genesplicing
 Arthur Robinson (1914–2000), American pediatrician, geneticist, pioneer on sex chromosome anomalies
 Herschel L. Roman (1914–1989), American geneticist, innovated in analysis in maize and budding yeast
 Irwin Rose (1926–2015), American biologist, Nobel Prize for ubiquitinmediated protein degradation
 Leon Rosenberg (born c. 1932), US physiciangeneticist, molecular basis of inherited metabolic disease
 David S Rosenblatt
 Peyton Rous (1879–1970), American tumor virologist and tissue culture expert, Nobel Prize
 Janet Rowley (born 1925), American cancer cytogeneticist who found Ph chromosome due to translocation
 Peter T. Rowley (1929–2006), American internist and geneticist, genetics of cancer and leukemia
 Frank Ruddle (19292013), US biologist, somatic cell genetics, human gene mapping, paved way for transgenic mice
 Ernst Rüdin (1874–1952), Swiss psychiatrist, geneticist and eugenicist who promoted racial hygiene
 Elizabeth S. Russell (1913–2001), US mammalian geneticist, pioneering work on pigmentation, bloodforming cells, and germ cells
 Liane B. Russell (born c. 1923), Austrianborn US mouse geneticist and radiation biologist
 William L. Russell (1910–2003), UKUS mouse geneticist, pioneered study of mutagenesis in mice
 Leo Sachs (1924–2013), GermanIsraeli molecular cancer biologist, colonystimulating factors, interleukins
 Ruth Sager (1918–1997), US geneticist, pioneer of cytoplasmic genetics, tumor suppressor genes
 Joseph Sambrook (born 1939), British viral geneticist
 Avery A. Sandberg, US internist, discovered XYY in 1961, expert on chromosomes in cancer
 Lodewijk A. Sandkuijl (1953–2002), Dutch expert on genetic epidemiology and statistical genetics
 Larry Sandler (1929–1987), US Drosophila geneticist, chromosome mechanics, devoted teacher
 John C. Sanford (born 1950), American horticultural geneticist and intelligent design advocate
 Fred Sanger (1918–2013), UK biochemist, two Nobel Prizes, sequence of insulin, DNA sequencing method
 Ruth Sanger (1918–2001), Australian expert on blood groups, along with husband Robert Race
 Karl Sax (1892–1973), American botanist and cytogeneticist, effects of radiation on chromosomes
 Paul Schedl (born 1947), US molecular biologist, genetic regulation of developmental pathways in fruit fly
 Albert Schinzel (born 1944), Austrian human geneticist, clinical genetics, karyotype–phenotype correlations
 Werner Schmid (1930–2002), Swiss pioneer in human cytogenetics, described cat eye syndrome
 Gertrud Schüpbach, SwissAmerican biologist, molecular and genetic mechanisms in oogenesis
 Charles Scriver (born 1930), Canadian pediatrician, biochemical geneticist, newborn metabolic screening
 Ernie Sears (1910–1991), Wheat Geneticist who pioneered methods of transferring desirable genes from wild relatives to cultivated wheat in order to increase wheat’s resistance to various insects and diseases
 Jay Seegmiller (1920–2006), US human biochemical geneticist, found cause of Lesch–Nyhan syndrome
 Fred Sherman (1932–2013), US geneticist, one of the “fathers” and mentors of modern yeast genetics
 Larry Shapiro, US pediatric geneticist, lysosomal storage disorders, X chromosome inactivation
 Lucy Shapiro, US molecular geneticist, gene expression during the cell cycle, bacterium Caulobacter
 Phillip Sharp (born 1944), US geneticist and molecular biologist, Nobel Prize for codiscovery of gene splicing
 Philip Sheppard (1921–1976), British population geneticist, lepidopterist, human blood group researcher
 G. H. Shull (1874–1954), American geneticist, made key discoveries including heterosis
 Torsten Sjögren
 Mark Skolnick (born 1946), American geneticist, developed Restriction Fragment Length Polymorphisms (RFLPs) for genetic mapping, and founded Myriad Genetics
 Obaid Siddiqi (born 1932), Indian neurogeneticist, pioneer on olfactory sense of fruit fly Drosophila
 David Sillence (born 1944), Australian clinical geneticist, pioneered training of Australian geneticists, research in bone dysplasias, classified osteogenesis imperfecta
 Norman Simmons (1915–2004), US, forgotten donor of pure DNA to Rosalind Franklin in double helix saga
 Piotr Słonimski (1922–2009), PolishParisian yeast geneticist, pioneer of mitochondrial heredity
 William S. Sly (born c. 1931), US biochemical geneticist, mucopolysaccharidosis type VII (Sly syndrome)
 Cedric A. B. Smith (1917–2002), British statistician, made key contributions to statistical genetics
 David W. Smith (1926–1981), US pediatrician, influential dysmorphologist, named fetal alcohol syndrome
 Hamilton Smith (born 1931), American microbiologist, Nobel Prize for restriction endonucleases
 Michael Smith (1932–2000), UKborn Canadian biochemist, Nobel Prize for sitedirected mutagenesis
 Oliver Smithies (born 1925), UK/US molecular geneticist, inventor, gel electrophoresis, knockout mice
 George Snell (1903–1996), US mouse geneticist, pioneer transplant immunologist, won Nobel Prize
 Lawrence H. Snyder (1901–1986), American pioneer in medical genetics, studied blood groups
 Robert R. Sokal (1925–2012), Austrianborn US biological anthropologist and biostatistician.
 Tracy M. Sonneborn (1905–1981), protozoan biologist and geneticist
 Ed Southern (born 1938), UK molecular biologist, invented Southern blot and DNA microarray technologies
 Hans Spemann (1869–1941) German embryologist, Nobel Prize for discovery of embryonic induction
 David Stadler, American geneticist, mechanisms of mutation and recombination in Neurospora
 L. J. Stadler (1896–1954), eminent American maize geneticist, father of David Stadler
 Frank Stahl (born 1929), American molecular biologist, the Stahl half of the MeselsonStahl experiment
 David States, US geneticist and bioinformatician, computational study of human genome and proteome
 G. Ledyard Stebbins (1906–2000), American botanist, geneticist and evolutionary biologist
 Michael Stebbins, American geneticist, science writer, editor and activist
 Emmy Stein (1879–1954), German botanist and geneticist
 Joan A. Steitz (born c. 1942), US molecular biologist, pioneering studies of snRNAs and snRNPs (snurps)
 Gunther Stent (1924–2008), Germanborn US molecular geneticist, phage worker, philosopher of science
 Curt Stern (1902–1981), Germanborn US Drosophila and human geneticist, great teacher
 Nettie Stevens (1861–1912), US geneticist, studied chromosomal basis of sex and discovered XY basis
 Miodrag Stojković (born 1964), Serbian geneticist, working in Europe on mammalian cloning
 George Streisinger (1927–1984), American geneticist, work on bacterial viruses, frameshift mutations
 List item Leonell Strong (1894–1982) American geneticist, mouse geneticist and cancer researcher
 Alfred Sturtevant (1891–1970), constructed first genetic map of a chromosome
 John Sulston (born 1942), British molecular biologist, Nobel Prize for programmed cell death in C. elegans
 James B. Sumner (1887–1955), American biochemist, Nobel Prize, found enzymes can be crystallized
 Maurice Super (d. 2006, age 69), S. Africanborn UK pediatric geneticist, studied cystic fibrosis
 Grant Sutherland, Australian molecular cytogeneticist, pioneer on human fragile sites, human genome
 Walter Sutton (1877–1916), US surgeon and scientist, proved chromosomes contained genes
 David Suzuki (born 1936), Canadian Drosophila geneticist, science broadcaster and environmental activist
 M. S. Swaminathan (born 1925), Indian agricultural scientist, geneticist, leader of Green Revolution in India
 Bryan Sykes, British human geneticist, discovered ways to extract DNA from fossilized bones
 Jack Szostak (born 1952), AngloUS geneticist, worked on recombination, artificial chromosomes, and on telomeres. He has been awarded a Nobel Prize for its work on telomeres.
 Jantina Tammes (1871–1947), Dutch geneticist, one of the first Dutch scientists to report on variability and evolution
 Edward Tatum (1909–1975), showed genes control individual steps in metabolism
 Joyce TaylorPapadimitriou (born 1932), British molecular biologist and geneticist
 Howard Temin (1934–1994), US geneticist, Nobel Prize for discovery of reverse transcriptase
 Alan Templeton (born c. 1948), US geneticist and biostatistician, molecular evolution, evolutionary biology
 Donnall Thomas (1920–2012) US physician, Nobel Prize for bone marrow transplantation for leukemia
 Nikolay TimofeevRessovsky (1900–1981), Russian radiation and evolution geneticist
 Alfred Tissières (1917–2003), Swiss molecular geneticist, pioneered molecular biology in Geneva
 Joe Hin Tjio (1919–2001), Javaborn geneticist who first discovered humans have 46 chromosomes
 Susumu Tonegawa (born 1939), Japanese molecular biologist, Nobel Prize for genetics of antibody diversity
 Erich von Tschermak (1871–1962) Austrian agronomist and one of the rediscoverers of Mendel‘s laws
 Lapchee Tsui, Chinese geneticist, sequenced first human gene (for cystic fibrosis) with Francis Collins
 Raymond Turpin (1895–1988), French pediatrician, geneticist, Lejeune’s codiscoverer of trisomy 21
 Axel Ullrich (born 1943), German molecular biologist, signal transduction, discovered oncogene, Herceptin
 Irene Ayako Uchida (1917–2013), Canadian geneticist and cytogeneticist. One of the first in Canada. Down syndrome
 Harold Varmus (born 1939), American Nobel Prizewinner for oncogenes, head of NIH
 Rajeev Kumar Varshney (born 1973), Indian Geneticist, Principal Scientist at ICRISAT and Theme Leader at Generation Challenge Programme
 Nikolai Vavilov (1887–1943), eminent Russian botanist and geneticist, antiLysenko, died in prison
 Craig Venter (born 1946), American molecular biologist and entrepreneur, raced to sequence the genome
 Jerome Vinograd (1913–1976), US, leader in biochemistry and molecular biology of nucleic acids
 Friedrich Vogel, German, leader in human genetics, coined term “pharmacogenetics“
 Bert Vogelstein (born 1949), US pediatrician and cancer geneticist, series of mutations in colorectal cancer
 Erik Adolf von Willebrand (1870–1949), Finnish internist who found commonest bleeding disorder
 Petrus Johannes Waardenburg (1886–1979), Dutch ophthalmologist, geneticist, Waardenburg syndrome
 C. H. Waddington (1905–1975), British developmental biologist, paleontologist, geneticist, embryologist
 Alfred Russel Wallace (1823–1913), Welsh, proposed natural selection theory independent of Darwin
 Douglas C. Wallace, US mitochondrial geneticist, pioneered the use of human mtDNA as a molecular marker
 Peter Walter, GermanUS molecular biologist studying protein folding and protein targeting
 Richard H. Ward (1943–2003), Englishborn New Zealand human and anthropological geneticist
 James D. Watson (born 1928), US molecular geneticist, Nobel Prize for discovery of the double helix
 David Weatherall, distinguished UK physician, geneticist, pioneer in hemoglobin and molecular medicine
 Robert Weinberg, US, discovered first human oncogene and first tumor suppressor gene
 Wilhelm Weinberg (1862–1937), German physician, formulated basic law of population genetics
 Spencer Wells (born 1969), US genetic anthropologist, head of Genographic Project to map past migrations
 Susan R. Wessler (born 1953), US plant molecular geneticist, transposable elements re genetic diversity
 Raymond L. White, US cancer geneticist, cloned APC colon cancer gene and neurofibromatosis gene
 Glayde Whitney (1939–2002) US behavioral geneticist, accused of supporting scientific racism
 Reed Wickner (born c. 1940) US molecular geneticist, yeast phenotypes due to prion forms of native proteins
 Alexander S. Wiener (1907–1976), U.S. immunologist, discovered Rh blood groups with Landsteiner
 Eric F. Wieschaus (born 1947), American developmental biologist and Nobel Prizewinner
 Maurice Wilkins (1916–2004), New Zealandborn British Nobel Prizewinner with Watson and Crick
 Huntington Willard (born c. 1953), US human geneticist, X chromosome inactivation, gene silencing
 Harold G. Williams (born 1929), US, Oklahoma cattle geneticist pioneer
 Robley Williams (1908–1995), US virologist, recreated tobacco mosaic virus from its RNA + protein coat
 Ian Wilmut (born 1944) UK reproductive biologist who first cloned a mammal (lamb named Dolly)
 Allan Wilson (1934–1991) New ZealandUS innovator in molecular study of human evolution
 David Sloan Wilson (born 1949), US evolutionary biologist and geneticist
 Edmund Beecher Wilson (1856–1939), US zoologist, geneticist, discovered XY and XX sex chromosomes
 Øjvind Winge (1886–1964), Danish biologist and pioneer in yeast genetics
 Chester B. Whitley (born 1950), US geneticist, pioneered treatment of lysosomal diseases
 Carl Woese (1928–2012), US biologist, defined Archaea as new domain of life, rRNA phylogenetic tool
 Ulrich Wolf (born 1933), German cytogeneticist, found chromosome 4p deletion in Wolf–Hirschhorn syndrome
 Melaku Worede (born 1936), Ethiopian conservationist and geneticist
 Sewall Wright (1889–1988), eminent US geneticist who, with Ronald Fisher, united genetics & evolution
 Charles Yanofsky (born 1925), American molecular geneticist, colinearity of gene and its protein product
 Floyd Zaiger (born 1926), fruit geneticist and entrepreneur
 Hans Zellweger (1909–1990) SwissUS pediatrician and clinical geneticist, described Zellweger syndrome
 Norton Zinder (1928–2012) American biologist and phage worker who discovered genetic transduction
 Rolf M. Zinkernagel (born 1944), Swiss scientist, won Nobel Prize for immune recognition of antigen
EVOLUTIONARY BIOLOGISTS
1. Charles Darwin & Alfred Russell Wallace
Introduced the theory of evolution.
2. R. A. Fisher
his work used mathematics to combine Mendelian genetics and natural selection; this contributed to the revival of Darwinism in the early 20th century revision of the theory of evolution known as the modern synthesis.
3. Sewall Wright
an American geneticist known for his influential work on evolutionary theory and also for his work on path analysis. He was a founder of population genetics alongside Ronald Fisher and J.B.S. Haldane, which was a major step in the development of the modern synthesis combining genetics with evolution. He discovered the inbreeding coefficient and methods of computing it in pedigree animals. He extended this work to populations, computing the amount of inbreeding between members of populations as a result of random genetic drift, and along with Fisher he pioneered methods for computing the distribution of gene frequencies among populations as a result of the interaction of natural selection, mutation, migration and genetic drift.
4. J. B. S. Haldane
demonstrated genetic linkage in mammals while subsequent works helped to create population genetics, thus establishing a unification of Mendelian genetics and Darwinian evolution by natural selection whilst laying the groundwork for modern evolutionary synthesis.
5. W. D. Hamilton
an English evolutionary biologist, widely recognised as one of the most significant evolutionary theorists of the 20th century.
Hamilton became famous through his theoretical work expounding a rigorous genetic basis for the existence of altruism, an insight that was a key part of the development of a genecentric view of evolution. He is considered one of the forerunners of sociobiology, as popularized by E. O. Wilson. Hamilton also published important work on sex ratios and the evolution of sex.
6. G. G. Simpson

7. John Maynard Smith
Maynard Smith was instrumental in the application of game theory to evolution and theorised on other problems such as the evolution of sex and signalling theory.
8. August Weismann
one of the founders of the science of genetics, who is best known for his opposition to the doctrine of the inheritance of acquired traits.
9. Motoo Kimura
one of the most influential theoretical population geneticists. He is remembered in genetics for his innovative use of diffusion equations to calculate the probability of fixation of beneficial, deleterious, or neutral alleles. Combining theoretical population genetics with molecular evolution data, he also developed the neutral theory of molecular evolution in which genetic drift is the main force changing allele frequencies.
10. Theodosius Dobzhansky

ZOOLOGISTS
Stephen Robert “Steve” Irwin, nicknamed “The Crocodile Hunter”, was an Australian wildlife expert, television personality, and conservationist. Irwin achieved worldwide fame from the television series The Crocodile Hunter, an internationally broadcast wildlife documentary series.
Dian Fossey was an American zoologist, primatologist, and anthropologist who undertook an extensive study of gorilla groups over a period of 18 years. She studied them daily in the mountain forests of Rwanda, initially encouraged to work there by anthropologist Louis Leakey.
Dame Jane Morris Goodall, DBE is an English primatologist, ethologist, anthropologist, and UN Messenger of Peace. Considered to be the world’s foremost expert on chimpanzees, Goodall is best known for her 55year study of social and family interactions of wild chimpanzees in Gombe Stream National park.
Charles Robert Darwin, FRS was an English naturalist and geologist, best known for his contributions to evolutionary theory. He established that all species of life have descended over time from common ancestors, and in a joint publication with Alfred Russel Wallace introduced his scientific theory of evolution.
John Bushnell “Jack” Hanna is an American zookeeper who is the Director Emeritus of the Columbus Zoo and Aquarium. He was Director of the zoo from 1978 to 1993, and is viewed as largely responsible for elevating its quality and reputation. Gregor Mendel
Gregor Johann Mendel was a Germanspeaking Moravian scientist and Augustinian friar who gained posthumous fame as the founder of the modern science of genetics.
Rachel Louise Carson was an American marine biologist and conservationist whose book Silent Spring and other writings are credited with advancing the global environmental movement.
James Dewey Watson is an American molecular biologist, geneticist and zoologist, best known as one of the codiscoverers of the structure of DNA in 1953 with Francis Crick.
Terri Irwin, AM is an AmericanAustralian,naturalist and author, the widow of Australian naturalist Steve Irwin and owner of Australia Zoo at Beerwah, Queensland, Australia. She costarred with her husband on The Crocodile Hunter, their unconventional television nature documentary series.
Roger Wolcott Sperry was a neuropsychologist, neurobiologist and Nobel laureate who, together with David Hunter Hubel and Torsten Nils Wiesel, won the 1981 Nobel Prize in Physiology and Medicine for his work with splitbrain research.
Louis Seymour Bazett Leakey, also known as L. S. B. Leakey, was a Kenyan paleoanthropologist and archaeologist whose work was important in establishing human evolutionary development in Africa, particularly through his discoveries in the Olduvai Gorge.
Jean Léopold Nicolas Frédéric Cuvier, known as Georges Cuvier, was a French naturalist and zoologist. Cuvier was a major figure in natural sciences research in the early 19th century and was instrumental in establishing the fields of comparative anatomy and paleontology.
Ernst Walter Mayr was one of the 20th century’s leading evolutionary biologists. He was also a renowned taxonomist, tropical explorer, ornithologist, and historian of science. His work contributed to the conceptual revolution that led to the modern evolutionary synthesis of Mendelian genetics.
ANTHROPOLOGISTS
Zora Neale Hurston was an American folklorist, anthropologist, and author. Of Hurston’s four novels and more than 50 published short stories, plays, and essays, she is best known for her 1937 novel Their Eyes Were Watching God.
Carlos Castaneda was an American author with a Ph.D. in anthropology. Starting with The Teachings of Don Juan in 1968, Castaneda wrote a series of books that describe his training in shamanism, particularly a group that he called the Toltecs.
Margaret Mead was an American cultural anthropologist who featured frequently as an author and speaker in the mass media during the 1960s and 1970s. She earned her bachelor degree at Barnard College in New York City and her M.A. and Ph.D. degrees from Columbia University. She wrote the book the coming of age in somoa about her field work there in the 1920s.
Florida donner
Florinda Donner is an American writer and anthropologist known as one of Carlos Castaneda’s “witches”.
Tobias Schneebaum was an American artist, anthropologist, and AIDS activist. He is best known for his experiences living, and traveling among the Harakmbut people of Peru, and the Asmat people of Papua, Western New Guinea, Indonesia then known as Irian Jaya.
Abū alRayhān Muhammad ibn Ahmad alBīrūnī, known as AlBiruni in English, was a Persian Muslim scholar and polymath from the Khwarezm region. AlBiruni is regarded as one of the greatest scholars of the medieval Islamic era and was well versed in physics, mathematics, astronomy, and natural science.
Clifford James Geertz was an American anthropologist who is remembered mostly for his strong support for and influence on the practice of symbolic anthropology, and who was considered “for three decades…the single most influential cultural anthropologist in the United States.”
Cultural Anthropologists
Marcel Mauss (18721950)
Mauss was a French sociologist and nephew of Emile Durkheim, the “founder of modern sociology”. He followed in his uncle’s footsteps and assisted him with his well renowned sociological projects. Mauss was inspired by the idea of analysing religion from a social perspective, which led Mauss to become a great proponent of “social ethnology” (usually a firsthand, and comparative, study of cultures and their social structures). He is most known for his theories about gift exchange among different groups around the world, his work, “The Gift,” described the relationship forged between the gift giver and the recipient. He explained that gifts are much more than objects, they represent moral links between people. Gifts become an obligation, whether bad or good, and the reciprocity that follows serves as a basis of social relationships.
Clifford Geertz (19262006)
Clifford Geertz was an American anthropologist who earned fame for his work on symbolic (or interpretive) anthropology. His unique focus was to analyse not just the form of cultural objects, but what those objects actually meant to specific groups of people. Geertz’s field work led to his theory that “things” within a culture can hold important symbolic meaning and help to form perspectives about the surrounding world. This can be seen in his oftencited essay “Deep Play: Notes on the Balinese Cockfight” in which Geertz describes the intricate symbolic meaning of the cock fighting in Bali, how it represents cultural ideas of masculinity and even how it creates a sort of microcosmic representation of their society. He became a pioneer in the use of “thick description” to explain his research methods, which aims to describe actions and subjects while recognizing their context and deeper meaning. His work “The Interpretation of Culture” is still a major resource of anthropological thought and teaching today.
Edward Sapir (18841939)
Edward Sapir was a PrussianAmerican anthropologist and linguist widely considered one of the most important contributors to the development of the discipline of linguistics. A student of Boas (see below) Sapir was able to develop the relationship between linguistics and anthropology. Sapir was interested in the ways that language and culture influence each other, and the relation between linguistic differences and differences in cultural world views. Sapir also emphasised the importance of psychology in anthropological thought; the nature of relationships between individuals is important for understanding cultural development. One of Sapir’s major contributions to linguistics is his classification of indigenous languages of the Americas.
Bronisław Malinowski (18841942)
Malinowski was one of the most important anthropologists of the 20th century and is most famous for his emphasis on the importance of fieldwork and participant observation. Malinowski’s ideas were a great influence and contributed to the building of modern anthropological methodology. His stress of the importance of fieldwork and in particular the concept of participant observation marked the shift from the era of so called ‘armchair anthropologists. He spent several years studying the indigenous people of the Trobriand Islands, Melanesia, and published his main work in 1922, titled ‘Argonauts of the Western Pacific’. This has become one of the most widely recognised texts in anthropology (ask any anthropology student!), and his ideas about immersion being the best way to observe a culture are of course still poignant today.
Lewis Henry Morgan (18181881)
Although he began his professional life as a lawyer, his research in the Iroquois and other Native American peoples became his main focus. He developed a particular interest in the way that people who were related interact and refer to each other and in turn how that affects relationships and overall society (this is also known as kinship systems). Morgan’s field work and travels brought him to his theory of “social evolution”, which he explained could be classified into three stages, “savagery, barbarism and civilization,” laid out in his 1877 book, “Ancient Society”. He suggested that humans follow a social progression which parallels surpluses of food and advancements in collecting that food.
Eric Wolf (19231999)
Wolf was influenced by Marxist ideals and his work soon earned him attention, he was sent to gather data in rural areas of Puerto Rico, and later research took him to Mexico and Europe, where he observed peasant societies. He argued that culture needs to be studied from a global perspective and also stressed that culture, including that of nonWestern people, is dynamic (doesn’t stay the same for long). In his book, “Europe and the People Without History,” Wolf theorized that as European society grew, affecting natives throughout areas such as Africa and the Americas, the aboriginal communities’ behaviours and practices changed as well. He argued that as powerful (capitalistic) nations expanded into new lands, the expansion inevitably caused a reaction within the native people and eventually changed their habits and ways of relating to each other.
Claude LéviStrauss (19082009)
Claude LéviStrauss is regarded as one of the most famous, respected and important social anthropologists of all time. He’s known as the “founder of structuralism” and made a name for himself far beyond the world of academia and his circle of anthropologists. He applied theories of structural linguistics to the field of anthropology and gained fame for a new way of thinking called structuralism. He put forward the idea that there are
worldwide unconscious structures, or laws, that exist in everything that we do (for example, rituals, mythologies and kinship), and this gives us the means to compare and analyse cultures. His fourvolume work, “Mythologiques,” examined the structure and duality of tribal myths throughout the Americas and their influence on culture. Some of his other notable works include “Tristes Tropiques” (“A World on the Wane”) and “Le Pensée Sauvage”(“The Savage Mind”).
Ruth Benedict (18871948)
Benedict was one of the first women to earn international recognition for her work in anthropology andfolklore and made huge progress in her research regarding culture and personality. She studied tribes in the American South West, and this research served as the basis for her hugely popular book, “Patterns of Culture.” She explored the connection between culture and the individual and emphasised that understanding traditional cultures could help us understand modern man. She worked as a graduate student with Franz Boas (see below) forming close bonds with him and Margaret Mead (also below).
Margaret Mead (19011978)
Margaret Mead is often regarded as the original rebel anthropologist of the United States, her easytofollow style of writing, controversial research regarding sex and outspoken personality heightened her fame even beyond the world of anthropology. Her research brought her to the South Pacific, specifically Samoa, where she suggested that culture, not just biology, has an impact adolescent behaviour (this was published in her first book, “Coming of Age in Samoa”). Through close observation of Samoan children, and the ease with which they entered adulthood, Mead came to the conclusion that teenage angst and stress had more to do with external factors than anything internal. She continued to return to Samoa for research, but also collected information in Papua New Guinea and Bali and this breadth of information led her to publish more than 30 books and hundreds of other works. Her openness about her own methodologies as well as her addressing of sensitive research topics such as sexuality, made her one of the most talked about anthropologists and read authors in the world.
Franz Boas (18581942)
Franz Boas is known as “the father of modern cultural anthropology”. He contributed to the establishment of an anthropology department at Columbia University that taught some of the world’s most promising students (including Ruth Benedict and Margaret Mead). He helped to challenge outdated beliefs and demystified advanced theories that allowed the development of entirely new and innovative ways of observing and analysing the human race. Unlike some of his peers at the time, Boas conducted research whilst considering the perspectives of other sciences, including linguistics, ethnology and even statistics, and spent time studying the Eskimos of the Canadian Arctic and Native Americans along the northern Pacific coast. Boas was a pioneer within the field of anthropology, pointing out that the individual is only as important as their social group, and that cultural settings affect people differently (even those of the same descent). He is often celebrated for refuting the notion of Western superiority with his theory of relativism, and was able to apply his theories practically in the form of disproving racist beliefs of the time.
Edward Burnett Tylor (18321917)
Tylor was a British anthropologist who many consider the founder of cultural anthropology. Tylor argued that people in different locations were all equally capable of progressing through culture in stages from savagery through barbarism and then to civilisation, and that “primitive” groups had reached their position by learning, not unlearning. His most widely recognised works, Primitive Culture (1871) and Anthropology (1881), defined the context of the scientific study of anthropology based on evolutionary theories (you can read more about social evolutionism here) which are now outdated but laid the foundations for anthropology as a science today. He also brought the theory of animism forward into common anthropological thought; he believed that animism was the first phase of development for religions.
Mary Douglas (19212007)
Mary Douglas was a British anthropologist whose interest lay with comparative religion, and is known for her writings on symbolism and culture. Her reputation was established by her book ‘Purity and Danger‘ (1966) which analyses ideas of ritual purity and impurity within different societies, and is considered a key text in social anthropology. Her concept of groupgrid was introduced in ‘Natural Symbols‘ (1970) and later refined into the foundations of cultural theory. Douglas also contributed to the creation of the Cultural Theory of risk and has also become known for her interpretation of the book of Leviticus.
Edmund Leach (19101989)
Another British anthropologist, Leach’s work inhabited a gap between structuralfunctionalism (see Radcliffe Brown) and structuralism, although he always considered himself a functionalist. Despite this, Leach worked extensively with LéviStrauss’ writings, and his book ‘Lévi Strauss’ has become used by many as a way of engaging with LéviStrauss’ work without having to navigate the often overcomplicated language. Leach’s first book was ‘Political Systems of Highland Burma’ (1954) which challenged theories of social structure and cultural change, and criticised generalisations about political systems in different societies. Leach also engaged critically with contemporary ideas on kinship systems, disagreeing especially with several aspects of Lévi Strauss’ kinship theory outlined in ‘Elementary Structures of Kinship’. Leach argued that kinship was in fact a flexible concept which shared commonalities with language structures, both in terms for kin and also the fluid nature of language and meaning.
Edward Evan (E.E.) Evans Pritchard (19021973)
EvansPritchard was Professor of Social Anthropology at the University of Oxford from 1946 to 1970. His most widely recognised work was based on fieldwork done among the Azande people of the upper Nile in 1926, and resulted in his classic text ‘Witchcraft, Oracles and Magic Among the Azande’ (1937). Later EvansPritchard began developing RadcliffeBrown’s program of structural functionalism and as a result his work on the Nuer (‘The Nuer’, ‘Nuer Religion’, and ‘Kinship and Marriage Among the Nuer’) and ‘African Political Systems’ have become classic texts in British social anthropology. In 1965, he published ‘Theories of Primitive Religion’ which argued against existing theories of what were then called “primitive” religious practices and also became a highly influential text. Some notable anthropologists who studied under EvansPritchard include Mary Douglas and Talal Asad.
Victor and Edith Turner (19201983)
Victor Turner was a Scottish anthropologist whose work is most often referred to as symbolic and interpretive anthropology. He spent much of his career studying the Ndembu tribe of Zambia, and his theoretical interest lay in the exploration of rituals. In his later career Turner shifted his attention and applied his studies of ritual practice to world religions and religious heroes. Turner is also known for expanding theories on the liminal phase, the transition state between states of being, by building on the work of Van Gennep which put forward that liminality consisted of a preliminal phase (separation), a liminal phase (transition), and a postliminal phase (reincorporation). Victor Turner was also married to Edith Turner, who worked alongside her husband on many projects and became a successful anthropologist in her own right, continuing to develop their topics after her husband’s death. Some of the Turner’s most notable work includes: ‘The Forest of Symbols: Aspects of Ndembu Ritual’ (1967); ‘Image and Pilgrimage in Christian Culture’ (1978), and ‘Liminality, Kabbalah, and the Media’ (1985).
Alfred R. RadcliffeBrown (18811955)
RadcliffeBrown was a British anthropologist widely considered the founder of the theory of structural functionalism and coadaptation. Originally trained in psychology he was greatly influenced by the work of Émile Durkheim and his studies of social function examine how customs aid in maintaining the overall stability of a society.
RadcliffeBrown travelled to the Andaman Islands and Western Australia to conduct fieldwork, these experiences serving as the inspiration for his later books The Andaman Islanders (1922) and The Social Organization of Australian Tribes (1930). In 1920 moved to Cape Town to become professor of social anthropology, founding the School of African Life, and later also founded the Institute of Social and Cultural Anthropology at Oxford.
Marvin Harris (19272001)
Harris was an American anthropologist, and was highly influential in the development of the theory of cultural materialism. He often focused on Latin America, but also focused on the Islas de la Bahia, Ecuador, Mozambique, and India where his research spanned the topics of evolution, culture, and race. Published in 1968, Harris’ ‘The Rise of Anthropological Theory’ (affectionately known as “The RAT” among graduate students) critically examined classical and contemporary macrosocial theory to construct new understanding of human culture that Harris came to call Cultural Materialism. Several of Harris’ other publications explore the cultural and material roots of dietary traditions in many cultures, his publications including: ‘Cows, Pigs, Wars, and Witches: The Riddles of Culture’ (1975); ‘Good to Eat: Riddles of Food and Culture’ (1998) and his coedited volume, ‘Food and Evolution: Toward a Theory of Human Food Habits’ (1987). Throughout his career, Harris helped to focus anthropological interest into culturalecological relationships.
Roy Rappaport (19261997)
Rappaport was an American anthropologist known for his contributions to the study of ritual and to ecological anthropology. His text, ‘Pigs for the Ancestors: Ritual in the Ecology of a New Guinea People’ (1968), is an ecological account of ritual among the Tsembaga Maring of New Guinea, and is often considered the most influential and most cited work in ecological anthropology. In this text Rappaport coined the distinction between a people’s cognized environment (how a people understand the effects of their actions in the world) and their operational environment (how an anthropologist interprets the environment through measurement and observation). Throughout his work Rappaport was interested in how ecosystems maintained themselves through regulatory force, and he aimed to show that this was done through adaptive cultural forms that maintain preexisting relationship with the environment.
Marshall Sahlins (1930present)
Sahlins is an American anthropologist best known for his ethnographic work in the Pacific and for his contributions to anthropological theory.He is known for theorising the interaction of structure and agency and his demonstrations of the power that culture has to shape people’s perceptions and actions. One of his most widely recognised text, ‘Stone Age Economics’ (1972) collects some of Sahlins’s key essays in substantivist economic anthropology. The substantivist approach puts forward the idea that economic life is produced through cultural rules that govern the production and distribution of goods, so any understanding of economic life has to start with cultural principles, not from the assumption that the economy is made up of independently acting, “economically rational” individuals. Hiss most famous essay from the collection, “The Original Affluent Society,” builds on this theme through an in depth exploration of huntergatherer societies. Other notable publications by Sahlins include: ‘Culture and Practical Reason’ (1976); ‘The Use and Abuse of Biology: An Anthropological Critique of Sociobiology’ (1976), and ‘Islands of
History’ (1985).
Nancy ScheperHughes (1944 present)
ScheperHughes is an American anthropologist known for her writing on the anthropology of the body, hunger, illness, medicine, psychiatry, mental illness, social suffering, violence and genocide. In 2009 her investigation of an international ring of organ sellers based in New York, New Jersey and Israel led to a number of arrests by the FBI. Her first book ‘Saints, Scholars and Schizophrenics: Mental Illness in Rural Ireland’ (1979), won the Margaret Mead Award from the Society for Applied Anthropology in 1980 and established her ability to provoke controversy through her writing. She has also discussed the challenges and ethics of ethnography, which are issues of growing importance as anthropologists are increasingly working in communities that can read and critique their work. She has also worked extensively as an activist and with social movements in Brazil (in defence of rural workers, against death squads, and for the rights of streetchildren) and in the United States (as a civil rights worker for the homeless mentally ill).
archaeologists
 Kamyar Abdi (born 1969) Iranian; Iran, Neolithic to the Bronze Age
 Aziz Ab’Saber (1924–2012) Brazilian; Brazil
 Johann Michael Ackner
 Dinu Adameșteanu
 James M. Adovasio (born 1944) USA; New World (esp. PreClovis) and perishable technologies
 Anagnostis Agelarakis (born 1956)
 Yohanan Aharoni (1919–1976) Israeli; Israel Bronze Age
 Ekrem Akurgal (1911–2002) Turkish; Anatolia
 Jorge de Alarcão (born 1934) Portuguese; Roman Portugal
 William F. Albright (1891–1971) U.S.A.; Orientalist
 Leslie Alcock (1925–2006) English; Dark Age Britain
 Susan E. Alcock (born 19??) American; Roman provinces
 Miranda AldhouseGreen (born 1947) British; British Iron Age and RomanoCeltic
 Abbas Alizadeh (born 1951) [nationality?]; Iran
 Jim Allen (born 19??) Australian; Oceania
 Sedat Alp (1913–2006) Turkish; Hittitology
 Ruth Amiran (1915–2005) Israeli; Tel Arad
 David G. Anderson (born 1949) American?; eastern North America
 Manolis Andronicos (1919–1992) Greek; Greece
 Remzi Oğuz Arık (1899–1954) Turkish; early Bronze Age Anatolia^{[1]}
 Mikhail Artamonov (1898–1972) Russian/Soviet; Khazar (Central Asia)
 Khaled alAsaad (1934–2015) Syrian; Palmyra
 Mick Aston (1946–2013) English; popularizer
 Richard J. C. Atkinson (1920–1994) English; England
 Frédérique AudoinRouzeau (born 1957) French
 Anthony Aveni (born 1938) American; archaeoastronomy
 Nahman Avigad (1905–1992) Israeli; Jerusalem, Massada
 Massoud Azarnoush (1946–2008) Iranian; Sassanid archaeology
 Churchill Babington (1821–1889) English; classical archaeology
 Paul Bahn (born 19??) English; prehistoric art (rock art), Easter Island
 Geoff Bailey (born 19??) English; paleoeconomy, shell middens, coastal archaeology, Greece
 Adolph Francis Alphonse Bandelier (1840–1914) American; American SouthWest, Mexico
 Rakhaldas Bandyopadhyay (1885–1930) Indian; Mohenjodaro, Harappa culture
 Ranuccio Bianchi Bandinelli (1900–1975) Italian; Estruscans & art
 Luisa Banti (18941978) Italian; Etruscology
 Taha Baqir (1912–1984) Iraqi; deciphered SumeroAkkadian mathematical tablets, Akkadian law code discoveries, Babylonia, Sumerian sites
 Pessah BarAdon (1907–1985) Israeli; Israel (Bet Shearim, Tel Bet Yerah, Nahal Mishmar hoard)
 Gabriel Barkay (born 1944) Israeli; Israel (Jerusalem, burials, art, epigraphy, glyptics in the Iron Age, Ketef Hinnom)
 Philip Barker (1920–2001) British; excavation methods, historic England
 Ofer BarYosef (born 1937) Israeli; Palaeolithic and Neolithic sites
 Thomas Bateman (1821–1861) English; England (Derbyshire)
 Leopoldo Batres (1852–1926) Mexican; MesoAmerica (Teotihuacan, Monte Albán, Mitla La Quemada, Xochicalco)
 Gertrude Bell (1868–1926) English; adventurer and Middle Eastern archaeologist, formed the Baghdad Archaeological Museum (now Iraqi Museum)
 Giovanni Battista Belzoni (1778–1823) Italian/Venetian /?Dutch; Egypt
 Erez BenYosef (born 19??); Israeli; archaeometallurgist;
 Crystal Bennett (19181987) British; Jordan
 Dumitru Berciu
 Lee Berger (born 1965) American; paleoanthropology
 Gerhard Bersu (1889–1964) German; Europe (England etc.)
 Charles Ernest Beule (1826–1874) French; Greece
 Paolo Biagi (born 1948) Italian; Eurasian Mesolithic and Neolithic, Pakistan prehistory
 Geoffrey Bibby (19172001) British; Arabia
 Clarence Bicknell (1842–1918) British; cataloged petroglyphs at Vallée des Merveilles, France
 Martin Biddle (born 1937) British; medieval and postmedieval archaeology in Great Britain
 Manfred Bietak (born 1940) Austrian; Egypt
 Fereidoun Biglari (born 1970) Iranian Kurdish; Paleolithic
 Lewis Binford (1930–2011) American; theory
 Hiram Bingham (1875–1956) American; discovered Machu Picchu
 Flavio Biondo (1392–1463) Italian; Rome
 Avraham Biran (1909–2008) Israeli; Near East (Israel (Tel Dan))
 Glenn Albert Black (1900–1964) American; US MidWest
 Carl Blegen (1888–1971 American; Troy
 Elizabeth Blegen (1888–1966) American; Greece, educator
 Frederick Jones Bliss (1857–1939) American; Palestine
 Bayar Dovdoi (1946–2010) Mongolian; Mongolia
 Giacomo Boni (1859–1925) Italian; Roman architecture
 François Bordes (1919–1981) French; paleolithic, typology, knapping
 Stephen Borhegyi (1921–1969) American; MesoAmerica^{[2]}
 Jacques Boucher de Crèvecœur de Perthes (1788–1868) French; France
 Jole Bovio Marconi (1897–1986) Italian; Neolithic Sicily
 Richard Bradley (born 1946) British; prehistoric Europe (especially Britain)
 Linda Schreiber Braidwood (1909–2003) American; Near East
 Charles Etienne Brasseur de Bourbourg (1814–1874) French; MesoAmerica
 James Henry Breasted (1865–1935) American; Egypt
 Adela Breton (1849–1923) British; Mexico
 Eric Breuer (born 1968) Swiss; Roman/Medieval chronology
 Jacques Breuer (born 1956) Belgian; Roman and Merovingian Belgium
 Robert Brier (born 1943) American; Egypt paleopathology
 Patrick M.M.A. Bringmans (born 1970) Belgian; Palaeolithic Archaeology & Paleoanthropology
 Srečko Brodar (1893–1987) Slovene; Upper Paleolithic
 Mary Brodrick (c. 1858–1933) English; Egyptology
 Myrtle Florence Broome (c. 1888–1978) English; Egyptology, illustrator
 Don Brothwell (19332016) British; paleopathology
 Elizabeth Brumfiel (1945–2012) American; Mesoamerica
 Hallie Buckley (born 19??) New Zealand; bioarchaeology
 Aubrey Burl (born 1926) British; British megalithic monuments
 Karl Butzer (born 1934) American; environmental archaeology
 Errett Callahan (born 1937) American; experimental archaeology
 Frank Calvert (1828–1908) English; Troy
 Elizabeth Warder Crozer Campbell (1893–1971) American; California
 Luigi Canina (1795–1856) Italian; Italy (Tusculum, Appian Way)
 Gheorghe I. Cantacuzino (b. 1938)
 Bob Carr (born 1947) American; Florida historic Indians
 Martin Carver (born 1941) British; Early Middle Ages in Northern Europe, Sutton Hoo
 Howard Carter (1874–1939) English; Egypt
 Alfonso Caso (1896–1970) Mexican; Mexico
 C. W. Ceram (1915–1972) German; popularizer
 Dilip Chakrabarti (born 19??) Indian?; South Asian archaeology (especially archaeological geography of the Ganges Plain)
 John Leland Champe (1895–1978) American?; archaeology of the Great Plains
 JeanFrançois Champollion (1790–1832) French; Egypt
 Kwangchih Chang (1931–2001) Chinese/Taiwanese; China
 Arlen F Chase (born 1953) American?; Mesoamerica
 Diane Zaino Chase (born 1953) American; Mesoamerica
 George Henry Chase (1874 – 1952) American; Heraion of Argos
 Alfredo Chavero (18411906) Mexican; Mexico
 Chen Mengjia (1911–1966) Chinese; China
 John F. Cherry (born 19??) Welsh; Aegean prehistory
 Vere Gordon Childe (1892–1957) Australian; Europe / neolithic
 Choi Monglyong (born 1946) Korean; Korea (Mumin pottery period)
 Leopoldo Cicognara (1767–1834) Italian; Italy
 Muazzez İlmiye Çığ (born 1914) Turkish; Sumerology
 Bob Clarke (Historian) English; Prehistoric and Modern Era
 David Clarke (1937–1976) English; theory
 John Desmond Clark (1916–2002) English; Africa
 Stephen Clarke (born 19??) Welsh; Wales
 Grahame Clark (1907–1995) British; Mesolith and economy
 Albert Tobias Clay (1866–1925) American; Assyriology
 Eric H. Cline (born 1960) Ancient Near East, Aegean prehistory
 FayCooper Cole (1881–1961) American; U.S. MidWest
 John M. Coles (born 1930) British; wetland archaeology, Bronze Age archaeology, experimental archaeology^{[3][4]}
 Donald Collier (1911–1995) American; Ecuadorian and Andean archaeology
 John Collis (born 1944) English; Iron Age Europe
 Sir Richard Colt Hoare (1758–1838) English, England
 Margaret Conkey (born 19??) France / paleolithic
 Robin Coningham (born 1965) British; South Asian archaeology and archaeological ethics
 Niculae Conovici
 Gudrun Corvinus (1931–2006?) German; India/Nepal/Africa
 George Cowgill (born 19??) American; Mesoamerica (Teotihuacan)
 O.G.S. Crawford (1886–1957) English; aerial archaeology
 Roger Cribb (1948–2007) Australian; Turkish Kurds & Australian Aborigines
 Ion Horaţiu Crişan (1928–1994)
 Joseph George Cumming (1812–1868) English; Isle of Man
 Barry Cunliffe (born 1939) British; Iron Age Europe, Celts
 Ben Cunnington (1861–1950) English; prehistoric England (Wiltshire)
 Maud Cunnington (1869–1951) Welsh; prehistoric Britain (Salisbury Plain)
 William Cunnington (1754–1810) English; prehistoric Britain (Salisbury Plain)
 James Curle (1861?–1944) Scottish; Roman Scotland (Trimontium), Gotland^{[5]}
 Florin Curta
 Ernst Curtius (1814–1896) German; Greece
 Clive Eric Cussler (born 1931) American; underwater archaeology
 Constantin Daicoviciu
 George F. Dales (1927–1992) American; Nippur, Indus valley civilizations
 Ahmad Hasan Dani (1920–2009) Pakistani; South Asian archaeology
 Glyn Daniel (1914–1986) Welsh; European Neolithic; popularization of archaeology
 Ken Dark (born 1961) British; Roman Europe
 Theodore M. Davis (1837–1915) American; Egypt
 William Boyd Dawkins (1837–1929) British; antiquity of man
 Touraj Daryaee (born 1967) Iranian; ancient Persia (Iran)
 Janette Deacon (born 1939) South African; rock art, heritage management
 Hilary Deacon (1936–2010) South African; African; antiquity of man
 James Deetz (1930–2000) American; Historical Archaeology
 James P. Delgado (born 1958) American; maritime archaeologist
 Robin Dennell (born 1947) British; prehistoric archaeologist
 Donald Brian Doe (19202005) British; Arabia
 Louis Felicien de Saulcy (1807–1880) French; Holy Land
 Jules Desnoyers (1800–1887) French; antiquity of man
 Rúaidhrí de Valera (1916–1978) Irish; megalithic tombs in Ireland
 Dragotin Dežman (1821–1889) Slovenian; Ljubljana Marshes, Iron Age in Lower Carniola
 Adolphe Napoleon Didron (1806–1867) French; Medievalist, Christian iconography
 Tom D. Dillehay (born 19??) AmericanChilean; ethnoarchaeologist, early occupation of the Americas
 Mihail Dimitriu
 Kelly Dixon (born 19??) American; historical archaeology of the American West
 Brian Dobson (1931–2012) British; Hadrian’s Wall, the Roman Army
 Dong Zuobin (1895–1963) Chinese/Taiwanese; oracle bones, Yinxu
 Wilhelm Dörpfeld (1853–1940) German; Greece
 Trude Dothan (born 1922) Austrian, Israel
 Hans Dragendorff (1870–1941) German; Roman ceramics
 Robert Dunnell (1947–2010) American; theory, U.S. MidWest
 Louis Dupree (19251989) American; Afghanistan
 E. C. L. During Caspers (1934–1996) Dutch; Prehistoric Mesopotamia, South Asian, and the Persian Gulf
 Elizabeth Eames (1918 – 2008) British; specialist in English medieval tiles
 Amelia Edwards (18311892) British; Egypt
 Kenan Erim (1929–1990) Turkish; Hellenistic Anatolia
 Ufuk Esin (1933–2008) Turkish; prehistoric Anatolia, archaeometry
 Sir Arthur Evans (1851–1941) British; Aegean archaeology (Minoan studies, Knossos, Linear A and B)
 Sir John Evans (1823–1908) English; British archaeology
 Georg Fabricius (1516–1571), German; Roman epigraphy
 Brian M. Fagan (born 19??) generalist, popularist, history of archaeology
 Panagiotis Faklaris (born 1950) Greek; classical archaeology, excavator of Vergina
 Rev. Bryan Faussett (1720–1776) English; AngloSaxon Kent (England)
 Carlo Fea (1753–1836) Italian; Roman archaeology, archaeological law
 Gary M. Feinman (born 1951) American; Mesoamerica, Oaxaca
 Sir Charles Fellows (1799–1860) British; Asia Minor
 Karl Ludwig Fernow (1763–1808) German; Roman archaeology
 J. Walter Fewkes (1850–1930) American; southWest USA (Hohokam; Pueblo, pottery)
 Israel Finkelstein (born 1949) Israeli; Bronze Age & Iron Age in Israel, Megiddo (Israel)
 George R. Fischer (born 1937) American; underwater archaeology
 Peter M. Fischer (born 19??) AustrianSwedish; Eastern Mediterranean, Near East
 Cleo Rickman Fitch (19101995) American; Roman archaeology
 William W. Fitzhugh (born 1943) American; circumpolar archaeology
 Kent Flannery (born 1934) American; Mesoamerica
 James A. Ford (1911–1968) American; Southeastern United States
 Alfred Foucher (1865–1952) French; Afghanistan (Gandahar art)
 Cyril Fox (1882–1967) English; Wales
 William Flinders Petrie (1853–1942) English; Egyptology, methodology
 George Frison (born 1924) American; Paleoindian archaeology, lithic tools
 Gayle J. Fritz (born 19??) American; paleoethnobotany, agriculture in North America
 Honor Frost (1924–2010) British; maritime archaeology, Mediterranean, stone anchors
 Christopher Gaffney (born 1962) British; geophysics
 Vincent Gaffney (born 1958) British; landscape archaeology
 Antoine Galland (1646–1715) French; numismatics, Middle East
 Thomas Gann (1867–1938) Irish; Mesoamerica, Maya
 JeanClaude Gardin (19252013) French; Bactria, theory in archaeology
 Percy Gardner (1846–1937) English; Classical archaeology
 Dorothy Garrod (1892–1968) British; Paleolithic
 Yosef Garfinkel (born 1956) Israeli; Israel
 John Garstang (1876–1954) British; Anatolia, Southern Levant
 William Gell (1777–1836) English; Classical archaeology
 Friedrich William Eduard Gerhard (1795–1867) German; Rome
 John Wesley Gilbert (1864–1923) first AfricanAmerican archaeologist; Classical
 Marija Gimbutas (1921–1994) LithuanianAmerican; Neolithic & Bronze Age
 Pere BoschGimpera (1891–1974) SpanishMexican; prehistoric Spain
 Einar Gjerstad (1897–1988) Swedish; Cyprus and Rome
 John Mann Goggin (1916–1963) American; typology, colonial Caribbean
 Albert Glock (1925–1992) American; Palestinian archaeology
 Franck Goddio (born 1947) French; underwater archaeology
 Lynne Goldstein (born 1953) American; prehistoric eastern North America; mortuary
 Albert Goodyear (born 19??) American; paleoIndians
 Ian Graham (born 1923) British; Mayans
 Boris Grakov (1899–1970) Soviet/Russian; Scythians and Sarmatians
 Kevin Greene, British; classical archaeology
 J. Patrick Greene (born 19??) British; Medieval England
 Canon William Greenwell (1820–1918) British; neolithic England
 Alan Greaves (born 1969) British; Turkey
 James Bennett Griffin (1905–1997) American; prehistoric eastern North America
 W. F. Grimes (1905–1988) Welsh; London
 Klaus Grote (born 1947) German; Lower Saxony (Germany)
 Nikolai Grube (born 1962) German; Mayan epigraphy
 Raimondo Guarini (1765–1852) Italian; Classical
 Prishantha Gunawardena (born 1968) Sri Lankan; Sri Lanka
 Guo Moruo (1892–1978) Chinese; China
 Gustaf VI Adolf of Sweden (1882–1973) Swedish; Classical
 Ion Halippa
 Robert Hall (1927–2012) American; U.S. MidWest
 Osman Hamdi Bey (1842–1911) Ottoman Turkish; Syria and Lebanon
 Robert Hamilton (1905–1995) British; Near Eastern archaeology
 Richard D. Hansen (born 19??) American; MesoAmerica
 Phil Harding (born 1950) British; Britain, flintknapping
 J.C. “Pinky” Harrington (1901–1998) American; U.S. historical archaeology
 James Penrose Harland (1891–1973) American; Aegean
 Emil Haury (1904–1992) American; Southwestern United States
 Zahi Hawass (born 1947) Egyptian; Egypt
 Christopher Hawkes (1905–1992) English; European archaeology
 Robert Heizer (1915–1979) American; California
 Edgar Lee Hewett (1865–1946) American; U.S. SouthWest, antiquities law
 Christian Gottlob Heyne (1729–1812) SaxonGerman; Classics
 Eric Higgs (1908–1976) English; economic archaeology
 Bert Hodge Hill (1875–19554) American; classical archaeology
 Thomas Higham, New Zealand; radiocarbon dating
 Ida Hill (1874–1958) American; classical archaeology
 Peter Hinton (born 19??) British; England
 Yizhar Hirschfeld (1950–2006) Israeli; Israel (Ramat HaNadiv, Qumran)
 Ian Hodder (born 1948) English; theory
 Birgitta Hoffmann (born 1969); Gask Ridge
 Michael A. Hoffman (1944–1990) American; Egyptology
 Frederick Webb Hodge (1864–1956) American?; North American Indians
 Frank Hole (born 193?) American; Near East
 Vance T. Holliday (born 19??) American?; Paleoindian and Great Plains geoarchaeology and archaeology
 John Horsley (1685–1732) British; Roman Britain
 Youssef Hourany (born 1931) Lebanese; archeologist
 Huang Wenbi (1893–1966) Chinese; China
 August Wilhelm Hupel
 John Hurst (1927–2003) British; English medieval archaeology
 Elinor Mullett Husselman (1900–1996) American; Coptic Historian, papyrologist
 Richard Indreko (19001961)Estonian; Estonia
 Glynn Isaac (1937–1985) South African; African paleoanthropology
 Cynthia IrwinWilliams (1936–1990) American; Southwestern archaeology
 Otto Jahn (1813–1869) German; classical world (art)
 Jacques Jaubert (born 19??) French; lower and middle Paleolithic, lithic technology
 Thomas Jefferson (1743–1826) US President; Virginia prehistory
 Jesse D. Jennings (1909–1997) USA; New World
 Llewellyn Jewitt (1816–1886) English; British antiquities
 Donald Johanson (born 1943) American; paleoanthropology, Ethiopia
 Jotham Johnson (1905–1967) American; Minturno (Italy), past president of the Archaeological Institute of America
 Rhys Maengwyn Jones (1941–2001) Welsh/Australian; Tasmania
 Chris Judge (19??) American; eastern U.S. (Woodland, Mississippian)
 Jonathan Joestar
 Seifollah Kambakhshfard (19292010) Iranian; Iron Age; Temple of Anahita
 Alice Beck Kehoe (born 1934) American; North America: early contact
 Eduard von Kallee (1818–1888) German; Germany: found 4 Roman castra on the Limes Germanicus
 Richard Kallee (1854–1933) German; studied 102 Alemannic tombs
 J. Charles Kelley (1913–1997) American; northwest Mexico
 Arthur Randolph Kelly (1900–1979) American; Southeastern USA
 Jonathan Mark Kenoyer (1952) American; Indus Valley Civilization
 Kathleen Kenyon (1906–1978) English; Britain, Near East (Jericho)
 Alfred V. Kidder (1885–1963) American; southwestern USA, Mesoamerica
 T.R. Kidder American?; geoarchaeology and archaeology of Southeastern United States
 Kristian Kristiansen (born 1948) Danish; Bronze Age Europe, heritage studies, archaeological theory
 Kim Wonyong (1922–1993) (south) Korean; Korea
 Athanasius Kircher (1602–1680) German; Egyptian hieroglyphics (“the father of Egyptology”)
 Richard Klein (born 1941) American; paleoanthropology (Africa, Europe)
 Amos Kloner (born 1940) Israeli; Talpiot Tomb (Israel), Hellenistic, Roman and Byzantine archaeology
 Sir Francis Knowles, 5th Baronet (1886–1953) English; anthropology and prehistory
 Alice Kober (1906–1950) American; Linear B
 Robert Koldewey (1855–1925) German; Near East (Babylon)
 Manfred Korfmann (1942–2005) German; Bronze Age Aegean and Anatolia (Troy)
 Gustaf Kossinna (1858–1931) German; Germany (Neolithic, Aryan concept)
 Hamit Zübeyir Koşay (1897–1984) Turkish; Early Bronze Age Anatolia
 Raiko Krauss (born 1973) German; prehistory
 Pasko Kuzman (born 1947) Macedonian; Ohrid, Macedonia
 Dorothy Lamb (1887–1967) British; classical archaeology
 Luigi Lanzi (1732–1810) Italian; Etruscans
 Pierre Henri Larcher (1726–1812) French; classical archaeology
 Donald Lathrap (1927–1990) American; South America, U.S. MidWest
 JeanPhilippe Lauer (1902–2001) French; Egypt
 Bo Lawergren (born 19??) American? ; music archaeology; Mesopotamia
 T. E. Lawrence (1888–1935) British; adventurer, Middle East
 Sir Austen Henry Layard (1817–1894) British; Middle East (Kuyunjik and Nimrud)
 Louis Leakey (1903–1972) British; archaeologist and paleoanthropologist, Africa
 Mary Leakey (1913–1996) British; archaeologist and paleoanthropologist, Africa
 Richard Leakey (born 1944) Kenyan; paleoanthropology, Africa
 Edward Thurlow Leeds (1877–1955) British; Keeper of the Ashmolean Museum 1928–1945
 Charles Lenormant (1802–1859) French; Egypt, Greece, Middle East
 François Lenormant (1837–1883) French; Assyriologist
 Mark P. Leone (born 1940) American; theory, historical archaeology
 André LeroiGourhan (1911–1986) French; theory, art, Paleolithic
 Jean Antoine Letronne (1787–1848) French; Greece, Rome, Egypt
 Gerson LeviLazzaris (born 1979) Brazilian; ethnoarchaeology
 Carenza Lewis (born 196?) British; popularizer; Medieval Britain
 Madeline Kneberg Lewis (1901–1996) American; typologist, Illustrator.
 David LewisWilliams (born 1934) cognitive archaeologist specialising in UpperPalaeolithic and Bushmen rock art
 Edward Lhuyd (1660–1709) Welsh; Britain
 Li Feng (born 1962) Chinese/American; early China
 Li Ji (Li Chi, 1896–1979) Chinese; Yinxu and Yangshao culture
 Li Xueqin (born 1933) Chinese; early China
 Mary Aiken Littauer (1912–2005) American; horses in prehistory
 Li Liu (born 1953) Chinese/American; neolithic and Bronze Age China
 Georg Loeschcke (1852–1915) German; Mycenaean pottery
 Victor Loret (1859–1946) French; Egypt
 William A. Longacre (born 1937) American; ethnoarchaeology^{[6]}
 Sir John Lubbock (1834–1913) English; terminology, evolution, generalist
 Rev. William Collings Lukis (1817–1892) British; megaliths of Great Britain and France
 Ma Chengyuan (1927–2004) Chinese; authority on ancient Chinese bronzes
 Robert Alexander Stewart Macalister (1870–1950) Irish; Palestine, Celtic archaeology
 Burton MacDonald (born 1939) Canadian; biblical archaeology
 Father John MacEnery (1797–1841) Irish; Paleolithic
 Richard MacNeish (1918–2001) American; Canada, Iroquois (U.S./Canada), MesoAmerica, discovered origins of maize
 Aren Maeir (born 1958) Israeli; Ancient Levant, Israel, Philistines
 Yousef Majidzadeh (born 19??) Iranian; Jiroft culture (Iran)
 Sadegh Malek Shahmirzadi (born 1940) Iranian; ancietn Persia (Iran)
 James Patrick Mallory (born 1945) IrishAmerican; IndoEuropean origins, protoCeltic culture
 Sir Max Mallowan (1904–1978) British; Middle East
 John Manley (born 1952) British; Roman Britain
 Marjan Mashkour
 Joyce Marcus (born 19??) American; Latin America
 AugusteÉdouard Mariette (1821–1881) French; Egypt
 Spyridon Marinatos (1901–1974) Greek; Greece, Mycenaeans
 Alexander Marshack (19182004) American; Paleolitic era
 James A. Marshall (died 2006) American; eastern North American earthworks^{[7]}
 John Hubert Marshall (1876–1958) British; Indus Valley Civilization, Taxila, Crete
 Marjan Mashkour (born 19??) Iranian; zooarchaeology
 J. Alden Mason (1885–1967) American; New World archaeology
 Gaston Maspero (1846–1916) French; Egypt
 Therkel Mathiassen (1892–1967) Danish; Arctic region
 Alfred P. Maudslay (1850–1931) British; Mayans
 Amihai Mazar (born 1942) Israeli; Israel, Biblical archaeology
 Benjamin Mazar (1906–1995) Israeli; Israel, Biblical archaeology
 Eilat Mazar (born 1956) Israeli; Jerusalem, Phoenicians
 Gaby Mazor (born 1944) Israeli; Bet She’an (Israeli)
 August Mau (1840–1909) German; Pompeii
 Charles McBurney (1914–1979) British; Britain (Upper Paleolithic), Libya, Iran, cave art
 Robert McGhee (born 1941) Canadian; Arctic
 Betty Meggers (born 1921) American; South America
 James Mellaart (19252012) British; discoverer of Çatalhöyük
 Paul Mellars (born 1939) British?; Neanderthals, European mesolithic
 Michael Mercati (1541–1593) Italian [born in Rome]; lithics
 Prosper Mérimée (1803–1870) French; French monuments
 Jerald T. Milanich (born 19??) American; U.S. southeast (Florida)
 Sir Ellis Minns (1874–1953) British; eastern Europe
 Constantin Moisil
 Oscar Montelius (1843–1921) Swedish; seriation, Europe (Scandinavia)
 Pierre Montet (1885–1966) French; Lebanon, Egypt (Tanis)
 Harri Moora
 Andrew M.T. Moore (born 19??) English; neolithic, Middle East
 Clarence Bloomfield Moore (1852–1936) American; southern United States
 Warren K. Moorehead (1866–1939) American; prehistoric eastern United States
 Sylvanus G. Morley (1883–1948) American; Mesoamerica, especially Maya
 Dan Morse (born 1935) American; Central Mississippi Valley
 Phyllis Morse (Anderson) (born 1934) American; Central Mississippi Valley
 John Robert Mortimer (1825–1911) English; England (barrows)
 Sabatino Moscati (1922–1997) Italian; Phoenicians
 Keith Muckelroy (1951–1980) British?; maritime archaeology
 John Mulvaney (born 1925) Australian; “Father of Australian archaeology”
 Margaret Murray (1863–1963) AngloIndian; Egyptologist
 Tim Murray (archaeologist) (born 19??) Australian?; history of archaeology
 Dimitri Nakassis (born 1975) American; Greece
 Ezzat Negahban (1926–2009) Iranian; Iran
 Sarah Milledge Nelson (born 1931) American; Korea, Hongshan (China), gender
 Ion Nestor
 Ehud Netzer (1934–2010) Israeli; Israel (Herodian architecture)
 Charles Thomas Newton (1816–1894) British; Classical archaeology
 Constantin S. NicolăescuPlopșor
 Christiane Desroches Noblecourt (born 1913) French; Egypt (Nubian temples)
 Francisco Nocete (born 1961) Spanish
 Ivor Noël Hume (born 1927) British?; eastern U.S. seaboard historical archaeology, method and theory of historical archaeology
 Kenneth Oakley (1911–1981) English; fluorine dating, exposed Piltdown Man hoax
 Jérémie Jacques Oberlin (1735–1806) Alsatian; France?, philology
 Alexandru Odobescu (1834 — 1895)
 Bjørnar Olsen, Norwegian; theory, material culture, Arctic
 John W. Olsen (born 1955) American; prehistory, Paleolithic, Central Asia
 Stanley John Olsen (1919–2003) American; historical archaeology and zooarchaeology
 Tahsin Özgüç (1916–2005) Turkish; Assyria
 Bertha Parker (1907–1978) Abenaki, Seneca; Southwest US archaeology and ethnology
 André Parrot (1901–1980) French; ancient Near East
 Timothy Pauketat (born 19??) American; Mississippian culture
 Vasile Pârvan (1882–1927)
 Deborah M. Pearsall (born 1950) American; paleoethnobotany (phytoliths)
 Richard J. Pearson (born 1938) Canadian; Pacific
 William Pengelly (1812–1894) British; England, paleolithic
 Peter N. Peregrine (born 1963) American; Mississippian culture, crosscultural studies
 Gregory Perino (1914–2005) American; Woodland, and Mississippian cultures in Illinois and Oklahoma
 William Matthew Flinders Petrie (1853–1942) British; Egypt, methodology, ceramic typology
 Stewart Perowne (1901–1989) British; Imadia and Beihan
 Philip Phillips (1900–1994) American; theory, eastern and central United States
 Alexandre Piankoff (18971966) Russian; Egypt^{[8]}
 Stuart Piggott (1910–1996) British; neolithic, Europe (especially Britain)
 John Pinkerton (1758–1826) Scottish; theory of Gothic superiority, Scottish protohistory
 Dolores Piperno (born 1949?) American; archaeobotany, maize, Panama
 Augustus Pitt Rivers (1827–1900) British; Britain (especially Dorset), method
 Nikolaos Platon (1909–1992) Greek; Minoan Crete
 Augustus Le Plongeon (1825–1908) BritishAmerican; photographer and antiquarian specializing in PreColumbian high cultures
 Natalia Polosmak (born 1956) Russian; Siberia: Altay: Pazyryk culture
 Alexandru Popa
 Cristian Popa
 Reginald Stuart Poole (1832–1895) English; Egypt (hieroglyphics and numismatics)
 Gregory Possehl (born 19??) American; South Asia, Indus Valley Civilization
 Timothy W. Potter (1944–2000), British; Classical archaeology
 Francis Pryor (born 1945) British; Bronze (Flag Fen, England) and Iron Ages
 Senarath Paranavithana (1896–1972) Sri Lankan; Sri Lanka
 Jules Etienne Joseph Quicherat (1814–1882) French; ancient Europe
 Philip Rahtz (born 1921) British; United Kingdom
 José Ramos Muñoz Spanish; Europe, northern Africa
 Sir Andrew Ramsay (1814–1891) Scottish; Pleistocene geology, stratigraphy
 Sir William Mitchell Ramsay (18511939) Scottish; Asia Minor and New Testament
 Katharina C. Rebay (born 1977) Austrian; Bronze & Iron Age Central Europe, mortuary analysis, gender
 William Rathje (born 1945) American; early civilizations, modern material culture studies, Mesoamerica
 Desire Raoul Rochette (1790–1854) French; Greece
 Jean Gaspard Felix RavaissonMollien (1813–1900) French; Classical sculpture
 Marion Rawson (18991980) American; classical archaeology
 Shahrokh Razmjou
 Ronny Reich (born 1947) Israeli; Jerusalem
 Colin Renfrew (born 1937) English; history of language, archaeogenetics
 Caspar Reuvens (1793–1835) Dutch; Roman archaeology in the Netherlands
 Julian Richards (born 1951) English; Stonehenge, popularizer
 Anne Strachan Robertson (19101997) Scottish; Numismatics
 Derek Roe (born 19??) British; paleolithic
 Wil Roebroeks (born 1955) Dutch, The Netherlands
 Malcolm J. Rogers (1890–1960) American; California
 John Romer (born 1941) British; Egypt, popularizer
 Jeffrey Royal (born 1964) American; Roman, maritime archaeology
 Michael Rostovtzeff (1870–1952) Ukrainian/Russian/American; Greece, Thrace, southern Russia
 Irving Rouse (1913–2006) American; Caribbean and migration
 Katherine Routledge (1866–1935) British; Easter Island
 Peter RowleyConwy (born 1951) Danish? Welsh?; environmental archaeology
 Adrian Andrei Rusu (b. 1951) Medieval archaeology, researcher at the Institute of Archaeology and Art History in ClujNapoca
 Simon Rutar (1851–1903) Slovenian; Slovenia
 Alberto Ruz Lhuillier (1906–1979) Mexican; PreColumbian MesoAmerica
 Donald P. Ryan (born 1957) American; Egypt (Valley of the Kings)
 Saad Abbas Ismail (born 1980) Kurdish; International archaeologist, Syria
 Sharada Srinivasan (born 19??) Indian; archaeometallurgy, India
 Roderick Salisbury (born 19??) American?; ideology, soil chemistry, GIS, S.E. Europe (Neolithic)
 Viktor Sarianidi (born 1929) Uzbekistani; Bronze Age, Central Asia
 Otto Schaden (born 1937–2015) American; Egypt
 Claude Schaeffer (1898–1982) French; Ugarit
 Michael Brian Schiffer (born 1947) American? (born in Canada); behavioral archaeology, method and theory
 Heinrich Schliemann (1822–1890) German; Troy, Mycenae, Tiryn
 PhilippeCharles Schmerling (1790–1836) Belgian; founder of paleontology: antiquity of man
 Carmel Schrire (born 1941) Australian; Australia, South Africa
 Francesco Scipone (1675–1755) Italian; Etruscans
 Mercy Seiradaki (19101993) English; Knossos
 Ovid R. Sellers (1884–1975) American; Biblical Old Testament
 Jean Baptiste Louis George Seroux D’Agincourt (1730–1814) French; ancient monumental art
 Alireza Shapour Shahbazi
 Michael Shanks (born 1959) English; Classical archaeology, theory
 Thurstan Shaw (born 1914) English; Africa (especially Nigeria)
 Alison Sheridan British; Bronze and Neolithic ages
 Bonggeun Sim (born 1943) South Korean; Korea
 William Robertson Smith (1846–1894) Scottish; Orientalist, Biblical scholar
 Stanley South (1928–2016) American; historical archaeology
 Janet D. Spector (1944–2011) American; North America
 E. Lee Spence (born 1947)American; marine archaeology
 Victor Spinei
 Flaxman Charles John Spurrell (1842–1915) English; prehistoric England, Egypt
 Rev. Frederick Spurrell (1824–1902) English; English archaeology (Essex and Sussex)
 Lady Hester Stanhope (1776–1839) British; Ashkelon
 Julie K. Stein, (born 19??) American; geoarchaeology and archaeology of shell middens and coastal archaeological sites
 Eunice Stebbens (1893–1992) American; Roman coins
 Marc Aurel Stein (1862–1943) Hungarian; Central Asia
 HansGeorg Stephan (born 1950) German; Medievalist, postMedieval archaeology, landscape archaeology, oven tiles
 George E. Stuart III (1935–2014) American; Mayan archaeology^{[9]}
 William Duncan Strong (1899–1962) American; Peru, U.S. MidWest, California, Honduras, seriation statistics
 Su Bai (1922–2018) Chinese; Chinese Buddhism, grottoes
 Su Bingqi (1909–1997) Chinese; ancient China
 Eleazar Sukenik (1889–1953) Israeli; Dead Sea scrolls
 Pál Sümegi (born 1960) Hungarian; environmental archaeology, Hungary
 Takaku Kenji (born 19??) Japanese; Korea^{[10]}
 Zemaryalai Tarzi (born 1939) Afghan; Afghanistan
 Joan du Plat Taylor (1906–1983) Scottish; maritime archaeology, Cyprus
 Walter Willard Taylor, Jr. (1913–1997) American; theory, Coahuila (Mexico)
 Julio C. Tello (1880–1947) Peruvian; Peru
 Alexander Thom (1894–1985) Scottish; engineer, Stonehenge
 David Hurst Thomas (born 19??), American; Spanish Borderlands, repatriation
 Julian Thomas (born 1959) British; northwest European Neolithic and Bronze Age
 J. Eric S. Thompson (1898–1975) English; Maya
 Christian Jürgensen Thomsen (1788–1865) Danish; originator of the ThreeAge System
 Christopher Tilley (born 19??) British; theory, Britain
 Tong Enzheng (1935–1997) Chinese; China
 Alfred Marston Tozzer (1877–1954) American; Mesoamerica (Maya)
 John C. Trever (19162006) American; Biblical archaeologist
 Bruce Trigger (1937–2006) Canadian; theory, comparative civilizations
 James Tuck (born 1940) American; eastern Canadian historical archaeology
 Ronald F. Tylecote (1916–1990) British; founder of archaeometallurgy
 Grigore Tocilescu (1850–1909)
 Henrieta Todorova (1933–2015) Bulgarian; Neolithic ^{[11]}
 Peter Ucko (1938–2007) British; Paleolithic art; archaeological politics
 Luigi Maria Ugolini (1895–1936) Italian; Albania
 David Ussishkin (born 1935) Israeli; Lachish, Jezreel Valley and Megiddo
 Heiki Valk
 Parviz Varjavand
 Roland de Vaux (1903–1971) French; Biblical archaeology: DeadSea Scrolls
 Marius Vazeilles (1881–1973) French; GalloRoman archaeology, Merovingian archaeology
 Alan Vince (1952–2009) British; British ceramics
 Zdenko Vinski (1913–1996) Croatian; Croatia
 Dominique Vivant Denon (1747–1827) French; Egyptian art
 Alexandru Vulpe
 Marc Waelkens (born 1948) Belgian; Turkish archaeology
 Alice Leslie Walker (1885–1954) American, classical archaeologist
 Wang Zhongshu (1925–2015) Chinese; Chinese and Japanese archaeology
 John Bryan WardPerkins (1912–1981) British; architectural history
 Charles Warren (1840–1927) British; engineer, police commissioner and Biblical archaeologist
 Helen Waterhouse (1913–1999), British; classical archaeology
 William Thompson Watkin (1836–1888), British; Roman Britain
 Patty Jo Watson (born 1932) American; North American archaeology
 Clarence H. Webb (1902–1991) American; southern United States prehistory
 Waldo Wedel (1908–1996) American; Great Plains prehistory
 Fred Wendorf (born 1925) archaeology and cultural development of arid environments
 Josef W. Wegner (born 1967) American; Egyptology
 Friedrich Gottlieb Welcker (1784–1868) German; philologist and archaeologist specializing in Greece
 Boyd Wettlaufer (1914–2009) Canadian; Father of Saskatchewan Archaeology
 Mortimer Wheeler (1890–1976) British; method, South Asia (especially the early Indus Valley), Maiden Castle (England)
 Tessa Verney Wheeler (1893–1936) British; method, British archaeology, cofounder of Institute of Archaeology
 Joyce White (born 19??) American; prehistoric Southeast Asia
 Alasdair Whittle (born 19??) European Neolithic
 Theodor Wiegand (1864–1936) German; Pergamum, aerial photography
 Malcolm H. Wiener (born 1935) American; Aegeanist, Prehistorian, President of INSTAP
 Gordon Willey (1913–2002) American; New World, method and theory
 Stephen Williams (born 19??) American; North America
 Johann Joachim Winckelmann (1717–1768) German; Hellenist art, Greek world
 Bryant G. Wood (born 1936) American; Palestine
 Peter Woodman (1943–2017), Irish; Irish Mesolithic
 Leonard Woolley (1880–1960) British; Ur in Mesopotamia
 Jens Jacob Asmussen Worsaae (1821–1885) Danish; paleobotanist, archaeologist, historian and politician, first to excavate and use stratigraphy to prove the Threeage system
 Wolfgang W. Wurster (1937–2003) German; architectural history; Mediterranean, high cultures of Peru and Ecuador
 Alison Wylie (born 19??) Canadian; philosophy of archaeology
 John Wymer (1928–2006) British; Paleolithic
 Xia Nai (1910–1985) Chinese; China
 Xu Xusheng (1888–1976) Chinese; discoverer of the Erlitou culture
 Yigael Yadin (1917–1984) Israeli; Masada, Hazor
 Inger Zachrisson (born 1936); Swedish; Sami people since the Iron Age
 Robert N. Zeitlin (born 1935) American; Mesoamerica (Zapotec), ancient political economies
 Zheng Zhenduo (1898–1958) Chinese; China
 Zheng Zhenxiang (born 1929) Chinese; discoverer of the Tomb of Fu Hao
 Irit Ziffer (born 1954) Israeli; symbols in ancient art
 Andreas Zimmermann (born 1969) German; quantitative methods
 Ezra B. W. Zubrow (born 1945) American; theory, GIS, demography, ecology, Circumpolar
 R. Tom Zuidema (19272016) American?; Incas
 Vladas Žulkus (born 1945) Lithuanian; Lithuania (Klaipėda, underwater archaeology)
 Marek Zvelebil (1952–2011) Czech; European stone age
Paleontologists
William Buckland (17841856)
Even at an early age, William Buckland found his interest in the field of paleontology. Among his contributions in the field were the following:
Key Contributions of William Buckland in Paleontology
 He wrote the first ever complete account of a dinosaur fossil.
 Later on, he called the giant reptilian organism the Megalosaurus (which will be later called as the dinosaur).
 He pioneered the used of fossilized fecal matter (called coprolites) in the reconstruction of the ideas about primitive ecosystems.
Stephen Jay Gould (19412002)
A professor at Harvard himself, Stephen Gould rose to fame in the field of paleontology during the 20th century.
Key Contributions of Stephen Jay Gould in Paleontology
 Perhaps, his greatest contribution was being the lead promoter of the theory about evolutionary change.
 His theory, better known as punctuated equilibrium, suggested that changes in fossil records are not a result of a slow and steady process but rather caused by a sporadic changes.
John Ostrom (19282005)
If you are greatly fascinated by the discovery of dinosaurs, this scientist is the one you should also give the credits to.
Key Contributions of John Ostrom in Paleontology
 In 1969, John Ostrom discovered the remains of an organism he called the “Deinonychus” which means “terrible claw“. As its name suggests, the human size animal is characterized by sharppointed claws and clutching hands.
 Years after, it was found out that this animal is a hundred and ten million year old dinosaur.
Alan Walker (1938)
Alan Walker is another great paleontologist who supposedly became interested in paleontology when he was 11 years old by examining fossils near his home.
Key Contributions of Alan Walker in Paleontology
 He studied on the very first stages of human evolution, particularly in the different epochs (Miocene, Pliocene, and Pleistocene) in the geologic time scale.
 Basically, he focused mainly on data and fossils obtained from East Africa. As a result, he was able to deduce ancient behaviors exhibited by the organisms’ biological remains.
 In addition to this, Walker discovered hundreds of fossils which include: skeleton of a young Homo erectus and a skull of an Australopithecus.
Henry Fairfield Osborn (18571935)
For 25 years, Osborn was the president of the American Museum of National History and had led the expansion of the museum in terms of research programs and its facilities.
Key Contributions of Henry Osborn in Paleontology
 In the early 20th century, Osborn rose to fame after leading various fossil hunting expeditions and after training new vertebrate paleontologists in the Western United States.
 Osborn also described and named several dinosaur species such as the Ornitholestes, Tyrannosaururs rex, Pentaceratops, and Velociraptor.
 Osborn also conducted several studies about the brains of T.rex by dissecting the fossils using a diamond chainsaw.
James Hall (18111898)
Dubbed by many as the “Father of Modern Geology”, James Hall is very much known for his work on the geosyncline principle in mountainbuilding.
Key Contributions of James Hall in Paleontology
 In this geosyncline principle, he discovered the main reason why a basin sinks–because of the gradual buildup of sediments forcing it to slowly subside.
 Aside from that, Hall also founded the famous New York Natural and History Museum.
Benjamin Franklin Mudge (18171879)
B.F.Mudge is very much known to be a collector of fossils. In fact, he was one of the very first paleontologists that documented detailed information about every fossil he found.
Key Contributions of Benjamin Franklin Mudge in Paleontology
 One of his greatest contribution in the field was his discovery of the Ichthyomis, the first “bird with teeth”.
 Together with John Parker, he founded the Kansas Academy of Science (formerly Kansas Natural History Society) in 1878.
Louis Agassiz (18071873)
A renowned American biologist and geologist, Louis Agassiz focused on living and fossil fishes on glaciers. Such discoveries founded the very basis for ichthyological (fish) identification and classification.
Key Contributions of Louis Agassiz in Paleontology
 During his time, as a result of his extensive research, Agassiz’s discoveries became another evidence that somehow disproved the theory of the “Biblical flood”.
 However, he focused too much on glaciers, being the main driving mechanism that changed the Earth’s geology, that he rejected the very idea of evolution.
John “Jack” Horner (1946)
Jack Horner’s research centered on the growth and behavior of dinosaurs. In particular, his contributions are the following:
Key Contributions of John Horner in Paleontology
 He discovered that like any other animals, dinosaurs do nurture their young. He also found that they were social animals and some can be found in groups.
 Furthermore, he found out that some dinosaurs are “unevolved” versions of other species.
 At present, he is on search of a way to reactivate dinosaur DNA in birds in order to “revive” and create modern dinosaurs.
John Fleagle (1946)
John Fleagle, by studying fossils, has extensively documented the evolutionary history and biology of higher primates including apes, monkeys, and humans.
Key Contributions of John Fleagle in Paleontology
 He worked on the functional and comparative anatomy of primates from Asia and Africa.
 He also studied primate behavioral abilities and compared their ecological roles in their communities.
Luis Alvarez (19111988)
An experimental physicist himself, Luis Alvarez also made a mark in the field of paleontology.
Key Contributions of Luis Alvarez in Paleontology
 Together with his son named Walter and colleagues, Luis Alvarez proposed the reason why dinosaurs became extinct—an destructive asteroid (the size of San Francisco) that slammed into planet Earth.
 Later, this idea was called the “Alvarez Hypothesis” in honor of their work.
Mary Anning (17991847)
Did you know that the creation of the tongue twister “She sells sea shells by the sea shore” was inspired from a paleontologist? One of the most renowned females in this field, Mary Anning is considered by many as the “Greatest Fossilist in the world”.
Key Contributions of Mary Anning in Paleontology
 Her greatest contribution was discovering the Jurassic fossils beds in Lyme Regis in Dorset. Aside from that, the London Geological Society awarded her for discovering the fossil of Ichthyosaurus.
Edwin Colbert (19052001)
As a paleontologist himself, Colbert’s expertise on the field had greatly improved after being the caretaker of the American Museum of Natural History for 40 years. Aside from that the following are Colbert’s remarkable contributions in the field of paleontology.
Key Contributions of Edwin Colbert in Paleontology
 He has led various expeditions that had excavated important dinosaur fossils like the Staurikosaurus.
 In South Africa, Colbert discovered the remains of the Lystrosaurus, a primitive therapsid (a mammallike reptile)
Charles Darwin (18091882)
When one talks about evolution, Charles Darwin is probably the first person that comes into his mind. Other Darwinian contributions in the field are the following.
Key Contributions of Charles Darwin in Paleontology
 Famous for that controversial theory, Darwin drew conclusions from the fossils and likelihood between related living organisms.
 After finalizing all the evidence he found, Darwin was able to write his book entitled On the Origin of Species by Means of Natural Selection.
George Cuvier (17691832)
Perhaps the most important person on this list, George Cuvier is referred by many as the “Father of Paleontology“. Below are just some of the reasons why.
Key Contributions of George Cuvier in Paleontology
 He was the founder of vertebrate paleontology as a separate scientific discipline.
 His contributions in the field include several research on the comparative biology of invertebrates and vertebrates.
 The principle of the endangerment and extinction of organisms also came from Cuvier.
Sociologists
#1: Emile Durkheim (18581917)
The first professor of sociology in France, Emile Durkheim is known as one of the three “fathers of sociology,” and he is credited with helping sociology be seen as actual science–which we think makes him pretty influential. He first made a splash with 1893’s “The Division of Labor in Society,” which refuted Karl Marx’s critique of industrialization. [Karl Marx is also one of the three founding fathers of sociology, but since he was born and died in the 19th century, he didn’t make this list.] Durkheim’s seminal work was introduced in his 1895 publication, “Suicide,” which pioneered the separation of social science from psychology (hence the acceptance of sociology as “legitimate science”). The work presented his research on the connection between social integration and suicide rates; in short, he theorized that individuals with low social interaction are more likely to commit suicide.
#2: Max Weber (18621920)
Along with Durkheim and Marx, Max Weber is cited as the third founding architect of sociology. Weber’s primary battle cry was the role of religion–not economics, a theory endorsed by Marx–as the catalyst of social change. His understanding of peoples’ actions emphasized the meaning or purpose behind them, and he’s famous for his theory of “Protestant Ethic,” which states that the cultural influences of the Protestant religion brought about the rise of capitalism. After the First World War, he was one of the founders of the liberal German Democratic Party.
#3: Charles Wright Mills (19161962)
C. Wright Mills is perhaps most famous for coining the phrase “power elite,” a term he used to describe the people who ran a government or organization because of their wealth and social status. This theory is usually seen as opposed to the goals of democracy, which aim for the government to be directed by the will of the masses–that is, of the entirety of the population, not just those with the money and power to achieve the political ends that benefit themselves first and foremost. Mills’ work focused on these alliances between the elites as well as the political engagement of intellectuals in the postWorld War II society.
#4: Daniel Bell (19192011)
Daniel Bell is the primary thought leader in the field of post industrialism, a concept that defines a society that has developed to a point where the service sector generates more wealth than the manufacturing sector. In such a society, the economy refocuses on providing services (like legal, science, IT, business, etc.) instead of goods; knowledge becomes a form of capital; the production of new ideas becomes the primary way to grow the economy (instead of increasing the amount of goods produced by increasing manual labor); and society becomes more capable of supporting a thriving creative culture thanks to nuanced changes in education. Bell popularized the concept in his 1973 book, “The Coming of the Post Industrial Society.”
#5: Erving Go man (19221982)
Named by fellow sociologists as one of the most influential of the 20th century, Erving Go man developed the theory of dramaturgy, which addresses the social construction of self. He believed that we are all actors playing our respective roles in everyday life, as outlined in his seminal 1959 book, “The Presentation of Self in Everyday Life.” Go man theorized that our concept of self is dependent on time, place, and audience–in other words, we work to fit ourselves to cultural norms and values in order to gain acceptance. His work on the concepts of stigma, spoiled identity, and impression management are also cited often.
#6: Michel Foucault (19261984)
Named by Times Higher Education as the most cited humanities author in 2007, Michel Foucault is known for his work in philosophy and criticism as well as sociology. Foucault is sometimes listed primarily as a philosopher, rather than a sociologist, but his contributions to the theory around the relationship of power and knowledge place him squarely in the “influential sociologists” category. He popularized the idea that institutions can use a combination of power and knowledge as a form of social control; for example, in the 18th century, unsavory members of society–the poor, sick, homeless, disagreeable–were described as “mad” and stigmatized. In this way, the powerful succeeded in defining knowledge.
#7: Jurgen Habermas (b. 1929)
A prominent German figure and an internationally respected intellectual, Jurgen Habermas has focused his work on the areas of critical theory and pragmatism. His theory of communicative rationality states that successful communication inherently leads to human rationality. It follows that if we come together in the public sphere and identify how people understand or misunderstand each other, we can reduce social conflict.
#8: Pierre Bourdieu (19302002)
Building on the work of Marx, Durkheim, Weber, and others, Pierre Bourdieu established what he called the “cultural deprivation theory,” which states that people tend to think higher class cultures are better than lower class cultures. As a result, members of the higher classes believe that members of the lower classes are to blame for their childrens’ shortcomings in learning and advancement. It follows that the higher classes’ assumptions of superiority are selfpropelling prophecies; to declare oneself better is an act of social positioning, not necessarily truth. The ruling classes, Bourdieu said, have the power to impose meaning, to instate their own cultural choices as “correct,” to declare their culture as worthy of being sought. But he cautioned that people should not assume higher classes are necessarily better; Bourdieu blamed the education system, not the values of the working class, for the gaps in the academic achievements of children (a theory that has gained traction, even after Bourdieu’s death). His most famous work is 1979’s “Distinction: A Social Critique of the Judgment of Taste.”
#9: Anthony Giddens (b. 1938)
Anthony Giddens is a prominent thinker in the field of sociology, having published at least 34 books since 1971. His contributions to sociology as a discipline have been threefold: In the ‘70s, he helped redefine the field itself through a reinterpretation of classic works on society. In the ‘80s, Giddens developed his theory of structuration–one of his biggest contributions to date and a pillar of modern sociological theory. The theory addresses a longstanding debate in social science over whether structure (recurring patterns) or agency (free choice) is the primary shaper of human behavior; Giddens theorizes that neither is prime, but that they work in conjunction and must be studied as such. Third, in the ‘90s Giddens began publishing work on his theories of modernity (the historical period marked by the move from feudalism toward capitalism and industrialization) and its relationship to globalization and politics; he suggests a Third Way that reconciles the policies of the political left and the political right in order to form a system of ethical socialism–a balance of capitalism and socialism.
#10: Gary Alan Fine (b. 1950)
An admirer of Erving Go man and a truly contemporary sociologist himself, Gary Alan Fine has made a number of contributions to the discipline in the area of social culture. His ethnographies have touched on topics of visual artists, high school debaters, restaurant establishment culture, and fantasy games like Dungeons & Dragons–all expressive cultural outlets shaped by our social system. Fine’s work focuses on how these groups give meaning to our shared experience. In addition, his work on collective experience and memory has helped clarify how reputations, rumors, and urban legends operate within our society. He’s published eight books in the past 20 years, including 2012’s “Tiny Publics: A Theory of Group Culture and Action.”
Psychologists
1
B. F. Skinner
B.F. Skinner’s staunch behaviorism made him a dominating force in psychology and therapy techniques based on his theories are still used extensively today, including behavior modification and token economies. Skinner is remembered for his concepts of operant conditioning and schedules of reinforcement.
2
Jean Piaget
Jean Piaget’s theory of cognitive development had a profound influence on psychology, especially the understanding of children’s intellectual growth. His research contributed to the growth of developmental psychology, cognitive psychology, genetic epistemology, and education reform.
Albert Einstein once described Piaget’s observations on children’s intellectual growth and thought processes as a discovery “so simple that only a genius could have thought of it.”
3
Sigmund Freud
When people think of psychology, many tend to think of Sigmund Freud. His work supported the belief that not all mental illnesses have physiological causes and he also offered evidence that cultural differences have an impact on psychology and behavior. His work and writings contributed to our understanding of personality, clinical psychology, human development, and abnormal psychology.
4
Albert Bandura
Albert Bandura’s work is considered part of the cognitive revolution in psychology that began in the late 1960s. His social learning theory stressed the importance of observational learning, imitation, and modeling.”Learning would be exceedingly laborious, not to mention hazardous, if people had to rely solely on the effects of their own actions to inform them what to do,” Bandura explained in his 1977 book “Social Learning Theory.”
5
Leon Festinger
Leon Festinger developed the theories of cognitive dissonance and social comparison. Cognitive dissonance is the state of discomfort you feel when you hold two conflicting beliefs. You may smoke even though you know it is bad for your health. His social comparison theory says that you evaluate your ideas by comparing them with what other people believe. You are also more likely to seek out other people who share your beliefs and values.
6
William James
Psychologist and philosopher William James is often referred to as the father of American psychology. His 1200page text, “The Principles of Psychology,” became a classic on the subject and his teachings and writings helped establish psychology as a science. In addition, James contributed to functionalism, pragmatism, and influenced many students of psychology during his 35year teaching career.
7
Ivan Pavlov
Ivan Pavlov was a Russian physiologist whose research on conditioned reflexes and classical conditioning influenced the rise of behaviorism in psychology. Pavlov’s experimental methods helped move psychology away from introspection and subjective assessments to objective measurement of behavior.
8
Carl Rogers
Carl Rogers placed emphasis on human potential, which had an enormous influence on both psychology and education. He became one of the major humanist thinkers and an eponymous influence in therapy with his clientcentered therapy. As described by his daughter Natalie Rogers, he was “a model for compassion and democratic ideals in his own life, and in his work as an educator, writer, and therapist.”
9
Erik Erikson
Erik Erikson’s stage theory of psychosocial development helped create interest and research on human development through the lifespan. An ego psychologist who studied with Anna Freud, Erikson expanded psychoanalytic theory by exploring development throughout the life, including events of childhood, adulthood, and old age.
10
Lev Vygotsky
Lev Vygotsky was a contemporary of some betterknown psychologists including Piaget, Freud, Skinner, and Pavlov, yet his work never achieved the same eminence during his lifetime. This is largely because many of his writing remained inaccessible to the Western world until quite recently.
It was during the 1970s that many of his writings were translated from Russian, but his work has become enormously influential in recent decades, particularly in the fields of educational psychology and child development.
While his premature death at age 38 put a halt to his work, he went on to become one of the most frequently cited psychologists of the 20thcentury.
11. Carl jung—Carl Jung
Known for
Analytical psychology
Psychological types Collective unconscious Complex
Archetypes
Anima and animus Synchronicity
Shadow
Extraversion and introversion
Carl Gustav Jung (/jʊŋ/; German: [ˈkarl ˈɡʊstaf ˈjʊŋ]; 26 July 1875 – 6 June 1961) was a Swiss psychiatrist and psychoanalyst who founded analytical psychology. His work has been influential not only in psychiatry but also in anthropology, archaeology, literature, philosophy, and religious studies. As a notable research scientist based at the famous Burghölzli hospital, under Eugen Bleuler, he came to the attention of the Viennese founder of psychoanalysis, Sigmund Freud. The two men conducted a lengthy correspondence and collaborated on an initially joint vision of human psychology.
mathematics formulas and universal constants
FORMULAS—BEAUTIFUL FORMULAS, SCIENTIFIC FORMULAS, UNIVERSAL PHYSICAL CONSTANTS
John hebert 5/13/18
CONTENTS—
Beautiful mathematics formulas
Scientific formulas
Universal physical constants
BEAUTIFUL FORMULAS
8/29/178/30/17;9/15/17;11/21/1711/22/17;12/25/17; 4/19/18
CONTENTS
 Dirac’s equation
 Einstein’s field equation
 Maxwell’s equations
 General relativity
 Special relativity
 Schrodinger’s equation
 Uncertainty principle
 Gibb’s statistical mechanics
 StephanBoltzmann law
 e=mc^2
 Laplace equation
 De broglie relationmatter wave
 Navierstokes equations
 Riemann zeta function
 Noether theorem
 Eulerlagrange equation
 Hamilton quanternion
 Standard model
 Lagrange formula
 cantor inequality
 Riemann hypothesis
 HawkingBekenstein entropy formula
 Heat equation
 wave equation
 poisson equation
 Waveparticle duality
 fundamental theorem of calculus
 Pythagorean theorem
 GaussBonnet theorem
 universal law of gravitation
 Newton’s 2nd law of motion
 kinetic energy
 Potential energy
 2nd law of thermodynamics
 principle of least action
 Spherical harmonics
 Cauchy residue theorem
 CallenSymanzik equation
 Minimal surface equation
 Euler 9 point center
 Mandelbrot set
 YangBaxter equation
 Divergence theorem
 Baye’s theorem
 logistic map
 Einstein’s law of velocity addition
 Photoelectric effect formula
 Faraday law
 Cauchy momentum equation
 De moivre’s theorem
 Fourier transform
 prime counting function
 Murphy’s law
 Summation formula
 Logarithmic spiral
 Heron’s formula
 Quadratic equation
 Euler line
 Pythagorean triple formula
 Euler’s formula
 Simplex method
 Proof of infinity of prime numbers
 Harmonic series
 Euler sums
 Cubic equation
 Quartic equation
 quintic equation
 Lorentz equation
 Eulerlagrange formula
 Euler product formula
 Eulermaclaurin formula
 Pi
 Exponent
 Natural logarithm
 Conic sections
 exponential growth or decay
 Calculation an orbit I.e. a comet
 interesting number idea 1
 interesting number idea 2
 interesting number idea 3
EQUATIONS
 1. Dirac equation
The Dirac differential equation from quantum mechanics predicted the existence of antimatter in 1928. Antimatter are particle of the same mass and spin, but have an opposite charges than their counterparts of matter.
2. Einstein field equation
The einstein field equations, or the einsteinhilbert equations is used to describe gravity classically. It uses geometry to model gravity’s effects.
3. Maxwell’s equations
James clerk maxwell formulated 4 differential equations which describes how charged particles produce an electric and magnetic force. They calculate motion of particles in electric and magnetic fields, and describe how electric charges and electric currents create electric and magnetic fields, and vice versa. The 1st equation can be used to calculate the electric field produced by a charge.
The 2nd equation calculates the magnetic field. The 3rd equation, called ampere’s law, shows how the magnetic fields circulate around electric currents and time varying electric fields. The 4th equation, named Faraday’s law, describes how the electric fields circulate around time varying magnetic fields.
4. General relativity
In 1915, Albert einstein formulated the general theory of relativity. It deals with space and time, two aspects of spacetime. Spacetime curves whenever there are gravity, matter, energy, and momentum. The general theory of relativity is centrally about the principle of equivalence. General relativity shows that light curves in an accelerating frame of reference. It also says that light will bend and it will slow down in the presence of massive amounts of matter.
5. SPECIAL RELATIVITY
The Lorentz Transformations is central to the special theory of relativity and forms its mathematical basis. The special theory of relativity says that the speed of light is the same regardless of the speed the observer travels. It also describes what is relative and what is absolute about time, space, and motion. It goes on to further calculate mass increase, length shrinkage, and how much time slows down for objects moving close to the speed of light, and that a person traveling close to the speed of light would age less than that of a stationary person.
6. Schrodinger’s equation
a differential equation that is the foundation of quantum mechanics. It is one of the most accurate theories of how subatomic particles behave. This equation describes a wave function of a particle or group of particles that have a certain value at every point in space for every given time. this function contains all the information that can be known about a particle or system. The wave function gives physical properties such as position, momentum, energy, etc as real values.
7. Uncertainty principle
This principle says that trying to measure a thing’s definite position will make its momentum less known, and viceversa.
8. GIBB’S STATISTICAL MECHANICS
Statistical mechanics, a branch of theoretical physics, uses probability theory to analyze the average behavior of a mechanical system wherein the state of the system is uncertain.
Statistical mechanics is commonly used to describe the thermodynamic behavior of large systems.
9. Stefan Boltzmann law
R=ÏƒT^{4}
where Ïƒ is the StefanBoltzmann constant, which is equal to 5.670 373(21) x 10^{8} W m^{2} K^{4}, and where R is the energy radiated per unit surface area and per unit time. T is temperature, which is measured in kelvin scale. this law is only usable for the energy radiated by blackbodies but can still be used. In quantum physics, the StefanBoltzmann law (sometimes known as Stefan’s Law) states that the black body’s radiation energy emitted from an object is directly proportional to the temperature of the object raised to the fourth power.
10. Mass energy equivalence
E=mc^2
In physics, mass energy equivalence says that any matter’s mass has an equivalent amount of energy and vice versa. these quantities are directly related to each another.
11. Laplace’s equation
In mathematics, Laplace’s equation is a secondorder partial differential equation. the harmonic functions are the solutions of Laplace’s equation, which are important in many fields of science, particularly in the fields of electromagnetism, astronomy, and fluid dynamics, where they are used to accurately describe the behavior of electric, gravitational, and fluid potentials. the Laplace equation is the steadystate heat equation when studying heat conduction.
12. DEBROGLIE RELATION/Matter wave
Î»=h/mv
Where Î» is the wavelength of the object, h is Planck’s constant, m is the mass of the object, and v is the velocity of the object. A correct alternate version of the formula is
Î»=h/p
Where p is the momentum. (Momentum equals mass times velocity). These equations asserts that matter exhibits a particlelike nature in some circumstances, and a wavelike characteristic at other times.
13. Navier Stokes equations
The Navier Stokes equations describe the motion of fluids. It results from applying newton’s 2nd law to fluid dynamics. They are very useful because they describe the physics of many things. They may be used to model weather, ocean currents, water flow in a pipe, the air’s flow around a wing, and the motion of stars inside a galaxy. The Navier Stokes equations also help with the design of aircraft and cars, the study of blood flow, the analysis of pollution, the design of power stations, and many other things. Along with Maxwell’s equations they can be used to model and study magnetohydrodynamics.
14. Riemann zeta function
Î¶(s)=âˆ‘n=1 to âˆž 1ns, Re(s)>1.
Where
Re(s) is the real part of the complex numbers. For example, if s=a+ib, then Re(s)=a. (where i^2=â1)
Riemann zeta function Î¶(s) in the complex plane. In mathematics, the Riemann zeta function, a very important function in number theory because of its relation to the distribution of prime numbers. It also has applications in other areas such as physics, probability theory, and applied statistics. The riemann hypothesis is a conjecture about the distribution of the zeros of the Riemann zeta function. the Riemann hypothesis is considered by many mathematicians to be the most important unsolved problem in pure mathematics.
15. Noether’s theorem
dX/dt=0
Emmy noether was an influential mathematician known for her landmark contributions to abstract algebra and theoretical physics.
Noether’s theorem can be stated as follows:
If a system has a continuous symmetry property, then there are corresponding quantities whose values are conserved in time.
A more complex version of the theorem involving fields states that:
To every differentiable symmetry generated by local actions, there corresponds a conserved current.
16. Euler Lagrange equation
In the calculus of variations, the Euler Lagrange equation, is a secondorder partial differential equation whose solutions are the functions for which a given functional is stationary. the Euler Lagrange equation is useful for solving optimization problems.
17. Quaternion
a + bi + cj + dk
where a, b, c, and d are real numbers, and i, j, and k are the fundamental quaternion units.
In mathematics, the quaternions are a number system which extend to the complex numbers, and are applied to in 3dimensional space. Quaternions find uses in both theoretical and applied mathematics, in particular for calculations involving 3dimensional rotations such as in 3dimensional computer graphics, computer vision and crystallographic texture analysis.
18. Standard Model (mathematical formulation) for particle physics
19. LAGRANGE FORMULA
Lagrangian mechanics reformulates classical mechanics. In Lagrangian mechanics, the trajectory of a system of particles is derived by solving the Lagrange equations. There are 2 forms of the equation the Lagrange equations of the first kind, and the Lagrange equations of the second kind.
20. CANTOR’S INEQUALITY/Cantor’s theorem
In elementary set theory, Cantor’s theorem is a basic result which states that, for any set A, the set of all subsets of A (the power sets of A, ð’«(A)) has a strictly greater cardinality than A itself. the theorem implies that there is no largest cardinal number (colloquially, “there’s no largest infinity”
21. Riemann hypothesis
The Riemann hypothesis is a mathematical conjecture. finding a proof of the hypothesis is considered by many mathematicians as one of the hardest and most important unsolved problems of pure mathematics. It is about a special function, the riemann zeta function. This function inputs and outputs complex numbers values. The inputs which give outputs of zero are called zeros of the zeta function. Many zeros have been found. And the “obvious” ones to find are the negative even integers. More have been computed and have real part 1/2. The hypothesis states all the undiscovered zeros must have real part 1/2. The functional equation also says all zeros (except the “obvious” ones) must be in the critical strip: real part is between 0 and 1. If proven, it would allow mathematicians to better describe how the prime numbers are placed among whole numbers. The Riemann hypothesis is so important and difficult to prove that the Clay Mathematics Institute has offered $1,000,000 to the first person to prove it.
22. HAWKINGBEKENSTEIN ENTROPY FORMULA
blackhole thermodynamics studies how to reconcile the laws of thermodynamics with the existence of Blackhole event horizons. It is an effort to understand the statistical mechanics of black holes has had a deep impact upon the understanding of quantum gravity, leading to the formulation of the holographic principle. The 2nd law of thermodynamics requires black holes to have entropy. If black holes had no entropy, then it would be possible to violate the second law of thermodynamics by throwing mass into the black hole. The increase of the entropy of the black hole more than compensates for the decrease of the entropy carried by the object that was absorbed by the black hole.
23. HEAT EQUATION
The heat equation is a parabolic partial differential equation that describes the distribution of heat (or variation in temperature) in a given region over time. The heat equation has basic importance in a range of scientific fields. In mathematics, such as probability theory and partial differential equations.
24. Wave equation
iâ„âˆ‚/âˆ‚tÎ¨(x,t)=H^Î¨(x,t)
where i is the imaginary number, Ïˆ (x,t) is the wave function, Ä§ is the reduced planck constant, t is time, x is position in space, Ä¤ is a mathematical object known as the Hamilton operator. Equations that describe waves as they occur in nature are called wave equations. Waves as they occur in rivers, lakes, and oceans are similar to those of sound and light. The problems describing waves come up in fields like acoustics, electromagnetic, and fluid dynamics. the problem of a vibrating string such as that of a musical instruments was studied. In quantum mechanics, the Wave function describes the probability of finding an electron somewhere in its matter wave. The wave function concept was first introduced in the schrodinger equation.
25. Poisson’s equation
âˆ‡^2Ï†=f.
(âˆ‚^2/âˆ‚x^2+âˆ‚^2/âˆ‚y^2+âˆ‚^2/âˆ‚z^2)Ï†(x,y,z)=f(x,y,z).
When f=0 identically we obtain laplace’s equation.
Poisson’s equation is a partial differential equation of elliptic type with a wide range of utility in mechanical engineering and theoretical physics. It arises, for example, in the description of the potential field caused by a given charge or mass density distribution; when the potential field is known, it allows calculation of the gravitational or electrostatic field. It is a generalization of laplace’s equation, which is also frequently seen in physics. Poisson’s equation may be solved using a green’s function.
26.Wave particle duality
in the 1700s and 1800s, there was a big argument among physicists about whether light was made of particles, or waves. Light seems to be both. Until the 20th century, most physicists thought that light was either one or the other, and that the scientists on the opposite side of the argument were wrong. Wave particle duality means that all particles show both wave and particle properties. This is a fundamental concept of quantum mechanics. Classical concepts of “particle” and “wave” do not completely describe the behavior of quantumscale objects.
27. Fundamental theorem of calculus
The fundamental theorem of calculus is fundamental in the study of calculus. This theorem shows the relationship between the derivative and the integral and between the definite integral and the indefinite integral. It has two parts, the first fundamental theorem of calculus and the second fundamental theorem of calculus. It asserts that the derivative and integral as inverse processes.
28. Pythagorean theorem
In mathematics, the Pythagorean theorem, is a statement about the sides of a right triangle. The Pythagorean theorem says that the area of a square on the hypotenuse (longest side of the triangle) is equal to the sum of the areas of the squares on the legs.
a^2+b^2=c^2.
29. Gauss Bonnet theorem
The Gauss Bonnet theorem or Gauss Bonnet formula in differential geometry is an important assertion about surfaces which connects their geometry (curvature) to their topology (the euler characteristic).
30. Newton’s law of universal gravitation
Fg=Gm1m2/r2,
Newton’s universal law of gravitation is a physical law that describes the attraction between two objects with mass.
In this equation:
F_{g} is the total gravitational force between the two objects.
G is the gravitational constant.
m_{1} is the mass of the first object.
m_{2} is the mass of the second object.
r is the distance between the centers of the objects.
In SI units, F_{g} is measured in newtons (N), m_{1} and m_{2} in kilograms (kg), r in meters (m), and the constant G is approximately equal to 6.674Ã—10^{11} N m^{2} kg
31. Newton’s 2nd law of motion
F=ma.
For a particle of mass m, the net force F on the particle is equal to the mass m times the particle’s acceleration a.
32. Kinetic energy
Kinetic energy is the energy that an object has because of its motion.
KE (joules)=(mass x velocity^2)/2
33. Potential energy
Potential energy is the energy that an object has because of its position on a gradient of potential energy called a potential field.
PE=gravity (9.81) x height x mass
34. Second law of thermodynamics
S (prime)S>=0
The second law of thermodynamics says that when energy changes from one form to another form, or matter moves freely, entropy (disorder) increases, in a closed system.
35. Principle of least action
The principle of least action can be used to obtain the equations of motion for that system. In relativity, a different action must be minimized or maximized. The principle can be used to derive newtonian, lagrangian and hamiltonian equations of motion, and even general relativity. The principle remains the focus in modern physics and mathematics, with applications in thermodynamics, fluid mechanics, the theory of relativity, mechanics, particle physics, and string theory and is a focus of modern mathematical investigation in morse theory. maupertuis principle and Hamilton’s principle are prime examples of the principle of stationary action.
36. SPHERICAL HARMONICS
In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often used to solve partial differential equations that commonly occur in science.
37. Cauchy Residue theorem
In complex analysis, the residue theorem, is a powerful tool to evaluate line integrals of analytic functions over closed curves; it can often be used to compute real integrals as well. It generalizes the cauchy integral theorem and cauchy integral formula. From a geometrical perspective, it is a special case of the generalized stoke’s theorem.
38. Callan Symanzik equation
In physics, the Callan Symanzik equation is a differential equation describing the evolution of the npoint correlation functions under variation of the energy scale at which the theory is defined. It involves the betafunction of the theory and the anomalous dimensions.
39. MINIMAL SURFACE EQUATION
In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature.
40. EULER’S 9 POINT CENTER/Ninepoint center
In geometry, the ninepoint center is a triangle center, a point defined from a given triangle in a way that does not depend on the placement or scale of the triangle. It gets its name because is the center of the 9point circle, a circle that passes through nine significant points of the triangle: the midpoints of the three edges, the feet of the three altitudes, and the points halfway between the orthocenter and each of the three vertices.
41 MANDELBROT SETS
The Mandelbrot set is an important example of a fractals in mathematics.The Mandelbrot set is essential for understanding chaos theory.
42. Yang Baxter equation
In physics, the Yang Baxter equation (or startriangle relation) is a consistency equation which was first introduced in the field of statistical mechanics. It depends on the idea that in some scattering situations, particles may preserve their momentum while changing their quantum internal states.
43. DIVERGENCE THEOREM
In vector calculus, the divergence theorem, also known as Gauss’s theorem or Ostrogradsky’s theorem, is a result that relates the flow (that is, flux) of a vector field through a surface to the behavior of the vector field inside the surface. it states that the sum of all sources (with sinks regarded as negative sources) gives the net flux out of a region. The divergence theorem is an important result for the mathematics of physics and engineering, especially in electrostatics and fluid dynamics. In physics and engineering, it is usually applied in three dimensions. However, it generalizes to any number of dimensions. In one dimension, it is equivalent to the fundamental theorem of calculus. In two dimensions, it is equivalent to green’s theorem. The theorem is a special case of the more general stoke’s theorem.
44. Bayes’ theorem
P(AB)=P(BA)P(A)P(B).
In probability theory, Bayes’ theorem shows the relation between a conditional probability and its reverse form. For example, the probability of a hypothesis given some observed pieces of evidence and the probability of that evidence given the hypothesis.
45. Logistic map
xn+1=rxn(1xn)
where xn is a number between zero and one that represents the ratio of existing population to the maximum possible population.
46. EINSTEIN’S LAW OF VELOCITY ADDITION/Velocityaddition formula
In relativistic physics, a velocityaddition formula is a threedimensional equation that relates the velocities of objects in different reference frames. Such formulas apply to successive lorentz transformations, so they also relate different frames. Accompanying velocity addition is a kinematic effect known as thomas procession, whereby successive noncollinear Lorentz boosts become equivalent to the composition of a rotation of the coordinate system and a boost. Standard applications of velocityaddition formulas include the doppler shift, doppler navigation, the aberration of light, and the dragging of light in moving water. It was observed by galilei that a person on a uniformly moving ship has the impression of being at rest and sees a heavy body falling vertically downward. This observation is now regarded as the first clear statement of the principle of mechanical relativity. The cosmos of Galileo consists of absolute space and time and the addition of velocities corresponds to composition of galilean transformations. The relativity principle is called galilean relativity. It is obeyed by newtonian mechanics. According to the theory of special relativity, the frame of the ship has a different clock rate and distance measure, and the notion of simultaneity in the direction of motion is altered, so the addition law for velocities is changed. The cosmos of special relativity consists of Minkowski spacetime and the addition of velocities corresponds to composition of lorentz transformations. In the special theory of relativity Newtonian mechanics is modified into relativistic mechanics.
47. PHOTOELECTRIC EFFECT FORMULA
The photoelectric equation involves; h = the Planck constant 6.63 x 10^{34} J s. f = the frequency of the incident light in hertz (Hz) … E_{k} = the maximum kinetic energy of the emitted electrons in joules (J)
The photoelectric effect refers to the emission of electrons or other free carriers when light is shone onto a material. Electrons emitted can be called photo electrons. It is commonly studied in electronic physics, as well as in fields of chemistry, such as quatuum chemistry or electrochemistry.
48. Faraday’s law of induction
Faraday’s law of induction is one of the basic laws of electromagnetism. The law explains the operation principles of generators, transformers and electric motors.
49. Cauchy momentum equation
The Cauchy momentum equation is a vector partial differential equation formulated by cauchy which describes the nonrelativistic momentum transport in any continuum.
50. De Moivre’s formula
The use of the process of mathematical induction can be used to prove a very significant theorem in mathematics called De Moivre’s theorem. If the complex number z = r(cos α + i sin α), then this pattern can be extended, using mathematical induction, to De Moivre’s theorem.
51. Fourier transform
The Fourier transform is a mathematical function that can be used to show the different parts of a continuous signal. It is used mostly to convert from time domain to frequency domain. Fourier transforms are frequently used to calculate the frequency range of a signal that changes over time. This kind of signal processing has many uses such as cryptography, oceanography, speech recognition, or handwriting recognition. Fourier transforms can also be used to solve differential equations. Fourier transform calculations requires understanding of integration and imaginary numbers. Computers are usually used to calculate Fourier transforms of complex signals. The Fast Fourier Transform is a method computers use to quickly calculate a Fourier transform.
52. Primecounting function
In mathematics, the primecounting function is the function counting the number of prime numbers less than or equal to some real number x. It is denoted by Ïe(x) (unrelated to the number Ie).
Number of primes in up to the number is x=x/lnx
53. MURPHY’S LAW FORMULA
Here, PM is the Murphy’s probability that something will go wrong. KM is Murphy’s constant (equal to one) and FM is Murphy’s factor, a very small number.
Murphy’s law states: “Anything that can go wrong will go wrong”.
54. SUMMATION FORMULA
In mathematics, summation (capital Greek sigma symbol: E) is the addition of a sequence of numbers; the result is their sum or total. If numbers are added in turn from left to right, any intermediate result is a partial sum. The numbers to be summed (called addends, or sometimes summands) may be integers, rational numbers, real numbers, or complex numbers. other types of values besides numbers can be added as well: vectors, matrices, polynomials and, in general, elements of any additive group (or even monoid).
55. Logarithmic spiral A logarithmic spiral, equiangular spiral or growth spiral is a special kind of spiral curve which appears often in nature. The logarithmic spiral was first described by descarte and later deeply investigated by Jakob bernoulli, who called it “the marvelous spiral”.
Logarithmic spirals in nature
In several natural phenomena one may find curves that are close to being logarithmic spirals. Here follows some examples and reasons:
The approach of a hawk to its prey. The approach of an insect to a light source. They are used to having the light source at a constant angle to their flight path. The arms of spiral galaxies. The arms of tropical cyclones, such as hurricanes. Many biological structures including spider webs and the shells of mullosks.
56. Heron’s formula
Heron’s formula states that the area of a triangle whose sides have lengths a, b, and c is
A=s(sa)(sb)(sc),
where a, b, c are the length of each of the triangle’s sides, and s is the semiperimeter of the triangle; that is,
s=(a+b+c)2.
In geometry, Heron’s formula gives the area of a triangle.
57. Quadratic equation
x=b+/ sqrt(b^24ac)/2a
A quadratic equation is an equation in the form of ax^{2} + bx + c, where a is not equal to 0. It makes a parabola (a “U” shape) when graphed on a coordinate plane.
58. Euler line
In geometry, the Euler line, is a line found from any triangle that is not equilateral. It is a central line of the triangle, and it passes through several important points determined from the triangle, including the orthocenter, the circumcenter, the centroid, the Exeter point and the center of the 9point circle of the triangle.
59. PYTHAGOREAN TRIPLES FORMULA
Euclid’s formula is a fundamental formula for generating Pythagorean triples given an arbitrary pair of integers m and n with m > n > 0. The formula states that the integers
a=m^2âˆ’n^2,
b=2mn,
c=m^2+n^2
form a Pythagorean triple
A Pythagorean triple consists of three positive integers a, b, and c, such that a^{2} + b^{2} = c^{2}. Such a triple is commonly written (a, b, c), and a wellknown example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k.
60. Euler’s formula
e^ix=cosx+isinx
Euler’s formula is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential functions. Euler’s formula is ubiquitous in mathematics, physics, and engineering. The physicist richard feynmann called the equation “our jewel” and “the most remarkable formula in mathematics”.
When
x=Ï
Euler’s formula evaluates to
e^i+1=0
which is known as ruler’s identity.
61.
Simplex method, Standard technique in linear programming for solving an optimization problem, usually one involving a function and several constraints expressed as inequalities. The inequalities define a polygonal region, and the solution is typically at one of the vertices. The simplex method is a systematic procedure for testing the vertices as possible solutions.
62. PROOF INFINITE NUMBER OF PRIME NUMBERS
Theorem.
There are infinitely many primes. Proof. Suppose that p_{1}=2 < p_{2} = 3 < … < p_{r} are all of the primes. Let P = p_{1}p_{2}…p_{r}+1 and let p be a prime dividing P; then p can not be any of p_{1}, p_{2}, …, p_{r}, otherwise p would divide the difference P–p_{1}p_{2}…p_{r}=1, which is impossible. So this prime p is still another prime, and p_{1}, p_{2}, …, p_{r} would not be all of the primes. 
63. Harmonic series (mathematics)
In mathematics, the harmonic series is the divergent infinite series:
Summation n=1 to infinity of 1/n=1+1/2+1/3+1/4+1/5+…
64. EULER SUMS
precise sum of the infinite series:
∑n=1 to ∞1/n^2=1/1^2+1/2^2+1/3^2+⋯=1.644934 or π^{2}/6
65. FORMULA FOR SOLUTION OF CUBIC EQUATION
In algebra, a cubic function is a function of the form f(x)=ax^3+bx^2+cx+d
in which a is nonzero.
Setting f(x) = 0 produces a cubic equation of the form
ax^3+bx^2+cx+d=0.
66. SOLUTION TO QUARTIC EQUATION
In algebra, a quartic function is a function of the form
f(x)=ax^4+bx^3+cx^2+dx+e,
where a is nonzero, which is defined by a polynomial of degree four, called a quartic polynomial.
The degree four (quartic case) is the highest degree such that every polynomial equation can be solved by radicals.
67. Quintic function
In algebra, a quintic function is a function of the form
g(x)=ax^5+bx^4+cx^3+dx^2+ex+f,
where a, b, c, d, e and f are members of a field, typically the rational numbers, the real numbers or the complex numbers, and a is nonzero. In other words, a quintic function is defined by a polynomials of degree five.
If a is zero but one of the coefficients b, c, d, or e is nonzero, the function is classified as either a quartic function, cubic function, quadratic function or linear function.
68. Lorentz force
In physics (particularly in electromagnetism) the Lorentz force is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge q moving with velocity v in the presence of an electric field E and a magnetic field B experiences a force
F=qE+qv —B
(in SI units).
69. Eulerlagrange formula
Lsubx(tsuby,q(t),qdot(t))d/dtLsubx(t,q(t),qdot(t))=0
In the calculus of variation, the EulerLagrange equation, Euler’s equation, or Lagrange’s equation, is a secondorder partial differential equation whose solutions are the functions for which a given functional is stationary.
70. Euler product formula In number theory, an Euler product is an expansion of a dirichlet series into an infinite product indexed by prime numbers. The original such product was given for the sum of all positive numbers raised to a certain powers proven by leonard euler. This series and its continuation to the entire complex plane would later become known as the riemann zeta function.
âˆpP(p,s)
71. Eulermaclaurin formula In mathematics, the EulerMaclaurin formula provides a powerful connection between integrals and sums. It is used to approximate integrals by finite sums, or to evaluate finite sums and infinite series using integrals and calculus. For example, many asymptotic expansions are derived from the formula, and faulhaber’s formula for the sum of powers is an immediate consequence.
72. Pi
pi=C/d
(pi is equal to the circumference divided by the diameter).
Pi is an endless string of numbers
Pi is a mathematical constant. It is the ratio of the distance around a circle to the circle’s diameter. This produces a number, and that number is always the same. This number starts 3.141592……. and continues without end, and are called irrational numbers.
The diameter is the longest straight line which can be fitted inside a circle. It passes through the center of the circle. The distance around a circle is known as the circumference. although the diameter and circumference are different for various circles, the number pi remains constant and its value never changes because the relationship between the circumference and diameter is always the same. the number pi was irrational; that is, it cannot be written as a fraction by normal standards, and it is part of the group of numbers known as transcendental, which are numbers that cannot be the solution to a polynomial equation. The properties of pi have allowed it to be used in many other areas of math besides geometry, which studies shapes. Some of these areas are complex analysis, trigonometry, and series. To find the area of a circle, use the formula (radius²). This formula is sometimes written as A=r^2, where r is the variable for the radius of any circle and A is the variable for the area of that circle.
To calculate the circumference of a circle with an error of 1 mm:
4 digits are needed for a radius of 30 meters
10 digits for a radius equal to that of the earth
15 digits for a radius equal to the distance from the earth to the sun.
73. Exponential function
In mathematics, an exponential function is a function that quickly grows. More precisely, it is the function
exp(x)=e^x, where e is ruler’s constant, an irrational number that is approximately 2.71828.
74. Natural logarithm
The natural logarithm of a number is its logarithm to the base of the mathematical constant e, where e is an irrational and transcendental number approximately equal to 2.718281828459. The natural logarithm of x is generally written as ln x, log_{e} x, or sometimes, if the base e is implicit, simply log x. The natural logarithm of x is the power to which e would have to be raised to equal x.
75. Conic sections
CONIC SECTIONS
Circle
(xg)^2+(yh)^2=radius^2
(g=x coordinate, h=y coordinate)
Parabola
y^2+/4ax
(a=x coordinate)
x^2=+/4ay
(a=y coordinate)
ellipse
x^2/a^2+y^2/b^2=1,
(a=x, b=y coordinates, or a=y, b=x coordinates)
Hyperbola
x^2/a^2y^2/b^2=1,
(a=x, b=y coordinates, or a=y, b=x coordinates)
76. Exponential growth and decay
y=A*exp^k*t
A=starting number of for example bacteria, t=length of growth time, k=constant, y=number of bacteria after t time
77. Calculating an orbit, i.e. of a comet
Calculations: orbit, period of orbit, perihelion, aphelion and eccentricity
(for example a comet)â€”
Use ellipse formula x^2/a^2+y^2/b^2=1
Then calculate from 2 coordinates in AUs with formula
x^2 x b^2 + y^2 x a^2=a^2 x b^2
find a and bÂ (the closest and furthest approaches)
Period years of orbit^3=distance (a from above)^2
Period=cuberoot(distance AUs of â above)^2
Perihelion=d=ac
c=(a^2b^2)^1/2 (c=distance from focus to center of ellipse)
aphelion=d=cb
perihelion=A x (1eccentricity)
aphelion=A x (1+ eccentricity)
A (semimajor axis)=(perihelion + aphelion)/2
eccentricity=1perihelion/A
eccentricity=aphelion/A1
To find formula for the orbit, use ellipse formula
x^2/a^2+y^2/b^2=1, then use formula
x^2 x b^2+y^2 x a^2=a^2 x b^2,
Use 2 location coordinates from the orbit, plug in one of the coordinates
Into the 2nd formula, then plug in the 2nd coordinates into the same
formula. Subtract one of the resulting formulas from the other resulting
formula, then solve for a or b with the formula that results from the
subtraction. Plug in the solution to a or b that was solved into one of the
Presubtraction formulas to find the a or b that has not been found yet.
Now, we have the a and b constants, so we plug them into the ellipse
Formula, and thus have the equation for the orbit of the stellar body,
I.e. a comet.
78. Interesting math example #1
1×1=1
11×11=121
111×111=12321
1111×1111=1234321
11111×11111=123454321
111111×111111=12345654321
Etc
79. Interesting math example #2
1×8+1=9
12×8+2=98
123×8+3=987
1234×8+4=9876
12345×8+5=98765
Etc
80. Interesting math example #3
1=.9999999
0.999
In mathematics, 0.999… (also written 0.9, among other ways), denotes the repeating decimal consisting of infinitely many 9 after the decimal point (and one 0 before it). This repeating decimal represents the smallest number no less than all decimal number 0.9, 0.99, 0.999, etc.^{[1]} This number can be shown to equal 1. In other words, “0.999…” and “1” represent the same number. There are many ways of showing this equality, from intuitive arguments to mathematically rigorous proof. The technique used depends on target audience, background assumptions, historical context, and preferred development of the real numbers, the system within which 0.999… is commonly defined. (In other systems, 0.999… can have the same meaning, a different definition, or be undefined.) More generally, every nonzero terminating decimals has two equal representations (for example, 7.52 and 7.51999..), a property true of all base representations. The utilitarian preference for the terminating decimal representation contributes to the misconception that it is the only representation. For this and other reasons such as rigorous proofs relying on nonelementary techniques, properties, and/or disciplines math students can find the equality sufficiently counterintuitive that they question or reject it. This has been the subject of several studies in mathematics education.
SCIENTIFIC FORMULAS—
MATHEMATICS
PHYSICS
ASTRONOMY
ROCKET SCIENCE
Capital  Lowcase  Greek Name  English 
Alpha  a  
Beta  b  
Gamma  g  
Delta  d  
Epsilon  e  
Zeta  z  
Eta  h  
Theta  th  
Iota  i  
Kappa  k  
Lambda  l  
Mu  m 
Nu  n  
Xi  x  
Omicron  o  
Pi  p  
Rho  r  
Sigma  s  
Tau  t  
Upsilon  u  
Phi  ph  
Chi  ch  
Psi  ps  
Omega  o 
POWERS
tera=10^12
giga=10^9
mega=10^6
myria=10^4
kilo=10^3
hecto=10^2
icosa=20
quindeca=15
hendeca=11
dec=10
non=9
octo=8
hepta=7
hexa=6
penta=5
tetra=4
tri=3
bi=2
uni=1
semi=.5
deci=10^1
centi=10^2
milli=10^3
micro=10^6
nano=10^9
pico=10^12
femto=10^15
atto=10^18
1 pound=.4545 kilograms
1 kilogram=2.2026432 pounds
1 mile=1.609 kilometers
1 kilometer=.62150404 kilometers
1 pound=16 ounces
1 pound=454.54 grams
1 ounce=28.040875 grams
Speed of light=299,792,458 meter/second
Temperature conversion—
From Fahrenheit to:
celsius=(Fahrenheit32) x .5556
kelvin=(fahrenheit32)/1.8+273.15
From celsius:
fahrenheit=(1.8 x celsius)+32
kelvin=celsius+273.15
From kelvin:
fahrenheit=1.8 x (kelvin273.15)+32
celsius=kelvin273.15
PRACTICAL MATHEMATICS FORMULAS PLATONIC SOLIDS—
1. Tetrahedron
Surface area=Sqrt3 x edge length^2 Volume=sqrt2/12 x edge length^3 2. Cube
Surface area=6 x edge length^2 volume=edge length^3
3. Octahedron
Surface area=2 x sqrt3 x edge length^2
volume=sqrt2/3 x edge length^3
4. Dodecahedron
Surface area=3 x sqrt(25+10 x sqrt5) x edge length^2 volume=(15+7 x sqrt5)/4 x edge length^3
5. Isocahedron
Surface area=5 x sqrt3 x edge length^2
volume=(5 x (3+sqrt5))/12 x edge
length^3
CIRCLE
Diameter D = 2 x Radius
Circumference C = 2 x Pi*Radius
area A = Pi x Radius^2
SPHERE
Surface area. A = 4 x Pi x Radius^2
volume V = 4/3 x Pi x Radius^3
Diameter of a sphere. d=cuberoot(3/4 x Pi x volume) x 2 SQUARE, RECTANGLE, PARALLELOGRAM
Area A=side 1 x side 2
VOLUME OF SQUARE, RECTANGLE, PARALLELOGRAM V=side 1 x side 2 x side
PYRAMID
Surface area=base area+.5 x slant length
Volume=base x depth x height/3
CYLINDER
Surface area=2 x pi x radius x (radius+height)
Volume=PI X radius^2 x length
CONE
Surface area=pi x radius x (radius+base to apex length) Volumes=Pi x radius^2 x height/3
TORUS
Surface area=4 x pi^2 x radius torus x radius of solid part volume=2 x pi^2 x radius torus x radius solid part^2
PYTHAGOREAN THEORM
a^2+b^2=c^2
a=length of one right angle’s leg
b=length of other right angle’s leg
c=length of hypotenuse
LAW OF SINES
a/sinA=b/sinB=c/sinC=2 x R=a x b x c/2 x area of triangle R=(a x b x c)/(squareroot((a+b+c) x (a+bc) x (b+ca)) Area of triangle=1/2 x a x b x sinC
LAWS OF COSINE
c^2=a^2+b^22 x a x b x cosC
cosC=(a^2+b^2+c^2)/2 x a x b
AREA OF A TRIANGLE
area=base x height x 1/2
AREA OF AN EQUILATERAL TRIANGLE area=(length of a side )^2 x SQRT(3)/4 AREA OF A TRAPEZOID
A=(top side+bottom side) x height/2
HERON’S FORMULA (area of any triangle) area=SRQT(s x (sside 1) x (sside 2) x (sside 3)) s=1/2 x (a + b + c)
SLOPE
m=(yy1)/(xx1)
(Y1 and x1 are locations on coordinate plane) POINT SLOPE EQUATION OF A LINE
Y y1=slope(xx1)
(Y1 and x1 are locations on coordinate plane) SLOPE INTERCEPT FORM FOR A LINE y=slope(x)+(y intercept)
DISTANCE FORMULA
distance=square root((xx1)^2+(yy1)^2+(zz1)^2)) (z1, y1, and x1 are locations on coordinate system) ALGEBRA FORMULAS
(a+b)^2=a^2+2 x a x b+b^2
(ab)^2=a^22 x a x b+b^2
x^2a^2=(x+a) x (xa)
x^3a^3=(xa) x (x^2+a x x+a^2) x^3+a^3=(x+a) x (x^2a x x+a^2)
a/b+c/d=(a x d+b x c)/b x d) a/bc/d=(a x db x c)/b x d
a/b x c/d=a x c/b x d
CONIC SECTIONS
Circle (xg)^2+(yh)^2=radius^2
(g=x coordinate, h=y coordinate) Parabola
y^2+/4ax
(a=x coordinate)
x^2=+/4ay
(a=y coordinate)
ellipse
x^2/a^2+y^2/b^2=1,
(a=x, b=y coordinates, or a=y, b=x coordinates) Hyperbola
x^2/a^2y^2/b^2=1,
(a=x, b=y coordinates, or a=y, b=x coordinates) QUADRATIC EQUATION x=(b+/squareroot(b^24ac))/2a
e=1/ln
ln=1/e
exp=1/log
log=1/exp
LAWS OF EXPONENTS
a^x x a^y=a^(x+y)
a^x/a^y=a^(xy)
(a^x)^y=a^(X x Y) (a*b)^x=a^x x b^x a^0=1
a^1=a
LAWS OF LOGARITHMS
log(base a)(M x N)=log(base a)(M)+log(base a(N) log(base a)(M/N)=log(base a)Mlog(base a)(N) logM^r=r X x logM
log(base a)(M)=logM/loga
TRIGONOMETRY
sineo/h
cosine=a/h
tangent=o/a
cosecant=h/o
secant=h/a
cotangent=a/o
(a=adjacent side of right triangle)
(o=opposite side of right triangle)
(h=hypotenuse of right triangle)
Pythagorean identities
sin^2(x)cos^2(x)=1
sec^2(x)tan^2(x)=1
csc^2cos^2(x)=1
Product relations
Sinxtanx x cosx
cosx=cotx x sinx
tanx=sinx x secx
cotx=cosx x cscx
Secxcscx x tanx
cscx=secx x cotx
Trigonometry functions
sinx=xx^3/3!+x^5/5!x^7/7!
cosx=1x^2/2!+x^4/4!x^6/6!
Inverse trigonometry functions
sin1x=x+(1/2 x 3) x x^3+(1 x 3/2 x 4 x 5) x x^5+(1 x 3 x 5/2 x 4 x 6 x 7) x x^7+… cos1x=pi/2(x+(1/2 x 3) x x^3+(1 x 3/2 x 4 x 5) x x^5+(1 x 3 x 5/2 x 4 x 6 x 7) x x^7+… tan1x=xx^3/3+x^5/5x^7/7+…
cot1x=pi/2x+x^3/3x^5/5+x^7/7…
Hyperbolic functions
sinhx=x+x^3/3!+x^5/5!+x^7/7!+…
coshx=1+x^2/2!+x^4/4!+x^6/6!+…
Inverse hyperbolic functions
sinh1x=x(1/2 x 3) x x^3+(1 x 3/2 x 4 x 5) x x^5(1 x 3 x 5/2 x 4 x 6 x 7) x x^7+… tanh1x=x+x^3/3+x^5/5+x^7/7+…
Nth TERM OF AN ARITHMETIC SEQUENCE
Nth term=a+(number of terms1)*d
(a=1st term, d=common difference)
SUM OF n TERMS OF AN ARITHMETIC SERIES
Sumn/2 x (a+nth term)
(a=1st term, d=common difference)
Nth TERMS OF A GEOMETRIC SEQUENCE
a(n)=a x r^(n1)
(r cannot equal 0.)
(a=1st term, r=common ratio, n=number of terms)
SUM OF THE n TERMS OF A GEOMETRIC SEQUENCE
sum=a x ((1r)^n)/(1r)
(r cannot equal 0, 1)
(a=1st term, n=number of terms, r=common ratio)
SUM OF AN INFINITE SERIES
s=n/(1r)
(If absolute value of r<1)
(n=number start with)
(r=how much keep multiplying by) (s=sum of infinite series)
COMBINATIONS
C(n,r)=n!/r!(nr)!
PERMUTATIONS
P(n,r)=n!(nr)!
BINOMIAL FORMULA
(a x xb)^n
CALCULUS (DIFFERENTIATION)
d/dx (x^n)=n x x^(n1)
d/dx sinx= cost
d/dx cosx= sinx
d/dx tanx=sec^2(x)
d/dx cotx=csc^2(x)
d/dx secxsecs x tanx
d/dx cscx= cscx x cotx
d/dx e^x=e^x
d/dx lnx=1/x
d/dx (u+v)=du/dx+dv/dx
d/dx(c x u)=c x du/dx
(chain rule)
d/dx (u x v)=(v x (du/dx)(u x (dv/dx)
(product rule)
d/dx(u/v)=(v x du/dxu x dv/dx)v^2
(quotient rule)
du=du/dx(dx)
CALCULUS (INTEGRATION)
The definite integral of t from a to b for definite integral f(t)=F(b)F(a)
Indefinite integral of x^r dx=x^(r+1)/(r+1)+c, (r cannot equal 1)
Indefinite integral of 1/x dx=ln(absolute value (x))+c
Indefinite integral of sinx dx=cosx+c
Indefinite integral of cosx dx=sinx+c
Indefinite integral of e^x dx=e^x+c
Indefinite integral of (f(x)+g(x))dx=indefinite integral f(x)+indefinite integral g(x) Indefinite integral of c x f(x) dx=c x (indefinite integral f(x))
indefinite integral of (u)dv=u x vindefinite integral (v)du
(integration by parts)
CENTER OF MASS
Center of mass (x)=((mass1) x (center of mass1)+(mass2) x (center of mass x 2))/ (mass1+mass2)
(A point representing the mean position of the matter in a body of system.)
Exponential growth/decay
Final amount=starting quantity x e^(k x time)
(Growth if k>1, decay if k<1)
VECTOR ANALYSIS
Norm (magnitude of a vector)=sqrt(x^2+y^2+z^2)
Dot product u (dot) v=(u1) x (v1)+(u2) x (v2)+(u3) x (v3)=u v cos(theta)
(theta is the angle between u and v, 0<=theta<=Pi)
Cross productÂ u x v=((u2) x (v3)(u3) x (v2))i((u1) x (v3)(u3) x (v1))j+((u1) x (v2)
(u2) x (v1))k
u x v=u x v sin(theta)
(Theta is angle between u and v, 0<=theta<=Pi)
2 vectors orthogonal if their dot product v and u=0 or transpose vector v and vector u=0.
Exponential growth and decay—
y=A exp^k*t
A=starting number of for example bacteria, t=length of growth time, k=constant, y=number of bacteria after t time
OUTLINE OF PHYSICS FORMULAS
*** Straight line motion ***
Velocity (meters/second)=distance (meters)/time (seconds) v=d/t (constant velocity)
v=2 x d/t (accelerating)
Distance (meters)=velocity (meters/second) x time (seconds) d=v x t
time (seconds)=distance (meters)/velocity (meters/second) t=d/v
t=sqrt(2 x distance/acceleration)
Acceleration (meters/second^2)=
((meters/second (end)meters/second (start)/)time (seconds))/2 a=(d2/td1/t)/2
Acceleration (meters/second^2)=2 x distance (meters)/time (second)^2 a=2 x d/t^2
Final velocity (meters/second)=initial velocity (meters/second)+ acceleration (meters/second^2 x time (seconds)
v(f)=v1+a x t
velocity^2=initial velocity+2 x acceleration x distance
v^2=v1+2 x a x d
Average velocity (meters/second)=initial velocity+final velocity/time v(average)=(v1+v2)/t
Average velocity=initial velocity+1/2 x acceleration x time v(average)=v1+1/2 x a x t
Distance (meters)=initial velocity x time+1/2 x acceleration x time^2 d=v1+1/2 x t x a x t^2
Distance=acceleration x time^2/2
d=a x t^2/2
Newton’s 2nd law of motion
Force (newtons)=mass (kilograms) x acceleration (meters/second^2) Fm x a
Falling bodies
velocity=gravity (9.81 meters/second^2 for the earth) x time
v=g x t
How far fallen in meters=1/2 x gravity x time^2 d=1/2 x g x t^2
Time fallen=sqrt(2 x height/gravity)
t=sqrt(2 x h/g)
velocity=sqrt(2 x gravity x height) v=sqrt(2 x g x h)
*** Circular motion ***
Uniform circular motion
Moment of inertia=mass x distance from axis^2
m(inertial)=m x d^2
Angular velocity=angular displacement/change in timeÂ (radians/second) v(angular)=d/t
Angular momentum=moment of inertia x angular velocity m(angular)=m(inertial) x v(angular)
Centripedal acceleration
Centripedal acceleration=velocity^2/radius of path (radians/second^2) a(centipedal)=v^2/r
Torque (newtonsmeter)
Centripetal force
Centripetal force=mass x velocity^2/radius of path
f(centripedal)=m x v^2/r
Gravitation
gravitation (newtons)=G x (mass(1) x mass(2))/radius^2
(G=6.67 x 10^11)
f=G x (m1 x m2)/r^2
Fundamental forces in nature— strong
W eak
Electromagnetic
Gravity
*** Energy ***
work
work (joules)=force (newtons) x distance (meters)
w=f x d
work=work output/work input x 100%
w=w(o)/w(i) x 100
Power
Power (watts)=work (joules)/time (seconds)
p=w/t
horsepower=746 watts
weight=mass x gravity
w=m x g
momentum=mass (kilograms) x velocity (meters/second) momentum=m x v
Energy
kinetic energy
KE (joules)=1/2 x mass (kilograms)x velocity (meters/second)^2 ke=1/2 x m x v^2
Potential energy
PE (joules)=mass x gravity (9.81 meters/second^2) x height (meters)
pe=m x g x h
Rest energy
Rest energy (joules)=mass x 300,000,000^2
Conservation of energy
MomentumÂ (kilogramsmeters/second)
Linear momentum
L. momentum=mass (kilograms)x velocity (meters/second) m(momentum)=m x v
Conservation laws
Conservation of massenergy
Conservation of linear momentum
Angular momentum
Conservation of angular momentum
Conservation of electric charge
Conservation of color charge
Conservation of weal isospin
Conservation of probability
Conservation of rest mass
Conservation of baryon number
Conservation of lepton number
Conservation of flavor
Conservation of parity
Invariance of charge conjugation
Invariance under time reversal
CP symmetry
Inversion or reversal of space, time, and charge
(there is a onetoone correspondence between each of the conservation laws and a differentiable symmetry in nature.)
Impulse
impulse=force (newtons) x time (seconds)
i=f x t
*** Relativity ***
special relativity
Lorentz transformation
General relativity
*** Fluids ***
Density
Specific gravity
kilograms/meter^3
Pressure
pressure=force/area
pressure=newtons/meters^3
p=f/d^3
Pressure in a fluid
pressure=density (kilograms/meters^3) x depth (meters) x weight (kilograms) p=d(density) x d(depth) x w
p=kg/d^3 x d x m
Archimede’s principlethe upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces.
Bernoulli’s principlesan increase in the speed of a fluid occurs
simultaneously with a decrease in pressure or a decrease in the fluid’s potential energy.
v^2/2+gz+p/Ï=constant
v is the fluid flow speed at a point on a streamline,
g is the gravitational acceleration
z is the elevation of the point above a reference plane,
with the positive zdirection pointing upward so in the direction
opposite to the gravitational acceleration,
p is the pressure at the chosen point, and
Ï is the density of the fluid at all points in the fluid.
*** Heat ***
internal heat
Temperature
Heat
1 kilocalorie=3.97 british thermal units (BTU)
1 BTU=.252 kilocalories
Specific heat capacity
Heat transferred=mass (kilograms) x specific heat capacity x temperature change (kelvin)
h=m x h x t
change of state
Heat of fusion
Heat of vaporization
pressure and boiling point
*** Kinetic theory of matter ***
Ideal gases
Boyle’s law
pressure(1) x volume(1)=pressure(2) x volume(2)
(temperature constant)
P1 x v1=p2 x v2
Absolute temperature scale
Temperature kelvin=temperature (celsius)+273.15
Charlie’s law
volume(1)/temperature(1)=volume(2)/temperature(2)
(pressure constant)
v1/t1=v2/t2
Ideal gas law
pressure(1) x volume(1)/temperature(1)=pressure(2) x volume(2)/temperature(2) P1 x v1/t1=p2 x v2/t2
Kinetic energy of gases
Molecular energy
KE (joules)=3/2 x K x temperature (kelvin)
(K=boltzmann’s constant=1.38 x 10^23 joules/kelvin
ke=3/2 x k x t
solids and liquids
Atoms and molecules
*** Thermodynamics ***
3 laws of thermodynamics
The four laws of thermodynamics are:
Zeroth law of thermodynamics: If two systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other.
This law helps define the notion of temperature.
1st law of thermodynamics: When energy passes, as work, as heat, or with matter, into or out from a system, the system’s inertial energy changes in accord with the law of conservation of energy. Equivalently, Perpetual motion machines of the 1st kind (machines that produce work without the input of energy) are impossible.
2nd law of thermodynamics: In a natural thermodynamic process, the sum of the entropies of the interacting thermodynamic systems increases. Equivalently, perpetual motion machines of the 2nd kind (machines that spontaneously convert thermal energy into mechanical work) are impossible.
3rd law of thermodynamics: The entropy of a system approaches a constant value as the temperature approaches absolute zero. With the exception of noncrystalline solids (glasses) the entropy of a system at absolute zero is typically close to zero, and is equal to the logarithm of the product of the quantum ground states.
entropy
The entropy of a system approaches a constant value as the temperature
absolute zero.
Mechanical equivalent of heat
Mech. Equiv. heat=4,185 x joules/kilocalories Mech. Equiv. heat=778 x footpounds/BTU
Heat engines
Engine efficiency
efficiency=1heat temperature absorbed/heat temperature given off eff=1h(temp. Absorbed)/h(temp. Given off)
Conduction
Convection
Radiation
*** Electricity ***
Electric charge
Charge of proton=1.6 x 10^19 coulombs
Charge of electron= 1.6 x 10^19 coulombs
Electric charge=current (amperes) x time taken (seconds)
Coulomb’s law
Electric force (newtons)=K x charge1 (coulombs) x charge2 (coulombs)/ distance (meters)^2
(K=9 x 10^9 newtonmeter^2/coulomb^2)
F=KÂ x c1 x c2/d^2
Atomic structure
Mass of proton=1.673 x 10^27 kilograms
Mass of neutron=1.675 x 10^27 kilograms Mass of electron=9.1 x 1031 kilograms Ions
Electric field
Electric field (newton/coulomb)=force (newtons)/charge (coulombs) E=f/c
force=charge x electric field
Electric lines of force
Potential difference
volts=work/charge
(1 volt= 1 joule/coulomb)
volt=electric field (newtons/coulomb)x distance (meters)
v=E x d
Electric field (newtons/coulombs)=volts/distance
E=v/d
Potential Difference=current (amperes)x resistance (ohms)=
energy transferred/charge (coulombs)
pd=I x r=e/c
Electric current
Electrical energy=voltage (volts)x current (amperes)x time taken (seconds) e=v x I x t
Electric current
Electric current (amperes)=charge (coulombs)/time interval (seconds)
(1 ampere=1 coulomb/second)
I=c/t
Electrolysis
Ohm’s law
Electric current (amperes)=volts/resistance (ohms)
(resistance (1 ohm))=1 volt/ampere)
I=v/r
resistance (ohms)=voltage (volts)/current (amperes)
r=v/I
voltage (volts)=current (amperes)x resistance (ohms)
v=I x r
Resisters in series
resistance=resistance(1)+resistance(2)+resistance(3)
R=r1+r2+r3
Resisters in parallel 1/resistance=1/resistance(1)+r1/resistance(2)+1/resistance(3) 1/R=1/r1+1/r2+1/r3
Kirchoff’’s law
current law=Summation (current)=0
Voltage law=summation (voltage)=0
Capacitance
1 farad=1 coulomb has 1 volt between plates
capacitance (farad)=charge (coulombs)/voltage (volts)
Work stored=work (charging)=1/2 x capacitance x voltage^2
W=w=1/2 x C x v
electric power
power (watts)=work done per unit time (joules)=voltage (volts)x charge
(coulombs)/time (seconds)
p=w=v x c/t
Power (watts)=current (amperes) x voltage (volts)=current (amperes)^2
x resistance (ohms)=voltage (volts)^2/resistance (ohms)
p=i x pd=i^2 x r=pd^2/r
Alternating current
power (watts)=1/2 x peak voltage x peak current x
cos (phase angle between current and voltage sine waves)
p=1/2 x v x I x cos(theta)
*** Magnetism ***
Magnetic field
1 tesla=1 newton/amperemeter
(tesla=weber/meter^2)
(1 gauss=10^4 teslas)
B (magnetic field)=K x I (straight line current)/distance (meters)
(K=2 x 10^7 newton/amperes^2
B=K x I/d
Magnetic field on a moving charge
Magnetic field on a current
B=Pi(3.14) x K x I/r
F=I x L x B
Magnetic field of solenoid
B=2 x Pi x K x N (number of turns)/L (length of solenoid) x I (current amperes) Forces between 2 currents
(K=2 x 10^7 newton/amperes^2
F/L=K x I(1) x I(2)/d
Lorentz force
F=charge x electric field+charge x velocity (cross product) magnetic field F=qE+qv x B
*** electromagnetism ***
Maxwell’s equations
Maxwell’s equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.
*** Electromagnetic induction ***
Generator
Motors
Alternating current
I=I (max)/sqrt(2)=.707 I (max)
V=I (max)sqrt(2)=.707 V (max)
Transformer
Primary voltage/secondary voltage=primary turns/secondary turns Primary current/secondary current=secondary turns/primary turns DC circuits
*** Waves ***
Frequency
1 hertz=1 cycle/second
W avelength
wave velocity (meters/second)=frequency (hertz) x wavelength (meters)
v=f x w
Acoustics
Optics
Electromagnetic waves
Velocity of light=c=3 x 10^8 meters/second=186,282 miles/second
Doppler effect
Frequency found by observer with respect to sound=frequency produced by source x (velocity sound+velocity observer)/(velocity soundvelocity source) f(o)=f(s) x (v+v(o))/(vv(s))
Frequency found by observer with respect to light=frequency produced by source x sqrt((1+relative velocity/c)/(1relative velocity/c))
f(o)=f(s) x sqrt((1+v/c)/(1v/c))
reflection and refraction of light
Index refraction=n=c/velocity in medium (meters/second)
r=c/v
Interference, diffraction, polarization
Particles and waves
*** Quantum physics ***
Uncertainty principlethe velocity of an object and its position
cannot both be measured exactly, at the same time, even in
theory.
The Schrodinger equation is used to find the allowed energy levels of quantum mechanical systems (such as atoms, or transistors). The associated wave function gives the probability of finding the particle at a certain position. … The solution to this equation is a wave that describes the quantum aspects of
a system.
The Pauli exclusion principle—
Quantum theory of light
Quantum energy=E=h x f
Planck’s constant=h=6.63 x 10^34 joulessecond
Xrays
Electron volt=planck’s constant x frequency
eV=h x f
Electron KE=xray photon energy
f=eV/h
momentum=kinetic energy (joules)/speed of light^2 (meters/second) p=ke/c^2
Kinetic Energy=planck’s constant x frequency
planck’s constant x speed light/wavelength
ke (joules)=6.63 x 10^34 joulessecond x frequency hertz(meter/second)
The Pauli exclusion principle is the quantum mechanical
principle which states that two or more identical fermions (particles with
halfinteger spin)
cannot occupy the same quantum state within a quantum system
simultaneously.
6.63 x 1^34 x 300,000,000 meters/f (meters) joules=h x f=h x c/lambda
Electron volt
1 eV=1.6 x 10^19 joules
1 KeV=10^3 eV
1 MeV=10^6 eV
1 GeV=10^9 eV
Kinetic energy=1/2 x mass x velocity^2=
planck’s constant x frequencyelecton volts
ke (joules)=1/2 x m x v^2=6.63 x 10^34 joulessecond x feV Matter waves
De Broglie wavelength=lambda=h/m x v (momentum=m x v)
wavelength=planck’s constant/(mass x meters/second) lambda=h/m x v
Solid state physics
***Nuclear and atomic physics ***
Nucleus
Mass (proton)=1.673 x 10^27 kilograms=1.007277 u
Mass (neutron)=1.675 x 10^27 kilograms=1.008665 u Nuclear structure
Binding energy
Mass defect= change m=((number protons x mass hydrogen)+ (number neutrons x mass neutrons))m
(mass hydrogen=1.007825 u)
Fundamental forces
Gravity
Electromagnetic
Weak interaction
Strong force
Fission and fusion
Radioactivity
Alpha particle=helium nuclei
Beta particle=electron
Gamma rays=high energy photons with frequencies greater than xrays neutron>proton+electron
proton>neutron+positron Radioactive decay and halflife Elementary particles and antimatter
ASTRONOMY FORMULAS
1. How to find the DISTANCE in parsecs to a star distance=10^((apparent magnitudeabsolute magnitude+5)/5)
2. APPARENT magnitude
apm=log d x 55+abm
apparent=log(distance) x 5 – 5 + absolute magnitude
3. How do you calculate the absolute magnitude of a star abm=((log L/log 2.516)4.83)
Absolute magnitude=((log(number of sun’s luminosity of star)/ log2.516)4.83
abm=(5 x log d5apm)
Absolute magnitude= (5 x log(distance parsecs)5apparent magnitude)
4. To find brightness of a star/number of suns
L=10^((abm4.83) x (log 2.516))
LUMINOSITY of star=10^((absolute magnitude of star4.83)*(log2.516))
luminosity increase=2.512^([magnitude increase]+4.83)
luminosity=mass^3.5Â (for main sequence stars)
Luminosity (watts)=4 x pi x radius(meters)^2 x temperature (kelvin)^4 x
5.67 x 10^8 watts maters^2 kelvin^4
5. Mass binary system
Suppose in an example, we calculate the masses of 2 stars in a binary star system: if the period of star a is 27 years and its distance from the common center of mass is 19 AUs, the
Distance^3/period^2=19^3/27^2=6859/729=9.4 solar masses for the total mass of the 2 stars.
The velocity of star a is 30,000 km./second and star b is 10,000 km/second, so 30,000/10,000=3.
The mass of star b is 9.4/(1+3)=2.25 solar masses.
The mass of star a is 9.42.25=7.15 solar masses.
So star a is 7.15 solar masses, and star b is 2.25 solar masses, and both added up equals 9.4 solar masses, the combined mass of the 2 stars.
6. Radius of a star
radius=(temperature sun (kelvin)/temperature star (kelvin))^2 x (2.512^(absolute magnitude sunabsolute magnitude star)^1.2)
radius=sqrt(luminosity)/(temperature kelvin)^2
7. size of star/orbit/object
size object miles=arcseconds size object x distance parsecs x 864,000
8. LT=10^10 x m(star)/m(sun)^2.5
lifetime=(10^10) x (mass of star/mass of sun)^2.5
9. To find ARC SECOND size—
Arcs second size=1/distance parsecs x number of suns size
9.5 DISTANCE (parsecs)– d=1/arcseconds
10. Galaxy distance in millions of light years
d=13,680 x rsh+8.338
distance (millions of light years)=13,680 x red shift+8.336
10.5 size of an object I.e. galaxy=number of megaparsecs x 1,000,000 x sin(arc seconds/360)
11. velocity of galaxy in kilometers/second
v=300,000 x rsh
velocity (kilometers per second)=300,000 x redshift
12. approximate number of stars in a galaxy=luminosity in number of suns galaxy/.02954
13. redshift
Rsh=mly8.338/13,680
redshift=(light years (millions)8.336)/13,680
14. Volume of a galaxy=4/3 x Pi x a x b^2
a=major axis, b=minor axis, (for elliptical galaxies)
15. Number of stars=volume/distance between stars^3
16. Average Distance between stars in light years=cube root(volume/number of stars)
16.5. Number of stars span across longest axis of galaxy=(3/4 x volume)/(Pi x a x b x n^2)
a=an axis length in light years, b=the other axis in light years, n=distance between stars light years
17. Escape velocity from a galaxy miles/second=
sqrt(.468 x 1.989 x 10^30 x 6.67 x 10^11 x number of stars/(4 x pi/3)/8 x .71353 x 2.697823 x 10^20)/1612.9
18. Surface gravity
gravity(meters/second^2)=
mass of star number of suns x 1.99 x
10^30 x 6.67 x 10^11/(size of star number of suns x 864000000 x 1.62/2)^2
19. Titusbode law
Distance (astronomical units)=3*2^n+4/10
(n=infinity, 0, 1, 2, 3, â€¦)
Mercury=infinity
Venus=0
earth=1
mars=2
Asteroid belt=3
jupiter=4
Etc
20. kepler’s 3 laws of planetary motion
1. Planets travel in elliptical orbits.
2. Equal areas are covered in in equal times in the elliptical orbit.
3. The distance in astronomical units to the 3rd power equals the time to travel one complete orbit in years to the 2nd power.
(time years)^2=(radius orbit astronomical units)^3
D=P^(2/3)
P=D^(3/2)
21. Velocity to achieve orbit=sqrt(G x M/distance from center of the earth)
22. Escape velocity=sqrt(G x M/r)
23. Four types of eccentric orbits
circle eccentricity=0
ellipse eccentricity= 01
parabola eccentricity=1
hyperbola eccentricity>1
24. Eccentricity=(greatest orbital distanceclosest orbital distance)/(closest orbital distance+greatest orbital distance) e=(d(greatest)d(closest))/(d(closest)+d(greatest))
25. Calculations: orbits, periods of orbits, perihelions, aphelions and eccentricities (for example a comet)
CIRCLE
Circular formula eccentricity=0
(xh)^2+(yk)^2=r^2. (#1)
(h=x coordinate and y=y coordinate ;r=radius of orbit)
period=2 x pi x sqrt(radius^3/(6.67 x 10^11 x mass of body the body is orbiting))
Velocity in orbit=sqrt(6.67 x 10^11 x
mass of body the body is orbiting/radius of orbit)
Centripetal acceleration=velocity^2/radius of orbit
ELLIPSE
Use ellipse formula x^2/a^2+y^2/b^2=1
Then calculate from 2 coordinates in AUs with formula
x^2 x b^2 + y^2 x a^2=a^2 x b^2
find a and b (the closest and furthest approaches)
Period years of orbit=distance (AU)^3/2
time=2 x pi x sqrt(a^3/G x M)
distance=period^2/3
velocity=sqrt(G x M x (2/r1/a))
eccentricity=(0<e<1)
eccentricity=sqrt(1b^2/a^2)
a (semimajor axis)=(perihelion + aphelion)/2
Semi minor axis (b)=sqrt((eccentricity^21) x a^2
Perihelion/aphelion=(1+eccentricity)/(1eccentricity)=aphelion distance/perihelion distance
Perihelion distance=semimajor axis x (1eccentricity)
aphelion distance=semimajor axis x (1+_eccentricity)
Simple way to calculate and orbit
1=X^2+Y^2. >Â 1=x^2+semimajor axis^2+y^2/semiminor axis^2
time in seconds to get to orbital position from 0 degrees going counterclockwise t=radians at current position of orbiting body/360 x sort(semi
major axis^3/6.67 x 10^11 x 1.989 x 10^30)
to find the angle at which the orbiting body is at from 0 degrees going counterclockwise x^2=p^2+1
q=sqrt(p)
r=sqrt(x)
s=q/r
arcsin(s)=angle of the orbiting body with respect to the focal body
to find distance to orbiting body from foci
x^2=p^2+p^2
cosy=x^2/P^2 x x^2
m=arccosy
cosm=1/n
q=1/cosm
q=distance to orbiting body from foci
To find formula for the orbit, use ellipse formula
x^2/a^2+y^2/b^2=1
PARABOLA
eccentricity=1
y=a x X^2+b x X +c
Calculate from 2 coordinates of the body in its orbit (a and b coordinates in
both instances)
Solve for x, then y, and will have the formula for the parabolic orbit.
Then will have the equation of the orbit like the quadratic equation above with
numerical figures for a and b.
Velocity of body in parabolic orbit
v=sqrt(2 x 6.67 x 10^11 x mass of body being orbited/radius of body)
Period of orbit does not have an orbit so undefined.
eccentricity=sqrt(1+b^2/a^2)
time in seconds to get to orbital position from 0 degrees going counterclockwise– t=radians at current position of orbiting body/360 x sqrt(semi
major axis^3/6.67 x 10^11 x 1.989 x 10^30)
to find the angle at which the orbiting body is at from 0 degrees going counterclockwise– g^2+(distance between foci/2 (‘p))^2=d^2
(d^2p^2g^2)/(2(p^2)(g^2))=cosx
cos1x=angle x
p^21^2=g^2
(1^2p^2g^2)/(2(p^2)(g^2))=cosL
cos1L=angle L
90xL=m
mx=n
n is the angle the orbiting body is at from 0 degrees going counterclockwise HYPERBOLA
eccentricity>1
x/ay/b=1. (#1)
xbya=ab.Â (#2)
Calculate from 2 coordinates of the body in its orbit (a and b coordinates in both instances) using (equation #2).
Solve for x, then y, and will have the formula (for #1 above) for the hyperbolic orbit.
Then will have the equation of the orbit like equation #1 with numerical figures for a and b.
Velocity of body at infinity in a hyperbolic orbit
velocity at an infinite distances away=sqrt(velocity^2escapevelocity^2)
Period of orbit does not have na orbit so undefined.
26. EXAMPLES OF CALCULATING ORBITS
STEPS TO CALCULATE AN ELLIPTICAL ORBIT
Suppose we measure 2 coordinates of a comet, one at (4AU,1AU) and the other at (0AU,3AU).
1) We plug in each of the coordinates, the 1st equals the x and the 2nd equals the y, each of the 2 coordinates into b^2 x x^2+a^2 x y^2=a^2 x b^2.
Then we subtract the 2 equations from each other. Next, we solve for both a and b. The resulting equation is x^2/2.376^2+y^2/1.68^2=1
and this is the equation of the orbit for the 2 given coordinates. The ellipse equation is x^2/2.376^2+y^2/1.68^2=1.
Solving for x and y gives
x=sqrt((15.65 x y^2)/2.8) and y=sqrt((12.8 x x^2/5.65).
2) perehelion=1.68AU, aphelion=2.376AU. (figures for constants a and b)
3) semimajor axis=A=(perihelion+aphelion)/2=(1.68+2.376)/2=1.9958AU
4) Semi minor axis=smaller figure of a and b=1.68AU.
5) focii=amaller figure of a and b=1.68AU.
6) distance center of ellipse to the foci=Aperihelion=.3158AU
7) period=aphelion^3/2=2.82 years (1,029.83 days)
8) eccentricity=1perihelion/A=.158
9) velocity at any instant=1.99 x 10^30 x 6.67 x 10^11 x (1/radius=1/A)=
At perihelion=20.07 miles/second, at aphelion=10.74 miles/second
10) Suppose we want to find the time from perihelion to a distance of 2 AU and its velocity there. We use the formulas
Semimajor axis^2+semimajor axis^2=x^2
cosx=x^2/2 x semimajor axis^2 x x^2; angle=arccosx
time=angle/360 x sqrt(semimajor axis^3/6.67 x 10^11 x 1.989 x 10^30)
The answer for time atÂ 2 AU=82.79/360 x sqrt(2.7186 x 10^34/1.32733 x 10^20)=
.22997 x 14311435.6=38.09 days at a velocity there at 12.995 miles/second.
HALLEY’S COMET
period=75.986 years.
focii=.6AU.
perihelion=.6AU.
aphelion=35.28AU.
Semimajor axis=17.94Au
eccentricity=.9855.
Velocity at perihelion=33.23 miles/second, aphelion=3.124 miles/second
STEPS TO CALCULATE A CIRCULAR ORBIT
Suppose 2 coordinates were recorded of a celestial body, one (3,2,646), and the other (1,3.873). It the celestial body has a circular orbit, the squares of each set of coordinates added together will equal the same defendant number. In this example,
3^2+2.646^2=15, and 1^2+3.873^2=16, so this is a circular orbit where the equation of the orbit is 4^2=x^2+y^2, where the 4 in the 4^2 is the radius of the circle, and the x and y are the
coordinates of the circular orbit. The eccentricity of of a circular orbit is equal to zero. STEPS TO CALCULATE A PARABOLIC ORBIT
Formulas
velocity=sqrt(2 x G x Mass central body/radius of orbiting body from central body) trajectory=(4.5 x G x M x Time seconds^2)^1/3
To find out whether 2 coordinates measurements of an orbiting body if a parabolic orbit, say coordinates (3,27) and (2,12), we need to set up a parabolic equation
y=b x x^2, then put into it separately the 2 coordinates. 27=b x 3^2, solve for b to arrive at equals to 3.
12=b x 2^2, b also equals 3.
Since b in both equations are equal to each other, the orbiting object is in a parabolic orbit. The equation for the orbit is y=3 x x^2. The period of orbit is infinitely long since the orbiting object never returns. The vertex of the orbit is (0,0). The foci is equal to 3/4. We arrive at this by always using 4 x p, and setting it equal to 3, the number equal to b. When 4 x p=3 is solved, p=3/4. So the focus is at (0,3/4).the velocity of the orbiting body at its closest approach to the central body is equal to 30.05 miles/second.
STEPS TO CALCULATE A HYPERBOLIC ORBIT
Suppose 2 coordinates of an orbiting celestial body are recored as being at (28.28, 10)AU and (34.64, 14.14)AU positions. We try using the hyperbolic equation
1=x^2/a^2y^2/b^2, solve for a and b, and the result equals 1, so this is a hyperbolic orbit. a=20 and b=10. The equation for the orbit is
1=x^2/20^2y^2/10^2.
Solving for x and y yields
x=sqrt(4004 x y^2), and y=sqrt(x^2/4100(.
The orbit’s eccentricity is equal to sqrt(a^2+b^2)/a=sqrt(400+100)/400=1.118, which is greater than 1, so this is a hyperbolic orbit.
For focii=sqrt(a^2+b^2)=22.33AU from the sun’s position, which is equal to 22.33 a=22.3320=20AU, which makes the focci=(20,0).
The period of this orbiting body is undefined since it will never return. To find the semimajor axis, we use the velocity formula
v=sqrt(6.67 x 10^11 x 1.99 x 10^30 x (2/r1/semimajor axis)).
r=2.33AU in meters and v=618,000 meters/second. Solving for the semimajor axis yields 1208.12.
Let us determine the velocity of the orbiting object at say 5AU from the sun.
v=sqrt(6.67 x 10^11 x 1,99 x 10^30 x (2/5AU in meters1/1208.12))=18.77 kilometers/second, or 11.64 miles/second.
If we wanted to calculate the velocity of the object when it gets as far away as the nearest star, 4.3 light years away,
it would be traveling 25.76 meter/second there.
27. Formulas to find masses, radius, and luminosities of WHITE DWARFS
(mass<=.75 suns)
(radius<=.00436 suns)
(luminosity<=.00365 suns)
radius=mass^18.68 mass=radius^.052966
luminosity=mass^19.5198 mass=luminosity^.05123
luminosity=radius^1.04494 radius=luminosity^.95699
28. Formulas to find masses, radius, and luminosities of MAIN SEQUENCE stars luminosity=mass^3.5
mass=luminosity^(.2857)
radius=(temperature kelvin sun/temperature kelvin star)^2 x
(2.512^(absolute magnitude sunabsolute magnitude star)
note main sequence star’s masses can be found by knowing the star’s luminosity and its temperature.
Type star Mass radius Temperature luminosity lifespan
O. +16. +6.6 +33,000 kelvin 55,000 to >200,000 >9.77 m/yrs
B 2.116. 1.86.6 10,00033,000 kelvin. 4224,000. 9.77 m/yrs1.57 b/yrs
A 1.42.1. 1.41.8. 7,50010,000 kelvin. 5.124. 1.57 b/yrs4.3 b/yrs F. 1.041.4. 1.151.4. 6,0007,500 kelvin. 2.45.1. 4.3 b/yrs9.07 b/yrs
G. .81.04. .961.15. 5,2006,000 kelvin .381.2. 9.07 b/yrs17.47 b/yrs K. .45.8. .7.96. 3,7005,200 kelvin. .08.38. 17.47 b/yrs73.62 b/yrs M. <=.45. <=.7. 2,0003,700 kelvin <.002.08. >73.62 b/yrs
29. Formulas to find SUBGIANT masses, radii, and luminosities
mass^.94475=radius
radius^1.0585^mass
mass^.84=radius
mass^4.2585=luminosity
luminosity^.2348=mass
radius^4.5076=luminosity
luminosity^.22185=radius
30. Masses, radius, and luminosities for GIANT stars
mass^1.7226=radius
radius^.58052=mass
mass^2.429=luminosity
luminosity^.4117=mass
radius^1.41=luminosity
luminosity^.7092=radius
31. Masses, radius, and luminosities for BRIGHT GIANT stars
mass^1.8578=radius
radius^.5383=mass
mass^5.2365=luminosity
luminosity^.19097=mass
radius^2.8186=luminosity
luminosity^.35397=radius
32. Finding masses, radius, and luminosities for SUPERGIANT stars—
mass^1.836=radius
radius^.547=mass
mass^3.84=luminosity
luminosity^.26=mass
radius^.209=luminosity
luminosity^.4785=radius
34. MASSES OF STARS AND THEIR FATES
Masses .0710 suns white dwarf
Masses .58 suns planetary nebulas
Masses >8 suns supernovas
Masses 1029 suns neutron stars
masses>29 suns black holes
35. Spectral type, temperature, color, mass, size, luminosity, % of stars
O 30,000 K blue >16 >6.6 >30,000 .00003%
B 10,00030,00 blue white 2.116 1.86.6 2530,000 .13%
A 7,50010,000 white blue 1.42.1 1.41.8 525 .6%
F 6,0007,500 yellow white 1.041.4 1.151.4 1.55 3%
G 5,2006,000 yellow .81.04 .961.15 .61.5 7.6%
K 3,7005,200 light orange .45.8 .7.96 .08.6 12.1%
M 2,4003,700 orange red .08.45 <=.7 <=.08 76.45%
The Hertzsprung Russell diagram relates stellar classification with absolute magnitude, luminosity, and surface temperature.
36. DISTRIBUTION OF TYPES OF STARS IN GALAXY
Giants and supergiants .946%
O star .0000256%
B stars .1105%
A stars .51085%
F stars 2.5545%
G stars 6.446%
K stars 10.313%
M stars 65.0295%
White dwarfs 8.515%
Brown dwarfs 110% (4.98% average estimate)
Neutron stars .8515%
Black holes .08515
DRAKE EQUATION ESTIMATE OF PERCENTAGE OF ADVANCED CIVILIZATIONS OF SYSTEMS STARS
Applies to 10% of all stars
36.5 averages:luminosities, masses, radius’s of stars in galaxies—
Average luminosity\=.271 suns
Average mass=.468 suns
Average radii=<.71353 suns
37. SEVERAL ABSOLUTE AND APPARENT MAGNITUDES WITH LUMINOSITIES LIST ABSOLUTE MAGNITUDES LIST
Gamma ray burst. 39.1 374,000 trillion suns
Quasars 33. 1,360 trillion suns
supernovas. 19.3. 4.49 billion suns
Supernova 1978a. 15.66. 157 million suns
Pistol star. 10.75 1.7 million suns
deneb 8.38. 192,424 suns
Betelgeuse. 5.5. 13,558 suns
Sun 4.83. 1 sun
Proxima centauri. 11.13. 1/331 suns
Sun in Andromeda galaxy. 29.07. 1/4.98 billion suns
Venus 29.23. 1/5.8 billion suns
Hubble telescope viewing limit. 31. 1/29.4 billion suns
James webb telescope viewing limit. 34. 1/466 billion suns
APPARENT MAGNITUDES LIST
sun. 26.72. 23.74 trillion suns
Full moon. 12.6. 9.38 million suns
Venus. 4.4. 4,922 suns
Sirius. 1.6. 373 suns
Most energetic gamma ray burst 12.2 billion light years away 3.77. (374,000 trillion suns)
Sun seen by us if it were in andromedas galaxy. 53.31 1/(2.48 x 10^19) suns
Type 2 supernova in Andromeda as seen from here— apparent magnitude— 4.94
Venus in Andromeda as seen from here— apparent magnitude— 53.47
Deneb in Andromeda as seen from here— apparent magnitude— 15.86
38. Formulas to find temperature kelvin from spectral class—
Temp.=1500 x spectral class number+10000
O0=20, O1=19,…, B9=1, A0=0
Temp.=187.27 x spectral class number+5880
A0=22, A1=21,…, G1=1, G2=0
Temp.=132.22 x spectral class number+3500
G2=18, G3=17,…, K9=1, M0=0, M1=1, M2=2,…, M9=9
39. Weight in tons per teaspoon of a neutron star, black hole, etc—
Weight/teaspoon=(1.989 x 10^30 x number of sun’s masses/907.185)/
(4 x pi/3 x (radius of star x 693979234.4)^3 x 202884.202)
Spaceflight formulas
Meaning of variables in the formulas—
v=velocity (meters/second)
vi=velocity initial (meters/second)
vf=velocity final (meters/second)
vexh=exhaust velocity (meters/second)
isp=seconds
m=mass (kilograms)
mi=initial mass (kilograms)
mf=final mass (kilograms)
mr=mass ratio
a=acceleration (meters/second^2)
f=force (newtons)
d=distance (meters)
t=time (seconds)
ke=kinetic energy (joules)
ed=energy density (joules/kilograms)
p=power (watts)
spp=specific power (kilowatts/kilograms)
mm=momentum (meters x kilograms)
i=impulse (thrust x seconds)
fr=fuel rate (kilograms/second)
mw=molecular weight
texh=temperature exhaust (kelvin)
eff=propulsive efficiency
r=radius (meters)
ecc=eccentricity
g=acceleration due to gravity
(9.81 meters/second^2)
At 1 meter/second velocity—
1 newton=2.2 pounds of thrust
1 newton=62.3689 ounces of thrust
1 newton=997.37 grams of thrust
.45 newtons=1 pound of thrust
Rocket equation
velocity
v=vexh x ln(mi/mf)
v=(d x 2)/t (when accellerating)
v=d/t (constant velocity)
v=sqrt(2 x a x d)
Velocity of exhaust
vexh=v/ln*(mi/mf)
vexh=.25 x sqrt(texh/mw)
Vexh (km/sec)=.0806 x sqrt(temperature kelvin)
Isp
isp=vexh/9.81
isp=f/(fr x 9.81)
isp=vf/(ln(mr) x 9.81)
isp=vf/ln(mr) x 9.81
isp=f x t
isp=f x t
Mass ratio
mr=e^(vf/isp x 9.81)
mr=mi/mf
mr=e^(v/vexh)
mr=e^(vf/(isp x 9.81))
Mass final
mf=mi/(e^(vf/vexh)
Mass initial
mi=mf x e^(vf/vexh)
mass
m=f/a
m=2 x ke/v^2
Force
f=m*a
f=ke/d
f=9.81 x isp x fr
acceleration
a=f/m
Energy
ke=1/2 x v^2 x m
ke=d x f
Energy density (rest mass energy)
ed=ke/m
Fuel flow rate
fr=f/vexh
fr=m/t
Distance
d=v x t/2 (with respect to accelerating)
d=v x t (constant velocity)
d=ke/f
d=v^2/2 x a
Time
t=(d x 2)/v (constant acceleration)
t=d/v (constant velocity)
t=((m x vf)^2/2)(m x mi)^2/2) x (1/f) x (2/vi+vf)
Power p=ke/t
p=f x d/t
Specific power
sp=(p/1000)/m
sp=f/mi
Momentum
M=v x m
Impulse â
i=f x t
Antimatter needed (kilograms)
m=ke/1.8 x 10^16
Propulsive efficiency
eff=2/(1+(vexh/vf))
eff=(vf/vexh)^2/(e^(vf/vexh)1)
(Maximum efficiency for ratio vf/vexh<1.6)
eff=f x g x isp/2 x p
UNIVERSAL PHYSICAL CONSTANTS
ATOMIC MASS UNITS
1.6605402 x 10^27 kilograms
(1/12 0f the mass of an atom of carbon12)
AVOGADRO NUMBER
6.0221367 x 10^23/moles
(mole=number of elementary entities that are in
carbon12 atoms in exactly 12 grams of carbon12)
BOHR’S MAGNETON
9.2740154 x 10^24 joules/tesla
(The magnetic moment of an electron caused by either its orbital
or spin angular momentum. Magnetic moment is a quantity that
determines the torque it will experience in an external magnetic
field. Torque is rotational force. A joule is equal to the work done on
an object when a force of 1 newton acts on the object in the direction
of motion through a distance of 1 meter: kilograms x meters^2/
seconds^2. A joule is also equal to 10 million ergs. A Tesla is a
derived unit of the strength of a magnetic field: kilograms/(seconds^2
x amperes.)
BOHR RADIUS
5.29177249 x 10^11 meters
(The mean radius of an electron around the nucleus of a hydrogen atom
at its ground state.)
BOLTZMANN CONSTANT
1.3806513 x 10^23 joules/kelvin
(A physical constant relating the average kinetic energy of
particles in a gas with the temperature of the gas. Kelvin
temperature scale is the primary unit of temperature measurement
in the physical sciences, but is often used in conjunction with the
celsius degree, which is of the same magnitude absolute zero in
kelvin is equal to 273.15 degrees celsius.)
ELECTRON CHARGE
1.60217733 x 10^19 coulombs
(Charge carried by a single electron. The coulomb is the quantity of
charge that has passed through the cross section of an electrical
conductor carrying one ampere within one second.)
ELECTRON CHARGE/MASS RATIO
1.75881962 x 10^11 coulombs/kilograms
(The importance of the chargetomass ratio, according to classical
electrodynamics, is that 2 particles with the same chargetomass ratio
move in the same path in a vacuum when subjected to the same electric
and magnetic fields.)
ELECTRON COMPTON WAVELENGTH
2.42631058 X 10^12 meters
(A compton wavelength of a particle is equal to the wavelength of a
photon whose energy is the same as the mass of the particle. The
compton wavelength of an electron is the characteristic length scale of
quantum electrodynamics. It is the length scale at which relativistic
quantum field theory becomes crucial for its accurate description.)
ELECTRON MAGNETIC MOMENT
9.2847701 x 10^24 joules/tesla
(The electron is a charged particle of 1e, where e is the unit of
elementary charge. Its angular momentum comes from 2 types of
rotation: spin and orbital motion.)
ELECTRON MAGNETIC MOMENT IN BOHR MAGNETONS
1.00159652193
(Bohr magneton is a physical constant and natural unit for expressing the
magnetic moment of an electron caused by either its orbital or spin
angular momentum. The electron magnetic moment, which is the
electron’s intrinsic spin magnetic moment, is approximately one Bohr
magneton.)
ELECTRON MAGNETIC MOMENT/PROTON MAGNETIC MOMENT
658.21068801
ELECTRON REST MASS
9.1093897 x 10^31 kilograms
ELECTRON REST MASS/PROTON REST MASS
5.44617013 x1 0^4
This is how much less mass the electron is as compared to the proton.
(1,836.21 times lighter than proton)
FARADAY CONSTANT
9.6458309 x 10^4 coulombs/mole
(The magnitude of electric charge per mole of electrons.)
FINE STRUCTURE CONSTANT
.00729735308
(The strength of the electromagnetic interaction between elementary
particles.)
GAS CONSTANT
8.3144710 x 10^joules/(mole x kelvin)
(A physical constant which is featured in many fundamental equations
in the physical sciences, such as the ideal gas law and the Nernst
equation.)
GRAVITATIONAL CONSTANT
6.67206 x 10^11 newtons x meters^3/(kilograms*second^2)
Denoted by letter G, it is an empirical physical constant involved
in the calculation of gravitational effects.
IMPEDENCE IN VACUUM
3.767303134 x 10^2 ohms
(The waveimpedence of a plane wave in free space. Electric field
strength divided by the magnetic field strength.)
SPEED OF LIGHT
299,792,458 meters/second
SPEED OF LIGHT IN A VACUUM SQUARED
89,875,517,873,681,764 meters^2/seconds^2
MAGNETIC FLUX QUANTUM
2.06783383 x 10^15 webers
(The measure of the strength of a magnetic field over a given area
taken perpendicular to the direction of the magnetic field.)
MOLAR IDEAL GAS VOLUME
22.41410×10^3 meters^3/moles
(As all gases that are behaving ideally have the same number density,
they will all have the same molar volume. It is useful if you want to
envision the distance between molecules in different samples.)
MUON REST MASS
1.8835327×10^28 kilograms
(A muon is an elementary particle similar to an electron, with an electric
charge of 1 and a spin of 1/2, but with a much greater mass.)
NEUTRON COMPTON WAVELENGTH
1.31959110 x 10^15 meters
(Explains the scattering of photons by electrons. The compton
wavelength of a particle is equal to the wavelength of a photon
whose energy is the same as the mass of the particle.)
NEUTRINO REST MASS
3.036463233*10^35 kilograms
NUCLEAR MAGNETON
5.0507866 X 10^27 Henry/meters
(A physical constant of magnetic moment. Using the mass of a proton,
rather than the electron, used to calculate the Bohr magneton. unit of
magnetic moment, used to measure proton spin and approximately
equal to 1.1,836 Bohr magneton.)
PERMEABILITY CONSTANT
12.5663706144 x 10^7 Henry/meters
(Magnetic constant, or the permeability of free space, is a measure of
the amount of resistance encountered when forming a magnetic field
in a classical vacuum.)
PERMITTIVITY CONSTANT
8.854187817 x 10^12 farad/meters
(A constant of proportionality that exists between electric displacement
and electric field intensity in a given medium.)
PLANCK’S CONSTANT
6.6260755×10^34 joules/hertz
6.62607004×10^34 meters^2 x kilograms/seconds
(This constant links the about of energy a photon carries with the
frequency of its electromagnetic wave.)
PROTON COMPTON WAVELENGTH
2.4263102367 x 10^12 meters
(The compton wavelength is a quantum mechanical property of a
particle. A convenient unit of length that is characteristic of an elementary
particle, equal to Planck’s constant divided by the product of the particles
mass and the speed of light.)
PROTON MAGNETIC MOMENT
1.41060761 x 10^26 joules/tesla
(The dipole of the proton. Protons and neutrons, both nucleons,
comprise the nucleus of an atom, and both nucleons act as small
magnets whose strength is measured by their magnetic moments.)
PROTON MAGNETIC MOMENT IN BOHR MAGNETONS
1.521032202 x 10^3
(A physical constant and the natural unit for expressing the magnetic
moment of an electron caused by either its orbit or spin angular
momentum.
PROTON MASS/ELECTRON MASS
1,836.152701
PROTON REST MASS
1.6726231 x 10^27 kilograms
RYDBERG CONSTANT
1.0973731534 x 10^7/meters
(A physical constant relating to atomic spectra, in the science of
spectroscopy. Appears in the Balmer formula for spectral lines of the
hydrogen atom.)
RYDBERG ENERGY
13.6056981 electronvolts
(It corresponds to the energy of the photon whose wavenumber is the
Rydberg constant, I.e. the ionization of the hydrogen atom. It describe
the wavelengths of spectral lines of many elements.)
STEFANBOLTZMANN CONSTANT
5.67051 x 10^8 weber/(meters^2 x kelvin^4)
(The power per unit area is directly proportional to the 4th power of the
thermodynamic temperature. It is the total intensity radiated over all
wavelengths as the temperature increases, of a black body which is
proportional to to 4th power of the thermodynamic temperature.)
Table of physical constants
Universal constants
Value
Quantity Symbol
299 792 458 m⋅s−1defined newtonian gravitational constant G
Relative standard uncertainty
Speed of light in a vacuum
6.67408(31)×10−11 m3⋅kg−1⋅s−2 Planck’s constant
6.626 070 040(81) × 10−34 J⋅s. Reduced planck’s constant=h/2 x pi
1.054 571 800(13) × 10−34 J⋅s.
4.7 × 10−5 1.2 × 10−8
1.2 × 10−8
Electromagnetic constants Quantity
Symbol
Value (SI units)
Relative standard uncertainty
Magnetic constant (vacuum permeability)μ0
4π × 10−7 N⋅A−2 = 1.256 637 061… × 10−6 N⋅A−2defined
Electric constant (vacuum permittivity)ε0=1/μ0c2 8.854 187 817… × 10−12 F⋅m−1defined
Characteristic impedance of vacuum Z0=μ0c
376.730 313 461… Ωdefined
Coulomb’s constant ke=1/4πε0
8.987 551 787 368 176 4 × 109 kg⋅m3⋅s−4⋅A−2defined
Elementary charge e
1.602 176 6208(98) × 10−19 C.
Bohr magneton μB=eħ/2me 9.274 009 994(57) × 10−24 J⋅T−1
conductance quantuum
7.748 091 7310(18) × 10−5 S.
inverse conductance quantum
G0−1=h/2e2
12 906.403 7278(29) Ω 2.3 × 10−10
Josephson constant
kJ=2e/h
4.835 978 525(30) × 1014 Hz⋅V−1 6.1 × 10−9
magnetic flux quantum
φ0=h/2e
2.067 833 831(13) × 10−15 Wb 6.1 × 10−9
nuclear magneton
μN=eħ/2mp
5.050 783 699(31) × 10−27 J⋅T−1 6.2 × 10−9
von Klitzing constant
RK=h/e2
25 812.807 4555(59) Ω 2.3 × 10−10
6.1 × 10−9
6.2 × 10−9 2.3 × 10−10
Atomic and nuclear constants Quantity
Symbol
Value (SI units)
Relative standard uncertainty bohr radius
a0=α/4πR∞
5.291 772 1067(12) × 10−11 m 2.3 × 10−9
classical electron radius
re=e2/4πε0mec2m_
2.817 940 3227(19) × 10−15 m 6.8 × 10−10
electron mass
me
9.109 383 56(11) × 10−31 kg 1.2 × 10−8
fermi coupling constant
GF/(ħc)3
1.166 3787(6) × 10−5 GeV−2 5.1 × 10−7
finestructure constant
α=μ0e2c/2h=e2/4πε0ħc
7.297 352 5664(17) × 10−3 2.3 × 10−10
Hartree energy
Eh=2R∞hc
4.359 744 650(54) × 10−18 J 1.2 × 10−8
proton mass
mp
1.672 621 898(21) × 10−27 kg 1.2 × 10−8
quantum of circulation
h/2me
3.636 947 5486(17) × 10−4 m2 s−1 4.5 × 10−10
Rydberg constant
R∞=α2mec/2h
10 973 731.568 508(65) m−1 5.9 × 10−12
Thomson cross section
(8π/3)re2
6.652 458 7158(91) × 10−29 m2 1.4 × 10−9
weak mixing angle
sin2θW=1−(mW/mZ)2 0.2223(21)
9.5 × 10−3
efimov factor
22.7
Physicochemical constants Quantity
Symbol Relative standard uncertainty
Value (SI units)
Atomic mass constant
mu=1u
1.660539040(20)×10−27 kg 1.2×10−8
avagadro’s constant
NA,L
6.022140857(74)×1023 mol−1 1.2×10−8
boltzmann’s constant
k=kB=R/NA
1.38064852(79)×10−23 J⋅K−1 5.7×10−7
faraday’s constant
F=NAe
96485.33289(59) C⋅mol−1 6.2×10−9
first radiation constant
c1=2πhc2
3.741 771 790(46) × 10−16 W⋅m2 1.2 × 10−8
for spectral radiance
c1L=c1/π
1.191 042 953(15) × 10−16 W⋅m2⋅sr−1 1.2 × 10−8
loschmidt constant
atT = 273.15 K and p = 101.325 kPa
n0=NA/Vm
2.686 7811(15) × 1025 m−3 5.7 × 10−7
gas constant
R
8.3144598(48) J⋅mol−1⋅K−1 5.7×10−7
molar Planck constant
NAh
3.990 312 7110(18) × 10−10 J⋅s⋅mol−1 4.5 × 10−10
molar volume of an ideal gas
atT = 273.15 K and p = 100 kPa
Vm=RT/p
2.271 0947(13) × 10−2 m3⋅mol−1
5.7 × 10−7
at T= 273.15 K and p= 101.325 kPa2.241 3962(13) × 10−2 m3⋅mol−1 5.7 × 10−7
sackertetrode constant
at
T= 1 K and p= 100 kPa S0/R=52/R=+ln[(2πmukT/h2)3/2kT/p]
−1.151 7084(14)1.2 × 10−6at T= 1 K and p = 101.325 kPa −1.164 8714(14)1.2 × 10−6
second radiation constant
c2=hc/k
1.438 777 36(83) × 10−2 m⋅K 5.7 × 10−7
stefanboltzmann constant
σ=π2k4/60ħ3c2
5.670367(13)×10−8 W⋅m−2⋅K−4 2.3×10−6
wien displacement law constant
b energy=hck−1/=hck^ 4.965 114 231…
2.8977729(17)×10−3 m⋅K
5.7×10−7
Wien’s entropy displacement law constant
b entropy=hck−1/=hck^ 4.791 267 357…
3.002 9152(05) × 10−3 m⋅K 5.7 × 10−7
Adopted values Quantity
Symbol
Value (SI units)
Relative standard uncertainty conventional value of josephson constant
KJ−90
4.835 979 × 1014 Hz⋅V−1
0 (defined)
conventional value of von klitzing constant
RK−90
25 812.807 Ω
0 (defined)
constant
Mu=M(12C)/12
1 × 10−3 kg⋅mol−1 0 (defined)
of carbon12
M(12C)=NAm(12C)
1.2 × 10−2 kg⋅mol−1 0 (defined)
Molar mass
standard acceleration of gravity (gee, freefall on Earth) gn
9.806 65 m⋅s−20 (defined) standard atmosphere
atm
101 325 Pa 0 (defined)
ATOMIC MASS UNITS
1.6605402 x 10^27 kilograms
(1/12 0f the mass of an atom of carbon12)
AVOGADRO NUMBER
6.0221367 x 10^23/moles
(mole=number of elementary entities that are in carbon12 atoms in exactly 12 grams of carbon12)
BOHR’S MAGNETON
9.2740154 x 10^24 joules/tesla
(The magnetic moment of an electron caused by either its orbital
or spin angular momentum. Magnetic moment is a quantity that determines the torque it will experience in an external magnetic
field. Torque is rotational force. A joule is equal to the work done on an object when a force of 1 newton acts on the object in the direction of motion through a distance of 1 meter: kilograms x meters^2/ seconds^2. A joule is also equal to 10 million ergs. A Tesla is a derived unit of the strength of a magnetic field: kilograms/(seconds^2 x amperes.)
BOHR RADIUS
5.29177249 x 10^11 meters
(The mean radius of an electron around the nucleus of a hydrogen atom at its ground state.)
BOLTZMANN CONSTANT
1.3806513 x 10^23 joules/kelvin
(A physical constant relating the average kinetic energy of particles in a gas with the temperature of the gas. Kelvin temperature scale is the primary unit of temperature measurement in the physical sciences, but is often used in conjunction with the celsius degree, which is of the same magnitude absolute zero in kelvin is equal to 273.15 degrees celsius.)
COSMOLOGICAL CONSTANT
R=1/2Rg=8 x pi x 6.67 x 10^11 x T
(T=energymomentum tensor)
The constant is a homogeneous energy density that causes the expansion of the universe to accelerate.
ELECTRON CHARGE
1.60217733 x 10^19 coulombs
(Charge carried by a single electron. The coulomb is the quantity of charge that has passed through the cross section of an electrical conductor carrying one ampere within one second.)
ELECTRON CHARGE/MASS RATIO
1.75881962 x 10^11 coulombs/kilograms
(The importance of the chargetomass ratio, according to classical electrodynamics, is that 2 particles with the same chargetomass ratio move in the same path in a vacuum when subjected to the same electric and magnetic fields.)
ELECTRON COMPTON WAVELENGTH 2.42631058 X 10^12 meters
(A compton wavelength of a particle is equal to the wavelength of a photon whose energy is the same as the mass of the particle. The compton wavelength of an electron is the characteristic length scale of quantum electrodynamics. It is the length scale at which relativistic quantum field theory becomes crucial for its accurate description.)
ELECTRON MAGNETIC MOMENT 9.2847701 x 10^24 joules/tesla
(The electron is a charged particle of 1e, where e is the unit of elementary charge. Its angular momentum comes from 2 types of rotation: spin and orbital motion.)
ELECTRON MAGNETIC MOMENT IN BOHR MAGNETONS 1.00159652193
(Bohr magneton is a physical constant and natural unit for expressing the magnetic moment of an electron caused by either its orbital or spin angular momentum. The electron magnetic moment, which is the electron’s intrinsic spin magnetic moment, is approximately one Bohr magneton.)
ELECTRON MAGNETIC MOMENT/PROTON MAGNETIC MOMENT 658.21068801
ELECTRON REST MASS
9.1093897 x 10^31 kilograms
ELECTRON REST MASS/PROTON REST MASS 5.44617013 x1 0^4
This is how much less mass the electron is as compared to the proton. (1,836.21 times lighter than proton)
FARADAY CONSTANT
9.6458309 x 10^4 coulombs/mole
(The magnitude of electric charge per mole of electrons.)
FINE STRUCTURE CONSTANT .00729735308
(The strength of the electromagnetic interaction between elementary particles.)
GAS CONSTANT
8.3144710 x 10^joules/(mole x kelvin)
(A physical constant which is featured in many fundamental equations in the physical sciences, such as the ideal gas law and the Nernst equation.)
GRAVITATIONAL CONSTANT
6.67206 x 10^11 newtons x meters^3/(kilograms*second^2)
Denoted by letter G, it is an empirical physical constant involved in the calculation of gravitational effects.
IMPEDENCE IN VACUUM
3.767303134 x 10^2 ohms
(The waveimpedence of a plane wave in free space. Electric field strength divided by the magnetic field strength.)
SPEED OF LIGHT
299,792,458 meters/second
SPEED OF LIGHT IN A VACUUM SQUARED 89,875,517,873,681,764 meters^2/seconds^2
MAGNETIC FLUX QUANTUM
2.06783383 x 10^15 webers
(The measure of the strength of a magnetic field over a given area taken perpendicular to the direction of the magnetic field.)
MOLAR IDEAL GAS VOLUME 22.41410×10^3 meters^3/moles
(As all gases that are behaving ideally have the same number density, they will all have the same molar volume. It is useful if you want to envision the distance between molecules in different samples.)
MOLAR MASS CONSTANT 1×10^3 kilograms/moles (relates relative atomic mass and molar mass)
MOLAR MASS OF CARBON12— 1.2×10^2 kilograms/moles (relates atomic mass of carbon12 and molar mass)
MUON REST MASS
1.8835327×10^28 kilograms
(A muon is an elementary particle similar to an electron, with an electric charge of 1 and a spin of 1/2, but with a much greater mass.)
NEUTRON COMPTON WAVELENGTH 1.31959110 x 10^15 meters
(Explains the scattering of photons by electrons. The compton wavelength of a particle is equal to the wavelength of a photon whose energy is the same as the mass of the particle.)
NEUTRINO REST MASS 3.036463233*10^35 kilograms
NUCLEAR MAGNETON
5.0507866 X 10^27 Henry/meters
(A physical constant of magnetic moment. Using the mass of a proton, rather than the electron, used to calculate the Bohr magneton. unit of magnetic moment, used to measure proton spin and approximately equal to 1.1,836 Bohr magneton.)
PERMEABILITY CONSTANT
12.5663706144 x 10^7 Henry/meters
(Magnetic constant, or the permeability of free space, is a measure of the amount of resistance encountered when forming a magnetic field in a classical vacuum.)
PLANCK CHARGE 1.875545956×10^18 coulombs (a quantity of electric charge)
PERMITTIVITY CONSTANT
8.854187817 x 10^12 farad/meters
(A constant of proportionality that exists between electric displacement and electric field intensity in a given medium.)
PLANCK’S CONSTANT
6.6260755×10^34 joules/hertz
6.62607004×10^34 meters^2 x kilograms/seconds
(This constant links the about of energy a photon carries with the frequency of its electromagnetic wave.)
PLANCK CONSTANT (REDUCED) 6.582119514×10^16 eVseconds
(hbar, in which h equals h divided by 2pi, is the quantization of angular momentum.)
PLANCK’S LENGTH 1.616229X10&35 meters
(the scale at which classical ideas about gravity and spacetime cease to be valid, and quantum effects dominate.)
PLANCK MASS 2.17647X10^8 kilograms
(derived approximately by setting it as the mass whose compton wavelength and schwarzschild radius are equal.)
PLANCK TIME 5.3916×10^44 seconds
(time needed for light to travel 1 planck length in a vacuum.)
PLANCK TEMPERATURE 1.416808×10^32 degrees kelvin
(if an object were to reach this temperature, the radiation it would emit would have a wavelength of 1.616×10^35 meters, Planck’s length, at which point quantum gravitational effects become relevant.)
PROTON COMPTON WAVELENGTH 2.4263102367 x 10^12 meters
(The compton wavelength is a quantum mechanical property of a particle. A convenient unit of length that is characteristic of an elementary particle, equal to Planck’s constant divided by the product of the particles mass and the speed of light.)
PROTON MAGNETIC MOMENT
1.41060761 x 10^26 joules/tesla
(The dipole of the proton. Protons and neutrons, both nucleons, comprise the nucleus of an atom, and both nucleons act as small magnets whose strength is measured by their magnetic moments.)
PROTON MAGNETIC MOMENT IN BOHR MAGNETONS 1.521032202 x 10^3
(A physical constant and the natural unit for expressing the magnetic moment of an electron caused by either its orbit or spin angular momentum.
RYDBERG CONSTANT
1.0973731534 x 10^7/meters
(A physical constant relating to atomic spectra, in the science of spectroscopy. Appears in the Balmer formula for spectral lines of the hydrogen atom.)
RYDBERG ENERGY
13.6056981 electronvolts
(It corresponds to the energy of the photon whose wavenumber is the Rydberg constant, I.e. the ionization of the hydrogen atom. It describe the wavelengths of spectral lines of many elements.)
STANDARD ACCELERATION ON EARTH BY GRAVITY 9.80665 meters/seconds^2
STANDARD ATMOSPHERE 101.325 pascals
(pressure, temperature, density, and viscosity of the earth’s atmosphere.)
STEFANBOLTZMANN CONSTANT
5.67051 x 10^8 weber/(meters^2 x kelvin^4)
(The power per unit area is directly proportional to the 4th power of the thermodynamic temperature. It is the total intensity radiated over all wavelengths as the temperature increases, of a black body which is proportional to to 4th power of the thermodynamic temperature. This constant is used to link a star’s temperature to the amount of light it emits.)
MAGNETIC CONSTANT (VACUUM PERMIABILITY) 1.256637061X10^6 NEWTONS/AMPERES^2
ELECTRIC CONSTANT (VACUUM PERMITTIVITY) 8.854187817X10^12 FARAD/METER
CHARACTERISTIC IMPEDANCE OF VACUUM 376.730313461 OHMS
COULOMB’S CONSTANT
8.9875517873881764X10^8 KILOGRAMS METERS^3/
SECONDS^4XAMPERES^2
ELEMENTARY CHARGE
1.6021766208X10^19 COULOMBS
CONDUCTIVE QUANTUM
7.748091731X10^8 SECONDS
INVERSE CONDUCTIVE QUANTUUM 12.9064037278 OHMS
JOSEPHSON CONSTANT
4.835978525X10^14 HERTZ/VOLTS
MAGNETIC FLUX QUANTUM 2.067831X10^15 WEBERS
NUCLEAR MAGNETON
5.050783699X10^27 JOULES/TESLAS
VON KILTZING CONSTANT 258.12807557 ohms
CLASSICAL ELECTRON RADIUS 2.8179403227X10^15 METERS
ELECTRON MASS
9.10938356×10^31 kilograms
FERMI COUPLING CONSTANT 1.1663787X10^5 GeV^2
FINESTRUCTURE CONSTANT 7.2972525664X10^3
HARTREE ENERGY
4.35974465X10^18 JOULES
PROTON MASS
1.6726219×10^27 kilograms
QUANTUM OF CIRCULATION
3.6369475486X10^4 METERS^2/SECONDS
THOMSON CROSS SECTION 6.6524587158X10^29 METERS^2
WEAK MIXING ANGLE .2223
EFIMOV FACTOR 22.7
FIRST RADIATION CONSTANT
3.74177179X10^16 WEBERMETERS^2
FIRST RADIATION CONSTANT (for spectral radiance) 1.191042953×10^16 webersmeters^2seconds/radius
Loschmidt constant
2.6867811×10^25 /meters^3
Molar planck constant
3.990312711×10^10 joulesseconds/moles
Molar volume of an ideal gas (at t=273.15 k and p=100 kpa) 2.2710947×10^2meters^3/moles
Molar volume of an ideal gas (at t=273.15 k and p=101.325 kpa) 2.2413962×10^2 meters^3/moles
Sackertetrode constant (at t=273.15 k and p=100 kpa) 1.1517084
Sackertetrode constant (at t=273.15 k and p=101.325 kpa) 1.1648714
Second radiation constant
1.438777×10^2 meters kelvin
Wien displacement law constant 2.8977729×10^3 meters kelvin
Wien entropy displacement constant 3.0029152×10^3 meters kelvin
Conventional value of Josephson constant 4.835979×10^14 hertz/volts
Conventional value of von Klitzing constant 25812.807 ohms
2 PARAMETERS OF THE HIGGS FIELD POTENTIAL V(H)=lambda*(R^2v^2)=lambda*H^42*v^2*H^2*lambda*v^4
(H is the higgs field)
the higgs field is an energy field that is thought to exist everywhere in the universe. the field is accompanied by a fundamental particle called the higgs boson, which the field uses to continuously interact with other particles. the process of giving a particle mass is known as the higgs effect.
SCIENCES FORMULAS
FORMULAS:BEAUTIFUL & SCIENTIFIC, and UNIVERSAL PHYSICAL CONSTANTS
BEAUTIFUL FORMULAS
8/29/178/30/17;9/15/17;11/21/1711/22/17;12/25/17; 4/19/18
CONTENTS
 Dirac’s equation
 Einstein’s field equation
 Maxwell’s equations
 General relativity
 Special relativity
 Schrodinger’s equation
 Uncertainty principle
 Gibb’s statistical mechanics
 StephanBoltzmann law
 e=mc^2
 Laplace equation
 De broglie relationmatter wave
 Navierstokes equations
 Riemann zeta function
 Noether theorem
 Eulerlagrange equation
 Hamilton quanternion
 Standard model
 Lagrange formula
 cantor inequality
 Riemann hypothesis
 HawkingBekenstein entropy formula
 Heat equation
 wave equation
 poisson equation
 Waveparticle duality
 fundamental theorem of calculus
 Pythagorean theorem
 GaussBonnet theorem
 universal law of gravitation
 Newton’s 2nd law of motion
 kinetic energy
 Potential energy
 2nd law of thermodynamics
 principle of least action
 Spherical harmonics
 Cauchy residue theorem
 CallenSymanzik equation
 Minimal surface equation
 Euler 9 point center
 Mandelbrot set
 YangBaxter equation
 Divergence theorem
 Baye’s theorem
 logistic map
 Einstein’s law of velocity addition
 Photoelectric effect formula
 Faraday law
 Cauchy momentum equation
 De moivre’s theorem
 Fourier transform
 prime counting function
 Murphy’s law
 Summation formula
 Logarithmic spiral
 Heron’s formula
 Quadratic equation
 Euler line
 Pythagorean triple formula
 Euler’s formula
 Simplex method
 Proof of infinity of prime numbers
 Harmonic series
 Euler sums
 Cubic equation
 Quartic equation
 quintic equation
 Lorentz equation
 Eulerlagrange formula
 Euler product formula
 Eulermaclaurin formula
 Pi
 Exponent
 Natural logarithm
 Conic sections
 exponential growth or decay
 Calculation an orbit I.e. a comet
 interesting number idea 1
 interesting number idea 2
 interesting number idea 3
EQUATIONS
 1. Dirac equation
The Dirac differential equation from quantum mechanics was formulated in 1928 which predicted the existence of antimatter, which are particle of the same mass and spin, but have an opposite charges than their counterparts of matter.
2. Einstein field equation
The einstein field equations, or the einsteinhilbert equations is used to describe gravity in a classical way. It uses geometry to model gravity’s effects.
3. Maxwell’s equations
James clerk maxwell formulated 4 differential equations to describe how charged particles produce an electric and magnetic force. They calculate the motion of particles in electric and magnetic fields. They describe how electric charges and electric currents create electric and magnetic fields, and vice versa. The 1st equation is used to calculate the electric field produced by a charge.
The 2nd equation is used to calculate the magnetic field. The 3rd equation, ampere’s law, shows how the magnetic fields circulate around electric currents and time varying electric fields. The 4th equation. Faraday’s law, shows how the electric fields circulate around time varying magnetic fields.
4. General relativity
Albert einstein, in 1915, formed the general theory of relativity which deals with space and time, two aspects of spacetime. Spacetime curves when there is gravity, matter, energy, and momentum. Central the the general theory of relativity is the principle of equivalence. The theory shows that light curves in an accelerating frame of reference. It also asserts that light will bend and it will slow down in the presence of a massive amount matter.
5. SPECIAL RELATIVITY
The Lorentz Transformations is the mathematical basis for the special theory of relativity. The special theory of relativity asserts that the speed of light is the same no matter what speed the observer travels. It also explains what is relative and what is absolute about time, space, and motion. It further describes how mass increases, length shrinks, time slows down for objects moving close to the speed of light, and that a person traveling close to the speed of light would age less than would a stationary person.
6. Schrodinger’s equation
This is a differential equation that is the basis of quantum mechanics. It is one of the most precise theories of how subatomic particles behave as fully as possible. This equation defines a wave function of a particle or group of particles that have a certain value at every point in space for every given time. the wave function contains all information that can be known about a particle or system. The wave function gives real values relating to physical properties such as position, momentum, energy, etc.
7. Uncertainty principle
This principle says that trying to pin a thing down to one definite position will make its momentum less well pinned down, and viceversa.
8. GIBB’S STATISTICAL MECHANICS
Statistical mechanics is a branch of theoretical physics which uses probability theory to study the average behavior of a mechanical system, where the state of the system is uncertain.
Statistical mechanics is commonly used to explain the thermodynamic behavior of large systems.
9. Stefan Boltzmann law
R=ÏƒT^{4}
where Ïƒ is the StefanBoltzmann constant, which is equal to 5.670 373(21) x 10^{8} W m^{2} K^{4}, and where R is the energy radiated per unit surface area and per unit time. T is temperature, which is measured in kelvin scale. this law is only usable for the energy radiated by blackbodies but is still useful none the less. In quantum physics, the StefanBoltzmann law (sometimes called Stefan’s Law) states that the black body radiation energy emitted by an object is directly proportional to the temperature of the object raised to the fourth power.
10. Mass energy equivalence
E=mc^2
In physics, mass energy equivalence asserts that anything having mass has an equivalent amount of energy and vice versa. these fundamental quantities are directly related to one another.
11. Laplace’s equation
In mathematics, Laplace’s equation is a secondorder partial differential equation. The solutions of Laplace’s equation are the harmonic functions, which are important in many fields of science, notably the fields of electromagnetism, astronomy, and fluid dynamics, because they can be used to accurately describe the behavior of electric, gravitational, and fluid potentials. In the study of heat conduction, the Laplace equation is the steadystate heat equation.
12. DEBROGLIE RELATION/Matter wave
Î»=h/mv
Where Î» is the wavelength of the object, h is Planck’s constant, m is the mass of the object, and v is the velocity of the object. An alternate but correct version of this formula is
Î»=h/p
Where p is the momentum. (Momentum is equal to mass times velocity). These equations merely say that matter exhibits a particlelike nature in some circumstances, and a wavelike characteristic at other times.
13. Navier Stokes equations
The Navier Stokes equations describe the motion of fluids. The equations result from applying newton’s 2nd law to fluid dynamics with the belief that the fluid stress is the sum of a diffusing vicious term (in relation to the gradient of velocity), plus a pressure term. They are very useful because they describe the physics of many things. They may be used to model weather, ocean currents, water flow in a pipe, the air’s flow around a wing, and the motion of stars inside a galaxy. The Navier Stokes equations in their full and simplified forms help with the design of aircraft and cars, the study of blood flow, the design of power stations, the analysis of pollution, and many other things. Together with Maxwell’s equations they can be used to model and study magnetohydrodynamics. The Navier Stokes equations are also of great interest in a purely mathematical sense. Somewhat surprisingly, given their wide range of practical uses, mathematicians have not yet proven that in three dimensions solutions always exist (existence), or that if they do exist, then they do not contain any singularities (or infinity or discontinuity) (smoothness). These are called the navierstokes existence and smoothness problems. The Navier Stokes equations dictate not position but rather velocity. A solution of the Navier Stokes equations is called a velocity field or flow field, which is a description of the velocity of the fluid at a given point in space and time. Once the velocity field is solved for, other quantities of interest (such as flow rate or drag force) may be found. This is different from what one normally sees in classical mechanics, where solutions are typically trajectories of position of a particle or deflection of a continuum. Studying velocity instead of position makes more sense for a fluid, however for visualization purposes one can compute various trajectories.
14. Riemann zeta function
Î¶(s)=âˆ‘n=1 to âˆž 1ns, Re(s)>1.
Where
Re(s) is the real part of the complex numbers. For example, if s=a+ib, then Re(s)=a. (where i^2=â1)
Riemann zeta function Î¶(s) in the complex plane. The color of a point s shows the value of Î¶(s): strong colors are for values close to zero and hue encodes the value’s argument. The white spot at s= 1 is the pole of the zeta function; the black spots on the negative real axis and on the critical line Re(s) = 1/2 are its zeros. In mathematics, the Riemann zeta function, is a prominent function of great significance in number theory. It is so important because of its relation to the distribution of prime numbers. It also has applications in other areas such as physics, probability theory, and applied statistics. The riemann hypothesis is a conjecture about the distribution of the zeros of the Riemann zeta function. Many mathematicians consider the Riemann hypothesis to be the most important unsolved problem in pure mathematics.
15. Noether’s theorem
dX/dt=0
Emmy noether was an influential mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics.
Noether’s theorem can be stated informally:
If a system has a continuous symmetry property, then there are corresponding quantities whose values are conserved in time.
A more sophisticated version of the theorem involving fields states that:
To every differentiable symmetry generated by local actions, there corresponds a conserved current.
16. Euler Lagrange equation
In the calculus of variations, the Euler Lagrange equation, Euler’s equation, or Lagrange’s equation (although the latter name is ambiguous), is a secondorder partial differential equation whose solutions are the functions for which a given functional is stationary. Because a differentiable functional is stationary at its local maxima and minima, the Euler Lagrange equation is useful for solving optimization problems in which, given some functional, one seeks the function minimizing or maximizing it. This is analogous to format’s theorem in calculus, stating that at any point where a differentiable function attains a local extremum its derivative is zero. In Lagrangian mechanics, because of Hamilton’s principle of stationary action, the evolution of a physical system is described by the solutions to the Euler Lagrange equation for the action of the system. In \classical mechanics, it is equivalent to newton’s law of motion, but it has the advantage that it takes the same form in any system of generalized coordinates, and it is better suited to generalizations. In classical field theory there is an analogous equation to calculate the dynamics of a field.
17. Quaternion
a + bi + cj + dk
where a, b, c, and d are real numbers, and i, j, and k are the fundamental quaternion units.
In mathematics, the quaternions are a number system that extends the complex numbers. they are applied to in 3dimensional space. A feature of quaternions is that multiplication of two quaternions is noncommutative. Hamilton defined a quaternion as the quotient of two directed lines in a threedimensional space^{]} or equivalently as the quotient of two vectors.
Quaternions find uses in both theoretical and applied mathematics, in particular for calculations involving 3dimensional rotations such as in 3dimensional computer graphics, computer vision and crystallographic texture analysis. In practical applications, they can be used alongside other methods, such as euler angles and rotation matrices, or as an alternative to them, depending on the application.
18. Standard Model (mathematical formulation) for particle physics
19. LAGRANGE FORMULA
Lagrangian mechanics is a reformulation of classical mechanics. In Lagrangian mechanics, the trajectory of a system of particles is derived by solving the Lagrange equations in one of two forms, either the Lagrange equations of the first kind, which treat constraints explicitly as extra equations, often using Lagrange multipliers; or the Lagrange equations of the second kind, which incorporate the constraints directly by judicious choice of generalized coordinates. In each case, a mathematical function called the Lagrangian is a function of the generalized coordinates, their time derivatives, and time, and contains the information about the dynamics of the system.
20. CANTOR’S INEQUALITY/Cantor’s theorem
In elementary set theory, Cantor’s theorem is a fundamental result that states that, for any set A, the set of all subsets of A (the power sets of A, ð’«(A)) has a strictly greater cardinality than A itself. For finite sets, Cantor’s theorem can be seen to be true by simple enumeration of the number of subsets. Counting the empty subset, a set with n members has 2^{n} subsets, so that if card(A) = n, then card(ð’«(A)) = 2^{n}, and the theorem holds because 2^{n} > n is true for all nonnegative integers.
the theorem implies that there is no largest cardinal number (colloquially, “there’s no largest infinity”
21. Riemann hypothesis
The Riemann hypothesis is a mathematical conjecture. Many people think that finding a proof of the hypothesis is one of the hardest and most important unsolved problems of pure mathematics.
The hypothesis is named after Bernhard riemann. It is about a special function, the riemann zeta function. This function inputs and outputs complex numbers values. The inputs that give the output zero are called zeros of the zeta function. Many zeros have been found. The “obvious” ones to find are the negative even integers. This follows from Riemann’s functional equation. More have been computed and have real part 1/2. The hypothesis states all the undiscovered zeros must have real part 1/2. The functional equation also says all zeros (except the “obvious” ones) must be in the critical strip: real part is between 0 and 1. The Riemann hypothesis says more: they are on the line given, in the image on the right (the white dots). If the hypothesis is false, this would mean that there are white dots which are not on the line given. If proven correct, this would allow mathematicians to better describe how the prime numbers are placed among whole numbers. The Riemann hypothesis is so important, and so difficult to prove, that the Clay Mathematics Institute has offered $1,000,000 to the first person to prove it.
22. HAWKINGBEKENSTEIN ENTROPY FORMULA
blackhole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of Blackhole event horizons. As the study of the statistical mechanics of blackbody radiation led to the advent of the theory of quantum mechanics, the effort to understand the statistical mechanics of black holes has had a deep impact upon the understanding of quantum gravity, leading to the formulation of the holographic principle. The 2nd law of thermodynamics requires that black holes have entropy. If black holes carried no entropy, it would be possible to violate the second law by throwing mass into the black hole. The increase of the entropy of the black hole more than compensates for the decrease of the entropy carried by the object that was swallowed.
23. HEAT EQUATION
The heat equation is a parabolic partial differential equation that describes the distribution of heat (or variation in temperature) in a given region over time. In the heat equation in two dimensions predicts that if one area of an otherwise cool metal plate has been heated, say with a torch, over time the temperature of that area will gradually decrease, starting at the edge and moving inward. Meanwhile the part of the plate outside that region will be getting warmer. Eventually the entire plate will reach a uniform intermediate temperature. The heat equation is of fundamental importance in diverse scientific fields. In mathematics, it is the prototypical parabolic partial differential equation. In probability theory, the heat equation is connected with the study of brownian motion via the Fokkerplanck equation.In financial mathematics, it is used to solve the blackscholes partial differential equation. The diffusion equation, a more general version of the heat equation, arises in connection with the study of chemical diffusion and other related processes. The heat equation is used in probability and describes random walks. It is also applied in financial mathematics for this reason. It is also important in riemannian geometry and thus topology: it was adapted by richard s. Hamilton when he defined the Ricci flow that was later used by Grigori perelmanto solve the topological poincare conjecture.
24. Wave equation
iâ„âˆ‚/âˆ‚tÎ¨(x,t)=H^Î¨(x,t)
where i is the imaginary number, Ïˆ (x,t) is the wave function, Ä§ is the reduced planck constant, t is time, x is position in space, Ä¤ is a mathematical object known as the Hamilton operator. The reader will note that the symbol âˆ‚/âˆ‚t denotes that the partial derivative of the wave function is being taken. Equations that describe waves as they occur in nature are called wave equations. Waves as they occur in rivers, lakes, and oceans are similar to those of sound and light. The problem of having to describe waves arises in fields like acoustics, electromagnetic, and fluid dynamics. Historically, the problem of a vibrating string such as that of a musical instruments was studied.Â In 1746, d’Alambert discovered the onedimensional wave equation, and within ten years Euler discovered the threedimensional wave equation. In quantum mechanics, the Wave function, usually represented by Î¨, or Ïˆ, describes the probability of finding an electron somewhere in its matter wave. To be more precise, the square of the wave function gives the probability of finding the location of the electron in the given area, since the normal answer for the wave function is usually a complex number. The wave function concept was first introduced in the legendary schrodinger equation.
25. Poisson’s equation
âˆ‡^2Ï†=f.
(âˆ‚^2/âˆ‚x^2+âˆ‚^2/âˆ‚y^2+âˆ‚^2/âˆ‚z^2)Ï†(x,y,z)=f(x,y,z).
When f=0 identically we obtain laplace’s equation.
In mathematics, Poisson’s equation is a partial differential equation of elliptic type with broad utility in mechanical engineering and theoretical physics. It arises, for instance, to describe the potential field caused by a given charge or mass density distribution; with the potential field known, one can then calculate gravitational or electrostatic field. It is a generalization of laplace’s equation, which is also frequently seen in physics. Poisson’s equation may be solved using a green’s function.
26.Wave particle duality
Wave particle duality is perhaps one of the most confusing concepts in physics, because it is so unlike anything we see in the ordinary world. Physicists who studied light in the 1700s and 1800s were having a big argument about whether light was made of particles shooting around like tiny bullets, or waves washing around like water waves. Light seems to do both. At times, light seems to go only in a straight line, as if it were made of particles. But other experiments show that light has a frequency and wavelength, just like a sound wave or water wave. Until the 20th century, most physicists thought that light was either one or the other, and that the scientists on the other side of the argument were simply wrong. Wave particle duality means that all particles show both wave and particle properties. This is a central concept of quantum mechanics. Classical concepts like “particle” and “wave” do not fully describe the behavior of quantumscale objects.
27. Fundamental theorem of calculus
The fundamental theorem of calculus is central to the study of calculus. It is the theorem that shows the relationship between the derivative and the integral and between the definite integral and the indefinite integral. It is broken into two parts, the first fundamental theorem of calculus and the second fundamental theorem of calculus.
The first fundamental theorem of calculus states that if the function f is continuous, then
d/dxâˆ«axf(t)dt=f(x)
This means that the derivative of the integral of a function f with respect to the variable t over the interval [a,x] is equal to the function f with respect to x. This describes the derivative and integral as inverse processes.
28. Pythagorean theorem
In mathematics, the Pythagorean theorem or Pythagoras’s theorem is a statement about the sides of a right triangle. One of the angles of a right triangle is always equal to 90 degrees. This angle is the right angle. The two sides next to the right angle are called the legs and the other side is called the hypotenuse. The hypotenuse is the side opposite to the right angle, and it is always the longest side. The Pythagorean theorem says that the area of a square on the hypotenuse is equal to the sum of the areas of the squares on the legs. In this picture, the area of the blue square added to the area of the red square makes the area of the purple square. If the lengths of the legs are a and b, and the length of the hypotenuse is c, then,
a^2+b^2=c^2.
Pythagorean Triples
Pythagorean Triples or Triplets are three whole numbers which fit the equation
a^2+b^2=c^2.
The triangle with sides of 3, 4, and 5 is a well known example. If a=3 and b=4, then
3^2+4^2=5^2
because
9+16=25. This can also be shown as 3^2+4^2=5.
The threefourfive triangle works for all multiples of 3, 4, and 5. In other words, numbers such as 6, 8, 10 or 30, 40 and 50 are also Pythagorean triples. Another example of a triple is the 12513 triangle, because
12^2+5^2=13
29. Gauss Bonnet theorem
The Gauss Bonnet theorem or Gauss Bonnet formula in differential geometry is an important statement about surfaces which connects their geometry (in the sense of curvature) to their topology (in the sense of the euler characteristic).
30. Newton’s law of universal gravitation
Fg=Gm1m2/r2,
Newton’s universal law of gravitation is a physical law that describes the attraction between two objects with mass.
In this equation:
F_{g} is the total gravitational force between the two objects.
G is the gravitational constant.
m_{1} is the mass of the first object.
m_{2} is the mass of the second object.
r is the distance between the centres of the objects.
In SI units, F_{g} is measured in newtons (N), m_{1} and m_{2} in kilograms (kg), r in meters (m), and the constant G is approximately equal to 6.674Ã—10^{11} N m^{2} kg
31. Newton’s 2nd law of motion
F=ma.
For a particle of mass m, the net force F on the particle is equal to the mass m times the particle’s acceleration a.
32. Kinetic energy
Kinetic energy is the energy that an object has because of its motion. This energy can be converted into other kinds, such as gravitational or electric potential energy, which is the energy that an object has because of its position in a gravitational or electric field.
Translational kinetic energy
The translational kinetic energy of an object is:
E translational=1/2mv^2
where m is the mass (resistance to linear acceleration or deceleration); v is the linear velocity.
Rotational kinetic energy
The rotational kinetic energy of an object is:
E rotational=1/2I^2
where I is the moment of inertia (resistance to angular acceleration or deceleration, equal to the product of the mass and the square of its perpendicular distance from the axis of rotation);
Ï is the angular velocity.
33. Potential energy
Potential energy is the energy that an object has because of its position on a gradient of potential energy called a potential field.
Actual energy (E = hf) is nonzero frequency angular momentum.
Potential energy (rest mass) is zero frequency angular momentum.
The potential fields are irrotationally radial (“electric”) fluxes of the vacuum and divide into two classes:
The gravitoelectric fields;
The electric fields.
The potential energy is negative. It is not a mere convention but a consequence of conservation of energy in the zeroenergy universe as an object descends into a potential field, its potential energy becomes more negative, while its actual energy becomes more positive, and, in accordance with the 2nd law of thermodynamics, tends to be radiated away, so that the object acquires a net negative potential energy, also known as the object’s binding energy.
In accordance with the minimal total potential energy principle, the universe’s matter flows towards ever more negative total potential energy. This cosmic flow is time.
Gravitational potential energy
Self gravitating sphere
The gravitational potential energy of a massive spherical cloud is proportional to its radius and causes the sphere to fall towards its own centre.
Earth
If an object is lifted a certain distance from the surface from the earth, the force experienced is caused by weight and height. Work is defined as force over a distance, and work is another word for energy.
Electric potential energy
Electric potential energy is experienced by charges both different and alike, as they repel or attract each other. Charges can either be positive (+) or negative (), where opposite charges attract and similar charges repel.
Elastic potential energy
Elastic potential energy is experienced when a rubbery material is pulled away or pushed together. The amount of potential energy the material has depends on the distance pulled or pushed. The longer the distance pushed, the greater the elastic potential energy the material has.
34. Second law of thermodynamics
S (prime)S>=0
The second law of thermodynamics says that when energy changes from one form to another form, or matter moves freely, entropy (disorder) increases, in a closed system.
Differences in temperature, pressure, and density tend to even out horizontally after a while. Due to the force of gravity, density and pressure do not even out vertically. Density and pressure on the bottom will be more than at the top.
Entropy is a measure of spread of matter and energy to everywhere they have access.
The most common wording for the second law of thermodynamics is essentially due to Rudolf Clausius: It is impossible to construct a device which produces no other effect than transfer of heat from lower temperature body to higher temperature body In other words, everything tries to maintain the same temperature over time.
There are many statements of the second law which use different terms, but are all equal. Another statement by Clausius is:
heat cannot of itself pass from a colder to a hotter body.
An equivalent statement by Lord kelvin is:
A transformation whose only final result is to convert heat, extracted from a source at constant temperature, into work, is impossible.
The second law only applies to large systems. The second law is about the likely behavior of a system where no energy or matter gets in or out. The bigger the system is, the more likely the second law will be true.
In a general sense, the second law says that temperature differences between systems in contact with each other tend to even out and that work can be obtained from these nonequilibrium differences, but that loss of thermal energy occurs, when work is done and entropy increases. Pressure, density and temperature differences in an isolated system, all tend to equalize if given the opportunity; density and pressure, but not temperature, are affected by gravity. A heat engine is a mechanical device that provides useful work from the difference in temperature of two bodies.
Quotes
The law that entropy always increases, holds, I think, the supreme position among the laws of nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations a then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation a well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.
–Sir Arthur Stanley Eddington, The Nature of the Physical World (1927)
The tendency for entropy to increase in isolated systems is expressed in the second law of thermodynamics — perhaps the most pessimistic and amoral formulation in all human thought.
—Greg Hill and Kerry Thornley. principia discordia(1965)
There are almost as many formulations of the second law as there have been discussions of it.
–Philosopher / Physicist P.W. Bridgman, (1941)
35. Principle of least action
The principle of least action a or, more accurately, the principle of stationary action â’s a variational principle that, when applied to the action of a mechanical system, can be used to obtain the equations of motion for that system. In relativity, a different action must be minimized or maximized. The principle can be used to derive newtonian, lagrangian and hamiltonian equations of motion, and even general relativity. The principle remains central in modern physics and mathematics, being applied in thermodynamics, fluid mechanics, the theory of relativity, mechanics, particle physics, and string theory and is a focus of modern mathematical investigation in morse theory. maupertuis principle and Hamilton’s principle exemplify the principle of stationary action.
36. SPHERICAL HARMONICS
In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial differential equations that commonly occur in science. The spherical harmonics are a complete set of orthogonal functions on the sphere, and thus may be used to represent functions defined on the surface of a sphere, just as circular functions (sines and cosines) are used to represent functions on a circle via fourier series. Like the sines and cosines in Fourier series, the spherical harmonics may be organized by (spatial) angular frequency. Further, spherical harmonics are basis functions for SO(3), the group of rotations in three dimensions, and thus play a central role in the group theoretic discussion of SO(3).
37. Cauchy Residue theorem
In complex analysis, a discipline within mathematics, the residue theorem, sometimes called Cauchy’s residue theorem, is a powerful tool to evaluate line integrals of analytic functions over closed curves; it can often be used to compute real integrals as well. It generalizes the cauchy integral theorem and cauchy integral formula. From a geometrical perspective, it is a special case of the generalized stoke’s theorem.
38. Callan Symanzik equation
In physics, the Callan Symanzik equation is a differential equation describing the evolution of the npoint correlation functions under variation of the energy scale at which the theory is defined and involves the betafunction of the theory and the anomalous dimensions.
39. MINIMAL SURFACE EQUATION
In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature. The term “minimal surface” is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint. Physical models of areaminimizing minimal surfaces can be made by dipping a wire frame into a soap solution, forming a soap film, which is a minimal surface whose boundary is the wire frame. However the term is used for more general surfaces that may selfintersect or do not have constraints. For a given constraint there may also exist several minimal surfaces with different areas.
40. EULER’S 9 POINT CENTER/Ninepoint center
In geometry, the ninepoint center is a triangle center, a point defined from a given triangle in a way that does not depend on the placement or scale of the triangle. It is socalled because it is the center of the 9point circle, a circle that passes through nine significant points of the triangle: the midpoints of the three edges, the feet of the three altitudes, and the points halfway between the orthocenter and each of the three vertices.
41 MANDELBROT SETS
The Mandelbrot set is a famous example of a fractals in mathematics.The Mandelbrot set is important for the chaos theory. The edging of the set shows a selfsimilarity, which is not perfect because it has deformations.
42. Yang Baxter equation
In physics, the Yang Baxter equation (or startriangle relation) is a consistency equation which was first introduced in the field of statistical mechanics. It depends on the idea that in some scattering situations, particles may preserve their momentum while changing their quantum internal states. It states that a matrix
R, acting on two out of three objects, satisfies
(RâŠ—1)(1âŠ—R)(RâŠ—1)=(1âŠ—R)(RâŠ—1)(1âŠ—R)
In one dimensional quantum systems,
R is the scattering matrix and if it satisfies the Yang Baxter equation then the system is integrable. The Yang Baxter equation also shows up when discussing knot theory and the braid groups where
R corresponds to swapping two strands. Since one can swap three strands two different ways, the Yang Baxter equation enforces that both paths are the same.
43. DIVERGENCE THEOREM
In vector calculus, the divergence theorem, also known as Gauss’s theorem or Ostrogradsky’s theorem, is a result that relates the flow (that is, flux) of a vector field through a surface to the behavior of the vector field inside the surface. More precisely, the divergence theorem states that the outward flux of a vector field through a closed surface is equal to the volume integral of the divergence over the region inside the surface. Intuitively, it states that the sum of all sources (with sinks regarded as negative sources) gives the net flux out of a region. The divergence theorem is an important result for the mathematics of physics and engineering, in particular in electrostatics and fluid dynamics. In physics and engineering, the divergence theorem is usually applied in three dimensions. However, it generalizes to any number of dimensions. In one dimension, it is equivalent to the fundamental theorem of calculus. In two dimensions, it is equivalent to green’s theorem. The theorem is a special case of the more general stoke’s theorem.
44. Bayes’ theorem
P(AB)=P(BA)P(A)P(B).
In probability theory and applications, Bayes’ theorem shows the relation between a conditional probability and its reverse form. For example, the probability of a hypothesis given some observed pieces of evidence and the probability of that evidence given the hypothesis.
45. Logistic map
xn+1=rxn(1xn)
where xn is a number between zero and one that represents the ratio of existing population to the maximum possible population.
46. EINSTEIN’S LAW OF VELOCITY ADDITION/Velocityaddition formula
In relativistic physics, a velocityaddition formula is a threedimensional equation that relates the velocities of objects in different reference frames. Such formulas apply to successive lorentz transformations, so they also relate different frames. Accompanying velocity addition is a kinematic effect known as thomas procession, whereby successive noncollinear Lorentz boosts become equivalent to the composition of a rotation of the coordinate system and a boost. Standard applications of velocityaddition formulas include the doppler shift, doppler navigation, the aberration of light, and the dragging of light in moving water. It was observed by galilei that a person on a uniformly moving ship has the impression of being at rest and sees a heavy body falling vertically downward. This observation is now regarded as the first clear statement of the principle of mechanical relativity. The cosmos of Galileo consists of absolute space and time and the addition of velocities corresponds to composition of galilean transformations. The relativity principle is called galilean relativity. It is obeyed by newtonian mechanics. According to the theory of special relativity, the frame of the ship has a different clock rate and distance measure, and the notion of simultaneity in the direction of motion is altered, so the addition law for velocities is changed. The cosmos of special relativity consists of Minkowski spacetime and the addition of velocities corresponds to composition of lorentz transformations. In the special theory of relativity Newtonian mechanics is modified into relativistic mechanics.
47. PHOTOELECTRIC EFFECT FORMULA
The photoelectric equation involves; h = the Planck constant 6.63 x 10^{34} J s. f = the frequency of the incident light in hertz (Hz) … E_{k} = the maximum kinetic energy of the emitted electrons in joules (J)
The photoelectric effect is the emission of electrons or other free carriers when light is shone onto a material. Electrons emitted in this manner can be called photo electrons. The phenomenon is commonly studied in electronic physics, as well as in fields of chemistry, such as quatuum chemistry or electrochemistry.
48. Faraday’s law of induction
Faraday’s law of induction is one of the basic laws of electromagnetism. The law explains the operation principles of generators, transformers and electric motors.
49. Cauchy momentum equation
The Cauchy momentum equation is a vector partial differential equation put forth by cauchy that describes the nonrelativistic momentum transport in any continuum.
50. De Moivre’s formula
The process of mathematical induction can be used to prove a very important theorem in mathematics known as De Moivre’s theorem. If the complex number z = r(cos α + i sin α), then. The preceding pattern can be extended, using mathematical induction, to De Moivre’s theorem.
51. Fourier transform
The Fourier transform is a mathematical function that can be used to show the different parts of a continuous signal. It is most used to convert from time domain to frequency domain. Fourier transforms are often used to calculate the frequency spectrum of a signal that changes over time. This kind of signal processing has many uses such as cryptography, oceanography, speech recognition, or handwriting recognition. Fourier transforms can also be used to solve differential equations. Calculating a Fourier transform requires understanding of integration and imaginary numbers. Computers are usually used to calculate Fourier transforms of anything but the simplest signals. The Fast Fourier Transform is a method computers use to quickly calculate a Fourier transform.
52. Primecounting function
In mathematics, the primecounting function is the function counting the number of prime numbers less than or equal to some real number x. It is denoted by Ï€(x) (unrelated to the number Ï€).
Number of primes in up to the number x=x/lnx
53. MURPHY’S LAW FORMULA
Here, PM is the Murphy’s probability that something will go wrong. KM is Murphy’s constant (equal to one) and FM is Murphy’s factor, a very small number.
Murphy’s law is an adage or epigram that is typically stated as: “Anything that can go wrong will go wrong”.
54. SUMMATION FORMULA
In mathematics, summation (capital Greek sigma symbol: âˆ‘) is the addition of a sequence of numbers; the result is their sum or total. If numbers are added sequentially from left to right, any intermediate result is a partial sum, prefix sum, or running total of the summation. The numbers to be summed (called addends, or sometimes summands) may be integers, rational numbers, real numbers, or complex numbers. Besides numbers, other types of values can be added as well: vectors, matrices, polynomials and, in general, elements of any additive group (or even monoid).
55. Logarithmic spiral A logarithmic spiral, equiangular spiral or growth spiral is a special kind of spiral spiral curve which often appears in nature. The logarithmic spiral was first described by descarte and later extensively investigated by Jakob bernoulli, who called it Spira mirabilis, “the marvelous spiral”.
Logarithmic spirals in nature
In several natural phenomena one may find curves that are close to being logarithmic spirals. Here follows some examples and reasons:
The approach of a hawk to its prey. Their sharpest view is at an angle to their direction of flight; this angle is the same as the spiral’s pitch.
The approach of an insect to a light source. They are used to having the light source at a constant angle to their flight path. Usually the sun is the only light source and flying that way will result in a practically straight line.
The arms of spiral galaxies. Our own galaxy, the milky way. is believed to have four major spiral arms, each of which is roughly a logarithmic spiral with pitch of about 12 degrees, an unusually small pitch angle for a galaxy such as the Milky Way. In general, arms in spiral galaxies have pitch angles ranging from about 10 to 40 degrees.
The arms of tropical cyclones, such as hurricanes.
Many biological structures including spider webs and the shells of mullosks. In these cases, the reason is the following: Start with any irregularly shaped twodimensional figure F_{0}. Expand F_{0} by a certain factor to get F_{1}, and place F_{1} next to F_{0}, so that two sides touch. Now expand F_{1} by the same factor to get F_{2}, and place it next to F_{1} as before. Repeating this will produce an approximate logarithmic spiral whose pitch is determined by the expansion factor and the angle with which the figures were placed next to each other. This is shown for polygonal figures in the accompanying graphic.
56. Heron’s formula
Heron’s formula states that the area of a triangle whose sides have lengths a, b, and c is
A=s(sa)(sb)(sc),
where s is the semiperimeter of the triangle; that is,
s=(a+b+c)2.
In geometry, Heron’s formula gives the area of a triangle by requiring no arbitrary choice of side as base or vertex as origin, contrary to other formulas for the area of a triangle, such as half the base times the height or half the norm of a cross product of two sides.
57. Quadratic equation
x=b+/ sqrt(b^24ac)/2a
A quadratic equation is an equation in the form of ax^{2} + bx + c, where a is not equal to 0. It makes a parabola (a “U” shape) when graphed on a coordinate plane.
Where the letters are the corresponding numbers of the original equation, ax^{2} + bx + c = 0. Also, a cannot be 0 for the formula to work properly.
The factored form of this equation is y = a(x âˆ’ s)(x âˆ’ t), where s and t are the zeros, a is a constant, and y and the two xs are ordered pairs which satisfy the equation.
58. Euler line
In geometry, the Euler line, is a line determined from any triangle that is not equilateral. It is a central line of the triangle, and it passes through several important points determined from the triangle, including the orthocenter, the circumcenter, the centroid, the Exeter point and the center of the 9point circle of the triangle.
59. PYTHAGOREAN TRIPLES FORMULA
Euclid’s formula is a fundamental formula for generating Pythagorean triples given an arbitrary pair of integers m and n with m > n > 0. The formula states that the integers
a=m^2âˆ’n^2,
b=2mn,
c=m^2+n^2
form a Pythagorean triple
A Pythagorean triple consists of three positive integers a, b, and c, such that a^{2} + b^{2} = c^{2}. Such a triple is commonly written (a, b, c), and a wellknown example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k.
60. Euler’s formula
e^ix=cosx+isinx
Euler’s formula is a mathematical formula in complex analysis that establishes the fundamental relationship between the trigonometric functions and the complex exponential functions. Euler’s formula is ubiquitous in mathematics, physics, and engineering. The physicist richard feynmann called the equation “our jewel” and “the most remarkable formula in mathematics”.
When
x=Ï
Euler’s formula evaluates to
e^i+1=0
which is known as ruler’s identity.
61.
Simplex method, Standard technique in linear programming for solving an optimization problem, typically one involving a function and several constraints expressed as inequalities. The inequalities define a polygonal region (see polygon), and the solution is typically at one of the vertices. The simplex method is a systematic procedure for testing the vertices as possible solutions.
62. PROOF INFINITE NUMBER OF PRIME NUMBERS
Theorem.
There are infinitely many primes. Proof. Suppose that p_{1}=2 < p_{2} = 3 < … < p_{r} are all of the primes. Let P = p_{1}p_{2}…p_{r}+1 and let p be a prime dividing P; then p can not be any of p_{1}, p_{2}, …, p_{r}, otherwise p would divide the difference P–p_{1}p_{2}…p_{r}=1, which is impossible. So this prime p is still another prime, and p_{1}, p_{2}, …, p_{r} would not be all of the primes. 
63. Harmonic series (mathematics)
In mathematics, the harmonic series is the divergent infinite series:
Summation n=1 to infinity of 1/n=1+1/2+1/3+1/4+1/5+…
Its name derives from the concept of overtones, or harmonics in music: the wavelengths of the overtones of a vibrating string are 1/2,1/3,1/4, etc., of the string’s fundamental wavelengths. Every term of the series after the first is the harmonic mean of the neighboring terms; the phrase harmonic mean likewise derives from music. The harmonic series can be counterintuitive to students first encountering it, because it is a divergent series even though the limit of the nth term as n goes to infinity is zero. The divergence of the harmonic series is also the source of some apparent paradoxes. One example of these is the “worm on a rubberband”. Suppose that a worm crawls along an infinitelyelastic onemeter rubber band at the same time as the rubber band is uniformly stretched. If the worm travels 1 centimeter per minute and the band stretches 1 meter per minute, will the worm ever reach the end of the rubber band? The answer, counterintuitively, is “yes”, for after n minutes, the ratio of the distance travelled by the worm to the total length of the rubber band is
1/100âˆ‘k=1 to n1^k
(In fact the actual ratio is a little less than this sum as the band expands continuously.) The reason is that the band expands behind the worm also; eventually, the worm gets past the midway mark and the band behind expands increasingly more rapidly than the band in front. Because the series gets arbitrarily large as n becomes larger, eventually this ratio must exceed 1, which implies that the worm reaches the end of the rubber band. However, the value of n at which this occurs must be extremely large: approximately e^{100}, a number exceeding 10^{43} minutes (10^{37} years). Although the harmonic series does diverge, it does so very slowly.
Another problem involving the harmonic series is the jeep problem.
Another example is the blockstacking problem: given a collection of identical dominoes, it is clearly possible to stack them at the edge of a table so that they hang over the edge of the table without falling. The counterintuitive result is that one can stack them in such a way as to make the overhang arbitrarily large, provided there are enough dominoes.
A simpler example, on the other hand, is the swimmer that keeps adding more speed when touching the walls of the pool. The swimmer starts crossing a 10meter pool at a speed of 2 m/s, and with every cross, another 2 m/s is added to the speed. In theory, the swimmer’s speed is unlimited, but the number of pool crosses needed to get to that speed becomes very large; for instance, to get to the speed of light (ignoring special relativity), the swimmer needs to cross the pool 150 million times. Contrary to this large number, the time required to reach a given speed depends on the sum of the series at any given number of pool crosses (iterations):
10/2âˆ‘k=1 to n1^k.
Calculating the sum (iteratively) shows that to get to the speed of light the time required is only 94 seconds. By continuing beyond this point (exceeding the speed of light, again ignoring special relativity), the time taken to cross the pool will in fact approach zero as the number of iterations becomes very large, and although the time required to cross the pool appears to tend to zero (at an infinite number of iterations), the sum of iterations (time taken for total pool crosses) will still diverge at a very slow rate.
64. EULER SUMS
precise sum of the infinite series:
∑n=1 to ∞1/n^2=1/1^2+1/2^2+1/3^2+⋯=1.644934 or π^{2}/6
65. FORMULA FOR SOLUTION OF CUBIC EQUATION
In algebra, a cubic function is a function of the form f(x)=ax^3+bx^2+cx+d
in which a is nonzero.
Setting f(x) = 0 produces a cubic equation of the form
ax^3+bx^2+cx+d=0.
The solutions of this equation are called roots of the polynomial f(x). If all of the coefficients a, b, c, and d of the cubic equation are real numbers then there will be at least one real root (this is true for all odd degree polynomials). All of the roots of the cubic equation can be found algebraically. (This is also true of a quadratic or quartic (fourth degree) equation, but no higherdegree equation, by the abelruffini theorem). The roots can also be found trigonometrically. Alternatively, numeric approximates of the roots can be found using rootfinding theorem like newton’s method. The coefficients do not need to be complex numbers. Much of what is covered below is valid for coefficients of any field with characteristic 0 or greater than 3. The solutions of the cubic equation do not necessarily belong to the same field as the coefficients. For example, some cubic equations with rational coefficients have roots that are nonrational (and even nonreal) complex numbers.
66. SOLUTION TO QUARTIC EQUATION
In algebra, a quartic function is a function of the form
f(x)=ax^4+bx^3+cx^2+dx+e,
where a is nonzero, which is defined by a polynomial of degree four, called a quartic polynomial.
Sometimes the term biquadratic is used instead of quartic, but, usually, biquadratic function refers to a quadratic function of a square (or, equivalently, to the function defined by a quartic polynomial without terms of odd degree), having the form
f(x)=ax^4+cx^2+e.
A quartic equation, or equation of the fourth degree, is an equation that equates a quartic polynomial to zero, of the form
ax^4+bx^3+cx^2+dx+e=0,
where a â‰ 0.
The derivative of a quartic function is a cubic function.
Since a quartic function is defined by a polynomial of even degree, it has the same infinite limit when the argument goes to positive or negative infinity. If a is positive, then the function increases to positive infinity at both ends; and thus the function has a global minimum. Likewise, if a is negative, it decreases to negative infinity and has a global maximum. In both cases it may or may not have another local maximum and another local minimum.
The degree four (quartic case) is the highest degree such that every polynomial equation can be solved by radicals.
67. Quintic function
In algebra, a quintic function is a function of the form
g(x)=ax^5+bx^4+cx^3+dx^2+ex+f,
where a, b, c, d, e and f are members of a field, typically the rational numbers, the real numbers or the complex numbers, and a is nonzero. In other words, a quintic function is defined by a polynomials of degree five.
If a is zero but one of the coefficients b, c, d, or e is nonzero, the function is classified as either a quartic function, cubic function, quadratic function or linear function.
Because they have an odd degree, normal quintic functions appear similar to normal cubic function when graphed, except they may possess an additional local maximum and local minimum each. The derivative of a quintic function is a quartic function.
Setting g(x) = 0 and assuming a â‰ 0 produces a quintic equation of the form:
ax^5+bx^4+cx^3+dx^2+ex+f=0.
Solving quintic equations in terms of radicals was a major problem in algebra, from the 16th century, when cubic and quartic equations were solved, until the first half of the 19th century, when the impossibility of such a general solution was proved, with the abelruffini theorem. Finding the roots of a given polynomial has been a prominent mathematical problem. Solving linear, quadratic, cubic and quartic equations by factorization into radicals can always be done, no matter whether the roots are rational or irrational, real or complex; there are formulae that yield the required solutions. However, there is no algebraic expression for general quintic equations over the rationals in terms of radicals. This also holds for equations of higher degrees. Some quintics may be solved in terms of radicals. However, the solution is generally too complex to be used in practice. Instead, numerical approximations are calculated using Rootfinding algorithms for polynomials. Some quintic equations can be solved in terms of radicals. These include the quintic equations defined by a polynomial that is reducible, such as x^{5} âˆ’ x^{4} âˆ’ x + 1 = (x^{2} + 1)(x + 1)(x âˆ’ 1)^{2}. For characterizing solvable quintics, and more generally solvable polynomials of higher degree, evariste galois developed techniques which gave rise to group theory and galois theory. Applying these techniques, arthur caylay found a general criterion for determining whether any given quintic is solvable.
68. Lorentz force
In physics (particularly in electromagnetism) the Lorentz force is the combination of electric and magnetic force on a point charge due to electromagnetic fields. A particle of charge q moving with velocity v in the presence of an electric field E and a magnetic field B experiences a force
F=qE+qv —B
(in SI units).
69. Eulerlagrange formula
Lsubx(tsuby,q(t),qdot(t))d/dtLsubx(t,q(t),qdot(t))=0
In the calculus of variation, the EulerLagrange equation, Euler’s equation, or Lagrange’s equation, is a secondorder partial differential equation whose solutions are the functions for which a given functional is stationary.
70. Euler product formula In number theory, an Euler product is an expansion of a dirichlet series into an infinite productindexed by prime numbers. The original such product was given for the sum of all positive numbers raised to a certain poweras proven by leonard euler. This series and its continuation to the entire complex plane would later become known as the riemann zeta function.
âˆpP(p,s)
71. Eulermaclaurin formula In mathematics, the EulerMaclaurin formula provides a powerful connection between integrals and sums. It can be used to approximate integrals by finite sums, or conversely to evaluate finite sums and infinite series using integrals and the machinery of calculus. For example, many asymptotic expansions are derived from the formula, and faulhaber’s formula for the sum of powers is an immediate consequence.
72. Pi
pi=C/d
(pi is equal to the circumference divided by the diameter).
Pi is an endless string of numbers
Pi is a mathematical constant. It is the ratio of the distance around a circle to the circle’s diameter. This produces a number, and that number is always the same. However, the number is rather strange. The number starts 3.141592……. and continues without end. Numbers like this are called irrational numbers.
The diameter is the longest straight line which can be fitted inside a circle. It passes through the center of the circle. The distance around a circle is known as the circumference. Even though the diameter and circumference are different for different circles, the number pi remains constant: its value never changes. This is because the relationship between the circumference and diameter is always the same.
A mathematician named Lambert also showed in 1761 that the number pi was irrational; that is, it cannot be written as a fraction by normal standards. Another mathematician named Lindeman was also able to show in 1882 that pi was part of the group of numbers known as transcendental, which are numbers that cannot be the solution to a polynomial equation.
Pi can also be used for figuring out many other things beside circles. The properties of pi have allowed it to be used in many other areas of math besides geometry, which studies shapes. Some of these areas are complex analysis, trigonometry, and series.
Today, there are different ways to calculate many digits of. This is of limited use though. Pi can sometimes be used to work out the area or the circumference of any circle. To find the circumference of a circle, use the formula C (circumference) = Ï times diameter. To find the area of a circle, use the formula (radius²). This formula is sometimes written as
A=r^2, where r is the variable for the radius of any circle and A is the variable for the area of that circle.
To calculate the circumference of a circle with an error of 1 mm:
4 digits are needed for a radius of 30 meters
10 digits for a radius equal to that of the earth
15 digits for a radius equal to the distance from the earth to the sun.
People generally celebrate March 14 as pi day because March 14 is also written as 3/14, which represents the first three numbers 3.14 in the approximation of pi.
73. Exponential function
In mathematics, an exponential function is a function that quickly grows. More precisely, it is the function
exp(x)=e^x, where e is ruler’s constant, an irrational number that is approximately 2.71828.
74. Natural logarithm
The natural logarithm of a number is its logarithm to the base of the mathematical constant e, where e is an irrational and transcendental number approximately equal to 2.718281828459. The natural logarithm of x is generally written as ln x, log_{e} x, or sometimes, if the base e is implicit, simply log x. The natural logarithm of x is the power to which e would have to be raised to equal x.
75. Conic sections
CONIC SECTIONS
Circle
(xg)^2+(yh)^2=radius^2
(g=x coordinate, h=y coordinate)
Parabola
y^2+/4ax
(a=x coordinate)
x^2=+/4ay
(a=y coordinate)
ellipse
x^2/a^2+y^2/b^2=1,
(a=x, b=y coordinates, or a=y, b=x coordinates)
Hyperbola
x^2/a^2y^2/b^2=1,
(a=x, b=y coordinates, or a=y, b=x coordinates)
76. Exponential growth and decay
y=A*exp^k*t
A=starting number of for example bacteria, t=length of growth time, k=constant, y=number of bacteria after t time
77. Calculating an orbit I.e. of a comet
Calculations: orbit, period of orbit, perihelion, aphelion and eccentricity
(for example a comet)â€”
Use ellipse formula x^2/a^2+y^2/b^2=1
Then calculate from 2 coordinates in AUs with formula
x^2 x b^2 + y^2 x a^2=a^2 x b^2
find a and bÂ (the closest and furthest approaches)
Period years of orbit^3=distance (a from above)^2
Period=cuberoot(distance AUs of â above)^2
Perihelion=d=ac
c=(a^2b^2)^1/2 (c=distance from focus to center of ellipse)
aphelion=d=cb
perihelion=A x (1eccentricity)
aphelion=A x (1+ eccentricity)
A (semimajor axis)=(perihelion + aphelion)/2
eccentricity=1perihelion/A
eccentricity=aphelion/A1
To find formula for the orbit, use ellipse formula
x^2/a^2+y^2/b^2=1, then use formula
x^2 x b^2+y^2 x a^2=a^2 x b^2,
Use 2 location coordinates from the orbit, plug in one of the coordinates
Into the 2nd formula, then plug in the 2nd coordinates into the same
formula. Subtract one of the resulting formulas from the other resulting
formula, then solve for a or b with the formula that results from the
subtraction. Plug in the solution to a or b that was solved into one of the
Presubtraction formulas to find the a or b that has not been found yet.
Now, we have the a and b constants, so we plug them into the ellipse
Formula, and thus have the equation for the orbit of the stellar body,
I.e. a comet.
78. Interesting math example #1
1×1=1
11×11=121
111×111=12321
1111×1111=1234321
11111×11111=123454321
111111×111111=12345654321
Etc
79. Interesting math example #2
1×8+1=9
12×8+2=98
123×8+3=987
1234×8+4=9876
12345×8+5=98765
Etc
80. Interesting math example #3
1=.9999999
0.999
In mathematics, 0.999… (also written 0.9, among other ways), denotes the repeating decimal consisting of infinitely many 9 after the decimal point (and one 0 before it). This repeating decimal represents the smallest number no less than all decimal number 0.9, 0.99, 0.999, etc.^{[1]} This number can be shown to equal 1. In other words, “0.999…” and “1” represent the same number. There are many ways of showing this equality, from intuitive arguments to mathematically rigorous proof. The technique used depends on target audience, background assumptions, historical context, and preferred development of the real numbers, the system within which 0.999… is commonly defined. (In other systems, 0.999… can have the same meaning, a different definition, or be undefined.) More generally, every nonzero terminating decimals has two equal representations (for example, 8.32 and 8.31999…), a property true of all base representations. The utilitarian preference for the terminating decimal representation contributes to the misconception that it is the only representation. For this and other reasons such as rigorous proofs relying on nonelementary techniques, properties, and/or disciplines math students can find the equality sufficiently counterintuitive that they question or reject it. This has been the subject of several studies in mathematics education.
scientific formulas
9/6/17; 9/14/17; 10/29/17; 11/11/17; finished 12/11/17
SCIENTIFIC FORMULAS—
MATHEMATICS
PHYSICS
ASTRONOMY
ROCKET SCIENCE
Capital  Lowcase  Greek Name  English 
Alpha  a  
Beta  b  
Gamma  g  
Delta  d  
Epsilon  e  
Zeta  z  
Eta  h  
Theta  th  
Iota  i  
Kappa  k  
Lambda  l  
Mu  m 
Nu n Xi x Omicron o
Lambda l Mu m
Nu  n  
Xi  x  
Omicron  o  
Pi  p  
Rho  r  
Sigma  s  
Tau  t  
Upsilon  u  
Phi  ph  
Chi  ch  
Psi  ps  
Omega  o 
POWERS
tera=10^12
giga=10^9
mega=10^6
myria=10^4
kilo=10^3
hecto=10^2
icosa=20
quindeca=15
hendeca=11
dec=10
non=9
octo=8
hepta=7
hexa=6
penta=5
tetra=4
tri=3
bi=2
uni=1
semi=.5
deci=10^1
centi=10^2
milli=10^3
micro=10^6
nano=10^9
pico=10^12
femto=10^15
atto=10^18
PRACTICAL MATHEMATICS FORMULAS PLATONIC SOLIDS—
1. Tetrahedron
Surface area=Sqrt3 x edge length^2 Volume=sqrt2/12 x edge length^3 2. Cube
Surface area=6 x edge length^2 volume=edge length^3
3. Octahedron
Surface area=2 x sqrt3 x edge length^2
volume=sqrt2/3 x edge length^3
4. Dodecahedron
Surface area=3 x sqrt(25+10 x sqrt5) x edge length^2 volume=(15+7 x sqrt5)/4 x edge length^3
5. Isocahedron
Surface area=5 x sqrt3 x edge length^2
volume=(5 x (3+sqrt5))/12 x edge
length^3
CIRCLE
Diameter D = 2 x Radius
Circumference C = 2 x Pi*Radius
area A = Pi x Radius^2
SPHERE
Surface area. A = 4 x Pi x Radius^2
volume V = 4/3 x Pi x Radius^3
Diameter of a sphere. d=cuberoot(3/4 x Pi x volume) x 2 SQUARE, RECTANGLE, PARALLELOGRAM
Area A=side 1 x side 2
VOLUME OF SQUARE, RECTANGLE, PARALLELOGRAM V=side 1 x side 2 x side
PYRAMID
Surface area=base area+.5 x slant length
Volume=base x depth x height/3
CYLINDER
Surface area=2 x pi x radius x (radius+height)
Volume=PI X radius^2 x length
CONE
Surface area=pi x radius x (radius+base to apex length) Volumes=Pi x radius^2 x height/3
TORUS
Surface area=4 x pi^2 x radius torus x radius of solid part volume=2 x pi^2 x radius torus x radius solid part^2 PYTHAGOREAN THEORM
a^2+b^2=c^2
a=length of one right angle’s leg
b=length of other right angle’s leg
c=length of hypotenuse
LAW OF SINES
a/sinA=b/sinB=c/sinC=2 x R=a x b x c/2 x area of triangle R=(a x b x c)/(squareroot((a+b+c) x (a+bc) x (b+ca)) Area of triangle=1/2 x a x b x sinC
LAWS OF COSINE
c^2=a^2+b^22 x a x b x cosC
cosC=(a^2+b^2+c^2)/2 x a x b
AREA OF A TRIANGLE
area=base x height x 1/2
AREA OF AN EQUILATERAL TRIANGLE area=(length of a side )^2 x SQRT(3)/4 AREA OF A TRAPEZOID
A=(top side+bottom side) x height/2
HERON’S FORMULA (area of any triangle) area=SRQT(s x (sside 1) x (sside 2) x (sside 3)) s=1/2 x (a + b + c)
SLOPE
m=(yy1)/(xx1)
(Y1 and x1 are locations on coordinate plane) POINT SLOPE EQUATION OF A LINE
Y y1=slope(xx1)
(Y1 and x1 are locations on coordinate plane) SLOPE INTERCEPT FORM FOR A LINE y=slope(x)+(y intercept)
DISTANCE FORMULA
distance=square root((xx1)^2+(yy1)^2+(zz1)^2)) (z1, y1, and x1 are locations on coordinate system) ALGEBRA FORMULAS
(a+b)^2=a^2+2 x a x b+b^2
(ab)^2=a^22 x a x b+b^2
x^2a^2=(x+a) x (xa)
x^3a^3=(xa) x (x^2+a x x+a^2) x^3+a^3=(x+a) x (x^2a x x+a^2) a/b+c/d=(a x d+b x c)/b x d) a/bc/d=(a x db x c)/b x d
a/b x c/d=a x c/b x d
CONIC SECTIONS
Circle (xg)^2+(yh)^2=radius^2
(g=x coordinate, h=y coordinate) Parabola
y^2+/4ax
(a=x coordinate)
x^2=+/4ay
(a=y coordinate)
ellipse
x^2/a^2+y^2/b^2=1,
(a=x, b=y coordinates, or a=y, b=x coordinates) Hyperbola
x^2/a^2y^2/b^2=1,
(a=x, b=y coordinates, or a=y, b=x coordinates) QUADRATIC EQUATION x=(b+/squareroot(b^24ac))/2a
LAWS OF EXPONENTS
a^x x a^y=a^(x+y)
a^x/a^y=a^(xy)
(a^x)^y=a^(X x Y) (a*b)^x=a^x x b^x a^0=1
a^1=a
LAWS OF LOGARITHMS
log(base a)(M x N)=log(base a)(M)+log(base a(N) log(base a)(M/N)=log(base a)Mlog(base a)(N) logM^r=r X x logM
log(base a)(M)=logM/loga
TRIGONOMETRY
sineo/h
cosine=a/h
tangent=o/a
cosecant=h/o
secant=h/a
cotangent=a/o
(a=adjacent side of right triangle)
(o=opposite side of right triangle)
(h=hypotenuse of right triangle)
Pythagorean identities
sin^2(x)cos^2(x)=1
sec^2(x)tan^2(x)=1
csc^2cos^2(x)=1
Product relations
Sinxtanx x cosx
cosx=cotx x sinx
tanx=sinx x secx
cotx=cosx x cscx
Secxcscx x tanx
cscx=secx x cotx
Trigonometry functions
sinx=xx^3/3!+x^5/5!x^7/7!
cosx=1x^2/2!+x^4/4!x^6/6!
Inverse trigonometry functions
sin1x=x+(1/2 x 3) x x^3+(1 x 3/2 x 4 x 5) x x^5+(1 x 3 x 5/2 x 4 x 6 x 7) x x^7+… cos1x=pi/2(x+(1/2 x 3) x x^3+(1 x 3/2 x 4 x 5) x x^5+(1 x 3 x 5/2 x 4 x 6 x 7) x x^7+… tan1x=xx^3/3+x^5/5x^7/7+…
cot1x=pi/2x+x^3/3x^5/5+x^7/7…
Hyperbolic functions
sinhx=x+x^3/3!+x^5/5!+x^7/7!+…
coshx=1+x^2/2!+x^4/4!+x^6/6!+…
Inverse hyperbolic functions
sinh1x=x(1/2 x 3) x x^3+(1 x 3/2 x 4 x 5) x x^5(1 x 3 x 5/2 x 4 x 6 x 7) x x^7+… tanh1x=x+x^3/3+x^5/5+x^7/7+…
Nth TERM OF AN ARITHMETIC SEQUENCE Nth term=a+(number of terms1)*d
(a=1st term, d=common difference)
SUM OF n TERMS OF AN ARITHMETIC SERIES Sumn/2 x (a+nth term)
(a=1st term, d=common difference)
Nth TERMS OF A GEOMETRIC SEQUENCE
a(n)=a x r^(n1), (r cannot equal 0.)
(a=1st term, r=common ratio)
SUM OF THE n TERMS OF A GEOMETRIC SEQUENCE s=a x ((1r^n)/(1r))
(r cannot equal 0, 1)
(n=number of terms, r=common ratio)
SUM OF AN INFINITE SERIES
s=n/(1r)
(If absolute value of r<1)
(n=number star with)
(r=how much keep multiplying x with forever) (s=sum of infinite series)
COMBINATIONS
C(n,r)=n!/r!(nr)!
PERMUTATIONS
P(n,r)=n!(nr)!
BINOMIAL FORMULA
(a x xb)^n
CALCULUS (DIFFERENTIATION)
d/dx (x^n)=n x x^(n1)
d/dx sinx= cost
d/dx cosx= sinx
d/dx tanx=sec^2(x)
d/dx cotx=csc^2(x)
d/dx sexsecs x tanx
d/dx cscx= cscx x cotx
d/dx e^x=e^x
d/dx lnx=1/x
d/dx (u+v)=du/dx+dv/dx
d/dx(c x u)=c x du/dx
dy/dx=dy/dx x du/dx
(chain rule)
d/dx (u x v)=(v x (du/dx)(u x (dv/dx)
(product rule)
d/dx(u/v)=(v x du/dxu x dv/dx/)v^2
(quotient rule)
du=du/dx(dx)
CALCULUS (INTEGRATION)
The definite integral of t from a to b for definite integral f(t)=F(b)F(a)
Indefinite integral of x^r dx=x^(r+1)/(r+1)+c, (r cannot equal 1)
Indefinite integral of 1/x dx=ln(absolute value (x))+c
Indefinite integral of sinx dx=cosx+c
Indefinite integral of cosx dx=sinx+c
Indefinite integral of e^x dx=e^x+c
Indefinite integral of (f(x)+g(x))dx=indefinite integral f(x)+indefinite integral g(x) Indefinite integral of c x f(x) dx=c x (indefinite integral f(x))
indefinite integral of (u)dv=u x vindefinite integral (v)du
(integration by parts)
CENTER OF MASS
Center of mass (x)=((mass1) x (center of mass1)+(mass2) x (center of mass x 2))/ (mass1+mass2)
(A point representing the mean position of the matter in a body of system.) VECTOR ANALYSIS
Norm (magnitude of a vector)=sqrt(x^2+y^2+z^2)
Dot product u (dot) v=(u1) x (v1)+(u2) x (v2)+(u3) x (v3)=u v cos(theta)
(theta is the angle between u and v, 0<=theta<=Pi)
Cross productÂ u x v=((u2) x (v3)(u3) x (v2))i((u1) x (v3)(u3) x (v1))j+((u1) x (v2)
(u2) x (v1))k
u x v=u x v sin(theta)
(Theta is angle between u and v, 0<=theta<=Pi)
2 vectors orthogonal if their dot product v and u=0 or transpose vector v and vector u=0.
Exponential growth and decay—
y=A exp^k*t
A=starting number of for example bacteria, t=length of growth time, k=constant, y=number of bacteria after t time
OUTLINE OF PHYSICS FORMULAS
*** Straight line motion ***
Velocity (meters/second)=distance (meters)/time (seconds) v=d/t (constant velocity)
v=2 x d/t (accelerating)
Distance (meters)=velocity (meters/second) x time (seconds) d=v x t
time (seconds)=distance (meters)/velocity (meters/second) t=d/v
t=sqrt(2 x distance/acceleration)
Acceleration (meters/second^2)=
((meters/second (end)meters/second (start)/)time (seconds))/2 a=(d2/td1/t)/2
Acceleration (meters/second^2)=2 x distance (meters)/time (second)^2 a=2 x d/t^2
Final velocity (meters/second)=initial velocity (meters/second)+ acceleration (meters/second^2 x time (seconds)
v(f)=v1+a x t
velocity^2=initial velocity+2 x acceleration x distance
v^2=v1+2 x a x d
Average velocity (meters/second)=initial velocity+final velocity/time v(average)=(v1+v2)/t
Average velocity=initial velocity+1/2 x acceleration x time v(average)=v1+1/2 x a x t
Distance (meters)=initial velocity x time+1/2 x acceleration x time^2 d=v1+1/2 x t x a x t^2
Distance=acceleration x time^2/2
d=a x t^2/2
Newton’s 2nd law of motion
Force (newtons)=mass (kilograms) x acceleration (meters/second^2) Fm x a
Falling bodies
velocity=gravity (9.81 meters/second^2 for the earth) x time
v=g x t
How far fallen in meters=1/2 x gravity x time^2 d=1/2 x g x t^2
Time fallen=sqrt(2 x height/gravity)
t=sqrt(2 x h/g)
velocity=sqrt(2 x gravity x height) v=sqrt(2 x g x h)
*** Circular motion ***
Uniform circular motion
Moment of inertia=mass x distance from axis^2
m(inertial)=m x d^2
Angular velocity=angular displacement/change in timeÂ (radians/second) v(angular)=d/t
Angular momentum=moment of inertia x angular velocity m(angular)=m(inertial) x v(angular)
Centripedal acceleration
Centripedal acceleration=velocity^2/radius of path (radians/second^2) a(centipedal)=v^2/r
Torque (newtonsmeter)
Centripetal force
Centripetal force=mass x velocity^2/radius of path
f(centripedal)=m x v^2/r
Gravitation
gravitation (newtons)=G x (mass(1) x mass(2))/radius^2
(G=6.67 x 10^11)
f=G x (m1 x m2)/r^2
Fundamental forces in nature— strong
W eak
Electromagnetic
Gravity
*** Energy ***
work
work (joules)=force (newtons) x distance (meters)
w=f x d
work=work output/work input x 100%
w=w(o)/w(i) x 100
Power
Power (watts)=work (joules)/time (seconds)
p=w/t
horsepower=746 watts
weight=mass x gravity
w=m x g
momentum=mass (kilograms) x velocity (meters/second) momentum=m x v
Energy
kinetic energy
KE (joules)=1/2 x mass (kilograms)x velocity (meters/second)^2 ke=1/2 x m x v^2
Potential energy
PE (joules)=mass x gravity (9.81 meters/second^2) x height (meters)
pe=m x g x h
Rest energy
Rest energy (joules)=mass x 300,000,000^2
Conservation of energy
MomentumÂ (kilogramsmeters/second)
Linear momentum
L. momentum=mass (kilograms)x velocity (meters/second) m(momentum)=m x v
Conservation laws
Conservation of massenergy
Conservation of linear momentum
Angular momentum
Conservation of angular momentum
Conservation of electric charge
Conservation of color charge
Conservation of weal isospin
Conservation of probability
Conservation of rest mass
Conservation of baryon number
Conservation of lepton number
Conservation of flavor
Conservation of parity
Invariance of charge conjugation
Invariance under time reversal
CP symmetry
Inversion or reversal of space, time, and charge
(there is a onetoone correspondence between each of the conservation laws and a differentiable symmetry in nature.)
Impulse
impulse=force (newtons) x time (seconds)
i=f x t
*** Relativity ***
special relativity
Lorentz transformation
*** Fluids ***
Density
Specific gravity
kilograms/meter^3
Pressure
pressure=force/area
pressure=newtons/meters^3
p=f/d^3
Pressure in a fluid
pressure=density (kilograms/meters^3) x depth (meters) x weight (kilograms) p=d(density) x d(depth) x w
p=kg/d^3 x d x m
Archimede’s principlethe upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces.
Bernoulli’s principlesan increase in the speed of a fluid occurs
simultaneously with a decrease in pressure or a decrease in the fluid’s potential energy.
v^2/2+gz+p/Ï=constant
v is the fluid flow speed at a point on a streamline,
g is the gravitational acceleration
z is the elevation of the point above a reference plane,
with the positive zdirection pointing upward so in the direction
opposite to the gravitational acceleration,
p is the pressure at the chosen point, and
Ï is the density of the fluid at all points in the fluid.
*** Heat ***
internal heat
Temperature
Heat
1 kilocalorie=3.97 british thermal units (BTU)
1 BTU=.252 kilocalories
Specific heat capacity
Heat transferred=mass (kilograms) x specific heat capacity x temperature change (kelvin)
h=m x h x t
change of state
Heat of fusion
Heat of vaporization
pressure and boiling point
*** Kinetic theory of matter ***
Ideal gases
Boyle’s law
pressure(1) x volume(1)=pressure(2) x volume(2)
(temperature constant)
P1 x v1=p2 x v2
Absolute temperature scale
Temperature kelvin=temperature (celsius)+273.15
Charlie’s law
volume(1)/temperature(1)=volume(2)/temperature(2)
(pressure constant)
v1/t1=v2/t2
Ideal gas law
pressure(1) x volume(1)/temperature(1)=pressure(2) x volume(2)/temperature(2) P1 x v1/t1=p2 x v2/t2
Kinetic energy of gases
Molecular energy
KE (joules)=3/2 x K x temperature (kelvin)
(K=boltzmann’s constant=1.38 x 10^23 joules/kelvin
ke=3/2 x k x t
solids and liquids
Atoms and molecules
*** Thermodynamics ***
3 laws of thermodynamics
The four laws of thermodynamics are:
Zeroth law of thermodynamics: If two systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other.
This law helps define the notion of temperature.
1st law of thermodynamics: When energy passes, as work, as heat, or with matter, into or out from a system, the system’s inertial energy changes in accord with the law of conservation of energy. Equivalently, Perpetual motion machines of the 1st kind (machines that produce work without the input of energy) are impossible.
2nd law of thermodynamics: In a natural thermodynamic process, the sum of the entropies of the interacting thermodynamic systems increases. Equivalently, perpetual motion machines of the 2nd kind (machines that spontaneously convert thermal energy into mechanical work) are impossible.
3rd law of thermodynamics: The entropy of a system approaches a constant value as the temperature approaches absolute zero. With the exception of noncrystalline solids (glasses) the entropy of a system at absolute zero is typically close to zero, and is equal to the logarithm of the product of the quantum ground states.
entropy
The entropy of a system approaches a constant value as the temperature
absolute zero.
Mechanical equivalent of heat
Mech. Equiv. heat=4,185 x joules/kilocalories Mech. Equiv. heat=778 x footpounds/BTU
Heat engines
Engine efficiency
efficiency=1heat temperature absorbed/heat temperature given off eff=1h(temp. Absorbed)/h(temp. Given off)
Conduction
Convection
Radiation
*** Electricity ***
Electric charge
Charge of proton=1.6 x 10^19 coulombs
Charge of electron= 1.6 x 10^19 coulombs
Electric charge=current (amperes) x time taken (seconds)
Coulomb’s law
Electric force (newtons)=K x charge1 (coulombs) x charge2 (coulombs)/ distance (meters)^2
(K=9 x 10^9 newtonmeter^2/coulomb^2)
F=KÂ x c1 x c2/d^2
Atomic structure
Mass of proton=1.673 x 10^27 kilograms
Mass of neutron=1.675 x 10^27 kilograms Mass of electron=9.1 x 1031 kilograms Ions
Electric field
Electric field (newton/coulomb)=force (newtons)/charge (coulombs) E=f/c
force=charge x electric field
Electric lines of force
Potential difference
volts=work/charge
(1 volt= 1 joule/coulomb)
volt=electric field (newtons/coulomb)x distance (meters)
v=E x d
Electric field (newtons/coulombs)=volts/distance
E=v/d
Potential Difference=current (amperes)x resistance (ohms)=
energy transferred/charge (coulombs)
pd=I x r=e/c
Electric current
Electrical energy=voltage (volts)x current (amperes)x time taken (seconds) e=v x I x t
Electric current
Electric current (amperes)=charge (coulombs)/time interval (seconds)
(1 ampere=1 coulomb/second)
I=c/t
Electrolysis
Ohm’s law
Electric current (amperes)=volts/resistance (ohms)
(resistance (1 ohm))=1 volt/ampere)
I=v/r
resistance (ohms)=voltage (volts)/current (amperes)
r=v/I
voltage (volts)=current (amperes)x resistance (ohms)
v=I x r
Resisters in series
resistance=resistance(1)+resistance(2)+resistance(3)
R=r1+r2+r3
Resisters in parallel 1/resistance=1/resistance(1)+r1/resistance(2)+1/resistance(3) 1/R=1/r1+1/r2+1/r3
Kirchoff’’s law
current law=Summation (current)=0
Voltage law=summation (voltage)=0
Capacitance
1 farad=1 coulomb has 1 volt between plates
capacitance (farad)=charge (coulombs)/voltage (volts)
Work stored=work (charging)=1/2 x capacitance x voltage^2
W=w=1/2 x C x v
electric power
power (watts)=work done per unit time (joules)=voltage (volts)x charge
(coulombs)/time (seconds)
p=w=v x c/t
Power (watts)=current (amperes) x voltage (volts)=current (amperes)^2
x resistance (ohms)=voltage (volts)^2/resistance (ohms)
p=i x pd=i^2 x r=pd^2/r
Alternating current
power (watts)=1/2 x peak voltage x peak current x
cos (phase angle between current and voltage sine waves)
p=1/2 x v x I x cos(theta)
*** Magnetism ***
Magnetic field
1 tesla=1 newton/amperemeter
(tesla=weber/meter^2)
(1 gauss=10^4 teslas)
B (magnetic field)=K x I (straight line current)/distance (meters)
(K=2 x 10^7 newton/amperes^2
B=K x I/d
Magnetic field on a moving charge
Magnetic field on a current
B=Pi(3.14) x K x I/r
F=I x L x B
Magnetic field of solenoid
B=2 x Pi x K x N (number of turns)/L (length of solenoid) x I (current amperes) Forces between 2 currents
(K=2 x 10^7 newton/amperes^2
F/L=K x I(1) x I(2)/d
Lorentz force
F=charge x electric field+charge x velocity (cross product) magnetic field F=qE+qv x B
*** electromagnetism ***
Maxwell’s equations
Maxwell’s equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.
*** Electromagnetic induction *** Generator
Motors
Alternating current
I=I (max)/sqrt(2)=.707 I (max)
V=I (max)sqrt(2)=.707 V (max)
Transformer
Primary voltage/secondary voltage=primary turns/secondary turns Primary current/secondary current=secondary turns/primary turns DC circuits
*** Waves ***
Frequency
1 hertz=1 cycle/second
W avelength
wave velocity (meters/second)=frequency (hertz) x wavelength (meters)
v=f x w
Acoustics
Optics
Electromagnetic waves
Velocity of light=c=3 x 10^8 meters/second=186,282 miles/second
Doppler effect
Frequency found by observer with respect to sound=frequency produced by source x (velocity sound+velocity observer)/(velocity soundvelocity source) f(o)=f(s) x (v+v(o))/(vv(s))
Frequency found by observer with respect to light=frequency produced by source x sqrt((1+relative velocity/c)/(1relative velocity/c))
f(o)=f(s) x sqrt((1+v/c)/(1v/c))
reflection and refraction of light
Index refraction=n=c/velocity in medium (meters/second)
r=c/v
Interference, diffraction, polarization
Particles and waves
*** Quantum physics ***
Uncertainty principlethe velocity of an object and its position
cannot both be measured exactly, at the same time, even in
theory.
The Schrodinger equation is used to find the allowed energy levels of quantum mechanical systems (such as atoms, or transistors). The associated wave function gives the probability of finding the particle at a certain position. … The solution to this equation is a wave that describes the quantum aspects of
a system.
The Pauli exclusion principle—
Quantum theory of light
Quantum energy=E=h x f
Planck’s constant=h=6.63 x 10^34 joulessecond
Xrays
Electron volt=planck’s constant x frequency
eV=h x f
Electron KE=xray photon energy
f=eV/h
momentum=kinetic energy (joules)/speed of light^2 (meters/second) p=ke/c^2
Kinetic Energy=planck’s constant x frequency=
planck’s constant x speed light/wavelength
ke (joules)=6.63 x 10^34 joulessecond x frequency hertz(meter/second)=
The Pauli exclusion principle is the quantum
mechanical
principle which states that two or more identical fermions (particles with
halfinteger spin)
cannot occupy the same quantum state within a quantum system
simultaneously.
6.63 x 1^34 x 300,000,000 meters/f (meters) joules=h x f=h x c/lambda
Electron volt
1 eV=1.6 x 10^19 joules
1 KeV=10^3 eV
1 MeV=10^6 eV
1 GeV=10^9 eV
Kinetic energy=1/2 x mass x velocity^2=
planck’s constant x frequencyelecton volts
ke (joules)=1/2 x m x v^2=6.63 x 10^34 joulessecond x feV Matter waves
De Broglie wavelength=lambda=h/m x v (momentum=m x v)
wavelength=planck’s constant/(mass x meters/second) lambda=h/m x v
Solid state physics
***Nuclear and atomic physics ***
Nucleus
Mass (proton)=1.673 x 10^27 kilograms=1.007277 u
Mass (neutron)=1.675 x 10^27 kilograms=1.008665 u Nuclear structure
Binding energy
Mass defect= change m=((number protons x mass hydrogen)+ (number neutrons x mass neutrons))m
(mass hydrogen=1.007825 u)
Fundamental forces
Gravity
Electromagnetic
Weak interaction
Strong force
Fission and fusion
Radioactivity
Alpha particle=helium nuclei
Beta particle=electron
Gamma rays=high energy photons with frequencies greater than xrays neutron>proton+electron
proton>neutron+positron Radioactive decay and halflife Elementary particles and antimatter
ASTRONOMY FORMULAS
1. How to find the DISTANCE in parsecs to a star distance=10^((apparent magnitudeabsolute magnitude+5)/5)
2. APPARENT magnitude
apm=log d x 55+abm
apparent=log(distance) x 5 – 5 + absolute magnitude
3. How do you calculate the absolute magnitude of a star abm=((log L/log 2.516)4.83)
Absolute magnitude=((log(number of sun’s luminosity of star)/ log2.516)4.83
abm=(5 x log d5apm)
Absolute magnitude= (5 x log(distance parsecs)5apparent magnitude)
4. To find brightness of a star/number of suns
L=10^((abm4.83) x (log 2.516))
LUMINOSITY of star=10^((absolute magnitude of star4.83)*(log2.516))
luminosity increase=2.512^([magnitude increase]+4.83)
luminosity=mass^3.5Â (for main sequence stars)
Luminosity (watts)=4 x pi x radius(meters)^2 x temperature (kelvin)^4 x
5.67 x 10^8 watts maters^2 kelvin^4
5. Mass binary system
Suppose in an example, we calculate the masses of 2 stars in a binary star system: if the period of star a is 27 years and its distance from the common center of mass is 19 AUs, the
Distance^3/period^2=19^3/27^2=6859/729=9.4 solar masses for the total mass of the 2 stars.
The velocity of star a is 30,000 km./second and star b is 10,000 km/second, so 30,000/10,000=3.
The mass of star b is 9.4/(1+3)=2.25 solar masses.
The mass of star a is 9.42.25=7.15 solar masses.
So star a is 7.15 solar masses, and star b is 2.25 solar masses, and both added up equals 9.4 solar masses, the combined mass of the 2 stars.
6. Radius of a star
radius=(temperature sun (kelvin)/temperature star (kelvin))^2 x (2.512^(absolute magnitude sunabsolute magnitude star)^1.2)
7. size of star/orbit/object
size object miles=arcseconds size object x distance parsecs x 864,000
8. LT=10^10 x m(star)/m(sun)^2.5
lifetime=(10^10) x (mass of star/mass of sun)^2.5
9. To find ARC SECOND measurement of object size from parsec DISTANCE and visa versa and SIZE of an object–
SIZE OF STAR IN ARCSECONDS–arcseconds=1/d (parsecs) x number of suns size ARCSECONDS– parallax=1/distance parsecs
DISTANCE (parsecs)– d=1/arcseconds
10. Galaxy distance in millions of light years
d=13,680 x rsh+8.338
distance (millions of light years)=13,680 x red shift+8.336
11. velocity of galaxy in kilometers/second
v=300,000 x rsh
velocity (kilometers per second)=300,000 x redshift
12. approximate number of stars in a galaxy=luminosity in number of suns galaxy/.02954
13. redshift
Rsh=mly8.338/13,680
redshift=(light years (millions)8.336)/13,680
14. Volume of a galaxy=4/3 x Pi x a x b^2
a=major axis, b=minor axis, (for elliptical galaxies)
15. Number of stars=volume/distance between stars^3
16. Average Distance between stars in light years=cube root(volume/number of stars) 16. Number of stars span across longest axis of galaxy=
(3/4 x volume)/(Pi x b^2 x n^3)
b=minor axis length light years, n=distance between stars light years
17. Escape velocity from a galaxy meters/second=
Mass galaxy kilograms x 1.989 x 10^30/(number of stars x
4,827,572.324)^2
18. Surface gravity
gravity(meters/second^2)=mass of star number of suns x 1.99 x
10^30 x 6.67 x 10^11/(size of star number of suns x 864000000 x 1.62/2)^2
19. Titusbode law
Distance (astronomical units)=3*2^n+4/10
(n=infinity, 0, 1, 2, 3, â€¦)
Mercury=infinity
Venus=0
earth=1
mars=2
Asteroid belt=3
jupiter=4
Etc
20. kepler’s 3 laws of planetary motion
1. Planets travel in elliptical orbits.
2. Equal areas are covered in in equal times in the elliptical orbit.
3. The distance in astronomical units to the 3rd power equals the time to travel one complete orbit in years to the 2nd power.
(time years)^2=(radius orbit astronomical units)^3
D=P^(2/3)
P=D^(3/2)
21. Velocity to achieve orbit=sqrt(G x M/distance from center of the earth)
22. Escape velocity=sqrt(G x M/r)
23. Four types of eccentric orbits
circle eccentricity=0
ellipse eccentricity= 01
parabola eccentricity=1
hyperbola eccentricity>1
24. Eccentricity=(greatest orbital distanceclosest orbital distance)/(closest orbital distance+greatest orbital distance) e=(d(greatest)d(closest))/(d(closest)+d(greatest))
25. Calculations: orbits, periods of orbits, perihelions, aphelions and eccentricities (for example a comet)
CIRCLE
Circular formula eccentricity=0
(xh)^2+(yk)^2=r^2. (#1)
(h=x coordinate and y=y coordinate ;r=radius of orbit)
period=2 x pi x sqrt(radius^3/(6.67 x 10^11 x mass of body the body is orbiting))
Velocity in orbit=sqrt(6.67 x 10^11 x
mass of body the body is orbiting/radius of orbit)
Centripetal acceleration=velocity^2/radius of orbit
ELLIPSE
Use ellipse formula x^2/a^2+y^2/b^2=1
Then calculate from 2 coordinates in AUs with formula
x^2 x b^2 + y^2 x a^2=a^2 x b^2
find a and b (the closest and furthest approaches)
Period years of orbit=distance (AU)^3/2
time=2 x pi x sqrt(a^3/G x M)
distance=period^2/3
velocity=sqrt(G x M x (2/r1/a))
eccentricity=(0<e<1)
eccentricity=sqrt(1b^2/a^2)
a (semimajor axis)=(perihelion + aphelion)/2
Semi minor axis (b)=sqrt((eccentricity^21) x a^2)
Simple way to calculate and orbit
1=X^2+Y^2. >Â 1=x^2+semimajor axis^2+y^2/semiminor axis^2
time in seconds to get to orbital position from 0 degrees going counterclockwise t=radians at current position of orbiting body/360 x sort(semi
major axis^3/6.67 x 10^11 x 1.989 x 10^30)
to find the angle at which the orbiting body is at from 0 degrees going counterclockwise x^2=p^2+1
q=sqrt(p)
r=sqrt(x)
s=q/r
arcsin(s)=angle of the orbiting body with respect to the focal body
to find distance to orbiting body from foci
x^2=p^2+p^2
cosy=x^2/P^2 x x^2
m=arccosy
cosm=1/n
q=1/cosm
q=distance to orbiting body from foci
To find formula for the orbit, use ellipse formula
x^2/a^2+y^2/b^2=1
PARABOLA
eccentricity=1
y=a x X^2+b x X +c
Calculate from 2 coordinates of the body in its orbit (a and b coordinates in
both instances)
Solve for x, then y, and will have the formula for the parabolic orbit.
Then will have the equation of the orbit like the quadratic equation above with
numerical figures for a and b.
Velocity of body in parabolic orbit
v=sqrt(2 x 6.67 x 10^11 x mass of body being orbited/radius of body)
Period of orbit does not have an orbit so undefined.
eccentricity=sqrt(1+b^2/a^2)
time in seconds to get to orbital position from 0 degrees going counterclockwise– t=radians at current position of orbiting body/360 x sqrt(semi
major axis^3/6.67 x 10^11 x 1.989 x 10^30)
to find the angle at which the orbiting body is at from 0 degrees going counterclockwise– g^2+(distance between foci/2 (‘p))^2=d^2
(d^2p^2g^2)/(2(p^2)(g^2))=cosx
cos1x=angle x
p^21^2=g^2
(1^2p^2g^2)/(2(p^2)(g^2))=cosL
cos1L=angle L
90xL=m
mx=n
n is the angle the orbiting body is at from 0 degrees going counterclockwise HYPERBOLA
eccentricity>1
x/ay/b=1. (#1)
xbya=ab.Â (#2)
Calculate from 2 coordinates of the body in its orbit (a and b coordinates in both instances) using (equation #2).
Solve for x, then y, and will have the formula (for #1 above) for the hyperbolic orbit.
Then will have the equation of the orbit like equation #1 with numerical figures for a and b.
Velocity of body at infinity in a hyperbolic orbit
velocity at an infinite distances away=sqrt(velocity^2escapevelocity^2)
Period of orbit does not have na orbit so undefined.
26. EXAMPLES OF CALCULATING ORBITS
STEPS TO CALCULATE AN ELLIPTICAL ORBIT
Suppose we measure 2 coordinates of a comet, one at (4AU,1AU) and the other at (0AU,3AU).
1) We plug in each of the coordinates, the 1st equals the x and the 2nd equals the y, each of the 2 coordinates into b^2 x x^2+a^2 x y^2=a^2 x b^2.
Then we subtract the 2 equations from each other. Next, we solve for both a and b. The resulting equation is x^2/2.376^2+y^2/1.68^2=1
and this is the equation of the orbit for the 2 given coordinates. The ellipse equation is x^2/2.376^2+y^2/1.68^2=1.
Solving for x and y gives
x=sqrt((15.65 x y^2)/2.8) and y=sqrt((12.8 x x^2/5.65).
2) perehelion=1.68AU, aphelion=2.376AU. (figures for constants a and b)
3) semimajor axis=A=(perihelion+aphelion)/2=(1.68+2.376)/2=1.9958AU
4) Semi minor axis=smaller figure of a and b=1.68AU.
5) focii=amaller figure of a and b=1.68AU.
6) distance center of ellipse to the foci=Aperihelion=.3158AU
7) period=aphelion^3/2=2.82 years (1,029.83 days)
8) eccentricity=1perihelion/A=.158
9) velocity at any instant=1.99 x 10^30 x 6.67 x 10^11 x (1/radius=1/A)=
At perihelion=20.07 miles/second, at aphelion=10.74 miles/second
10) Suppose we want to find the time from perihelion to a distance of 2 AU and its velocity there. We use the formulas
Semimajor axis^2+semimajor axis^2=x^2
cosx=x^2/2 x semimajor axis^2 x x^2; angle=arccosx
time=angle/360 x sqrt(semimajor axis^3/6.67 x 10^11 x 1.989 x 10^30)
The answer for time atÂ 2 AU=82.79/360 x sqrt(2.7186 x 10^34/1.32733 x 10^20)=
.22997 x 14311435.6=38.09 days at a velocity there at 12.995 miles/second.
HALLEY’S COMET
period=75.986 years.
focii=.6AU.
perihelion=.6AU.
aphelion=35.28AU.
Semimajor axis=17.94Au
eccentricity=.9855.
Velocity at perihelion=33.23 miles/second, aphelion=3.124 miles/second
STEPS TO CALCULATE A CIRCULAR ORBIT
Suppose 2 coordinates were recorded of a celestial body, one (3,2,646), and the other (1,3.873). It the celestial body has a circular orbit, the squares of each set of coordinates added together will equal the same defendant number. In this example,
3^2+2.646^2=15, and 1^2+3.873^2=16, so this is a circular orbit where the equation of the orbit is 4^2=x^2+y^2, where the 4 in the 4^2 is the radius of the circle, and the x and y are the
coordinates of the circular orbit. The eccentricity of of a circular orbit is equal to zero. STEPS TO CALCULATE A PARABOLIC ORBIT
Formulas
velocity=sqrt(2 x G x Mass central body/radius of orbiting body from central body) trajectory=(4.5 x G x M x Time seconds^2)^1/3
To find out whether 2 coordinates measurements of an orbiting body if a parabolic orbit, say coordinates (3,27) and (2,12), we need to set up a parabolic equation
y=b x x^2, then put into it separately the 2 coordinates. 27=b x 3^2, solve for b to arrive at equals to 3.
12=b x 2^2, b also equals 3.
Since b in both equations are equal to each other, the orbiting object is in a parabolic orbit. The equation for the orbit is y=3 x x^2. The period of orbit is infinitely long since the orbiting object never returns. The vertex of the orbit is (0,0). The foci is equal to 3/4. We arrive at this by always using 4 x p, and setting it equal to 3, the number equal to b. When 4 x p=3 is solved, p=3/4. So the focus is at (0,3/4).the velocity of the orbiting body at its closest approach to the central body is equal to 30.05 miles/second.
STEPS TO CALCULATE A HYPERBOLIC ORBIT
Suppose 2 coordinates of an orbiting celestial body are recored as being at (28.28, 10)AU and (34.64, 14.14)AU positions. We try using the hyperbolic equation
1=x^2/a^2y^2/b^2, solve for a and b, and the result equals 1, so this is a hyperbolic orbit. a=20 and b=10. The equation for the orbit is
1=x^2/20^2y^2/10^2.
Solving for x and y yields
x=sqrt(4004 x y^2), and y=sqrt(x^2/4100(.
The orbit’s eccentricity is equal to sqrt(a^2+b^2)/a=sqrt(400+100)/400=1.118, which is greater than 1, so this is a hyperbolic orbit.
For focii=sqrt(a^2+b^2)=22.33AU from the sun’s position, which is equal to 22.33 a=22.3320=20AU, which makes the focci=(20,0).
The period of this orbiting body is undefined since it will never return. To find the semimajor axis, we use the velocity formula
v=sqrt(6.67 x 10^11 x 1.99 x 10^30 x (2/r1/semimajor axis)).
r=2.33AU in meters and v=618,000 meters/second. Solving for the semimajor axis yields 1208.12.
Let us determine the velocity of the orbiting object at say 5AU from the sun.
v=sqrt(6.67 x 10^11 x 1,99 x 10^30 x (2/5AU in meters1/1208.12))=18.77 kilometers/second, or 11.64 miles/second.
If we wanted to calculate the velocity of the object when it gets as far away as the nearest star, 4.3 light years away,
it would be traveling 25.76 meter/second there.
27. Formulas to find masses, radius, and luminosities of WHITE DWARFS (mass<=.75 suns)
(radius<=.00436 suns)
(luminosity<=.00365 suns)
radius=mass^18.68 mass=radius^.052966
luminosity=mass^19.5198 mass=luminosity^.05123
luminosity=radius^1.04494 radius=luminosity^.95699
28. Formulas to find masses, radius, and luminosities of MAIN SEQUENCE stars luminosity=mass^3.5
mass=luminosity^(.2857)
radius=(temperature kelvin sun/temperature kelvin star)^2 x
(2.512^(absolute magnitude sunabsolute magnitude star)
note main sequence star’s masses can be found by knowing the star’s luminosity and its temperature.
Type star Mass radius. Temperature luminosity lifespan
O. +16. +6.6 +33,000 kelvin 55,000 to >200,000 >9.77 m/yrs
B 2.116. 1.86.6 10,00033,000 kelvin. 4224,000. 9.77 m/yrs1.57
b/yrs
A 1.42.1. 1.41.8. 7,50010,000 kelvin. 5.124. 1.57 b/yrs4.3 b/yrs F. 1.041.4. 1.151.4. 6,0007,500 kelvin. 2.45.1. 4.3 b/yrs9.07 b/yrs
G. .81.04. .961.15. 5,2006,000 kelvin .381.2. 9.07 b/yrs17.47 b/yrs K. .45.8. .7.96. 3,7005,200 kelvin. .08.38. 17.47 b/yrs73.62 b/yrs M. <=.45. <=.7. 2,0003,700 kelvin <.002.08. >73.62 b/yrs
29. Formulas to find SUBGIANT masses, radii, and luminosities MASS TO LUMINOSITY
O type subgiant stars luminosity=100,0001 million luminosity^.295=mass
luminosity^.2=radius
mass^.675=radius
B type subgiant stars luminosity=35040,000 luminosity^.245=mass luminosity^.205=radius
mass^.84=radius
A type subgiant stars luminosity=20200 luminosity^.203=mass luminosity^.256=radius
mass^1.26=radius
F type subgiant stars luminosity=8300 luminosity^.19=mass
luminosity^.37=radius
mass^1.94=radius
G type subgiant star luminosity=1.16 luminosity^.15=mass luminosity^.5=radius mass^3.57=radius
K type subgiant stars luminosity=345 luminosity^.1mass luminosity^.625=radius mass^4.15=radius
30. Masses, radius, and luminosities for GIANT stars O type giant stars luminosity=30,000 to >2 million luminosity^.27=mass
luminosity^.206=radius
mass^.756=radius
B type giant stars luminosity=33035,000 luminosity^.24=mass luminosity^.223=radius mass^.936=radius
A type giant star luminosity=108,000 luminosity^.227=mass luminosity^.244=radius mass^1.08=radius
F type giant stars luminosity=10100 luminosity^.195=mass luminosity^.363=radius mass^1.86=radius
G type giant stars luminosity=1575 luminosity^.19=mass luminosity^.57=radius mass^2.89=radius
K type giant stars luminosity=30275 luminosity^.11=mass luminosity^.625=radius mass^5.7=radius
M type giant stars luminosity=8003,700 luminosity^.098=mass luminosity^.65=radius
mass^6.7=radius
31. Masses, radius, and luminosities for BRIGHT GIANT stars O type bright giant stars luminosity=65,000320,000 luminosity^.27=mass
luminosity^.22=radius
mass^.795=radius
B type bright giant stars 25,00040,000 luminosity^.23=mass
luminosity^.3=radius
mass^1.23=radius
A type bright giant stars luminosity=3,00015,000 luminosity^.24=mass
luminosity^.37=radius
mass^1.665=radius
F type bright giant stars luminosity=5002,500 luminosity^.23=mass
luminosity^.44=radius
mass^2.1=radius
G type bright giant stars luminosity=1501,000 luminosity^.22=mass
luminosity^.4=radius
mass^2.3=radius
K type bright giant stars luminosity=2003,500 luminosity^.21=mass
luminosity^.58=radius
mass^6=radius
M type bright giant stars luminosity=60025,000 luminosity^.19=mass
luminosity^.65=radius
mass^8.1=radius
32. Finding masses, radius, and luminosities for SUPERGIANT stars Supergiant stars luminosity=120,0002 million luminosity^.213=mass
luminosity^.56=radius
mass^2.63=radius
33. Close formula for mass to radius and radius to mass of STARS MASSES 40 to GREATER THAN 200 SOLAR MASSES
(crudely estimated formulas) luminosity^.325=mass
luminosity^.519=radius
mass^1.6=radius
34. MASSES OF STARS AND THEIR FATES Masses .0710 suns white dwarf
Masses .58 suns planetary nebulas
Masses >8 suns supernovas
Masses 1029 suns neutron stars
masses>29 suns black holes
35. Spectral type, temperature, color, mass, size, luminosity, % of stars
O 30,000 K blue >16 >6.6 >30,000 .00003%
B 10,00030,00 blue white 2.116 1.86.6 2530,000 .13%
A 7,50010,000 white blue 1.42.1 1.41.8 525 .6%
F 6,0007,500 yellow white 1.041.4 1.151.4 1.55 3%
G 5,2006,000 yellow .81.04 .961.15 .61.5 7.6%
K 3,7005,200 light orange .45.8 .7.96 .08.6 12.1%
M 2,4003,700 orange red .08.45 <=.7 <=.08 76.45%
The Hertzsprung Russell diagram relates stellar classification with absolute magnitude, luminosity, and surface temperature.
36. DISTRIBUTION OF TYPES OF STARS IN GALAXY
Giants and supergiants .946%
O star .0000256%
B stars .1105%
A stars .51085%
F stars 2.5545%
G stars 6.446%
K stars 10.313%
M stars 65.0295%
White dwarfs 8.515%
Brown dwarfs 110% (4.98% average estimate)
Neutron stars .8515%
Black holes .08515
DRAKE EQUATION ESTIMATE OF PERCENTAGE OF ADVANCED CIVILIZATIONS OF SYSTEMS STARS
Applies to 10% of all stars
37. SEVERAL ABSOLUTE AND APPARENT MAGNITUDES WITH LUMINOSITIES LIST ABSOLUTE MAGNITUDES LIST
Gamma ray burst. 39.1 374,000 trillion suns
Quasars 33. 1,360 trillion suns
supernovas. 19.3. 4.49 billion suns
Supernova 1978a. 15.66. 157 million suns
Pistol star. 10.75 1.7 million suns
deneb 8.38. 192,424 suns
Betelgeuse. 5.5. 13,558 suns
Sun 4.83. 1 sun
Proxima centauri. 11.13. 1/331 suns
Sun in Andromeda galaxy. 29.07. 1/4.98 billion suns
Venus 29.23. 1/5.8 billion suns
Hubble telescope viewing limit. 31. 1/29.4 billion suns
James webb telescope viewing limit. 34. 1/466 billion suns
APPARENT MAGNITUDES LIST
sun. 26.72. 23.74 trillion suns
Full moon. 12.6. 9.38 million suns
Venus. 4.4. 4,922 suns
Sirius. 1.6. 373 suns
Most energetic gamma ray burst 12.2 billion light years away 3.77. (374,000 trillion suns)
Sun seen by us if it were in andromedas galaxy. 53.31 1/(2.48 x 10^19) suns
Type 2 supernova in Andromeda as seen from here— apparent magnitude— 4.94
Venus in Andromeda as seen from here— apparent magnitude— 53.47
Deneb in Andromeda as seen from here— apparent magnitude— 15.86
38. Formulas to find temperature kelvin from spectral class—
Temp.=1500 x spectral class number+10000
O0=20, O1=19,…, B9=1, A0=0
Temp.=187.27 x spectral class number+5880
A0=22, A1=21,…, G1=1, G2=0
Temp.=132.22 x spectral class number+3500
G2=18, G3=17,…, K9=1, M0=0, M1=1, M2=2,…, M9=9
Spaceflight formulas
Meaning of variables in the formulas—
v=velocity (meters/second)
vi=velocity initial (meters/second)
vf=velocity final (meters/second)
vexh=exhaust velocity (meters/second)
isp=seconds
m=mass (kilograms)
mi=initial mass (kilograms)
mf=final mass (kilograms)
mr=mass ratio
a=acceleration (meters/second^2)
f=force (newtons)
d=distance (meters)
t=time (seconds)
ke=kinetic energy (joules)
ed=energy density (joules/kilograms)
p=power (watts)
spp=specific power (kilowatts/kilograms)
mm=momentum (meters x kilograms)
i=impulse (thrust x seconds)
fr=fuel rate (kilograms/second)
mw=molecular weight
texh=temperature exhaust (kelvin)
eff=propulsive efficiency
r=radius (meters)
ecc=eccentricity
g=acceleration due to gravity
(9.81 meters/second^2)
Rocket equation
velocity
v=vexh x ln(mi/mf)
v=(d x 2)/t (when accellerating)
v=d/t (constant velocity)
v=sqrt(2 x a x d)
Velocity of exhaust
vexh=v/ln*(mi/mf)
vexh=.25 x sqrt(texh/mw)
Isp
isp=vexh/9.81
isp=f/(fr x 9.81)
isp=vf/(ln(mr) x 9.81)
isp=vf/ln(mr) x 9.81
isp=f x t
Mass ratio
mr=e^(vf/isp x 9.81)
mr=mi/mf
mr=e^(v/vexh)
mr=e^(vf/(isp x 9.81))
Mass final
mf=mi/(e^(vf/vexh)
Mass initial
mi=mf x e^(vf/vexh)
mass
m=f/a
m=2 x ke/v^2
Force
f=m*a
f=ke/d
f=9.81 x isp x fr
acceleration
a=f/m
Energy
ke=1/2 x v^2 x m
ke=d x f
Energy density (rest mass energy)
ed=ke/m
Fuel flow rate
fr=f/vexh
fr=m/t
Distance
d=v x t/2 (with respect to accelerating)
d=v x t (constant velocity)
d=ke/f
d=v^2/2 x a
Time
t=(d x 2)/v (constant acceleration)
t=d/v (constant velocity)
t=((m x vf)^2/2)(m x mi)^2/2) x (1/f) x (2/vi+vf)
Power p=ke/t
p=f x d/t
Specific power
sp=(p/1000)/m
Momentum
M=v x m
Impulse â
i=f x t
Antimatter needed (kilograms) m=ke/1.8 x 10^16
Propulsive efficiency eff=2/(1+(vexh/vf))
eff=(vf/vexh)^2/(e^(vf/vexh)1)
(Maximum efficiency for ratio vf/vexh<1.6) eff=f x g x isp/2 x p
UNIVERSAL PHYSICAL CONSTANTS
ATOMIC MASS UNITS
1.6605402 x 10^27 kilograms
(1/12 0f the mass of an atom of carbon12)
AVOGADRO NUMBER
6.0221367 x 10^23/moles
(mole=number of elementary entities that are in
carbon12 atoms in exactly 12 grams of carbon12)
BOHR’S MAGNETON
9.2740154 x 10^24 joules/tesla
(The magnetic moment of an electron caused by either its orbital
or spin angular momentum. Magnetic moment is a quantity that
determines the torque it will experience in an external magnetic
field. Torque is rotational force. A joule is equal to the work done on
an object when a force of 1 newton acts on the object in the direction
of motion through a distance of 1 meter: kilograms x meters^2/
seconds^2. A joule is also equal to 10 million ergs. A Tesla is a
derived unit of the strength of a magnetic field: kilograms/(seconds^2
x amperes.)
BOHR RADIUS
5.29177249 x 10^11 meters
(The mean radius of an electron around the nucleus of a hydrogen atom
at its ground state.)
BOLTZMANN CONSTANT
1.3806513 x 10^23 joules/kelvin
(A physical constant relating the average kinetic energy of
particles in a gas with the temperature of the gas. Kelvin
temperature scale is the primary unit of temperature measurement
in the physical sciences, but is often used in conjunction with the
celsius degree, which is of the same magnitude absolute zero in
kelvin is equal to 273.15 degrees celsius.)
ELECTRON CHARGE
1.60217733 x 10^19 coulombs
(Charge carried by a single electron. The coulomb is the quantity of
charge that has passed through the cross section of an electrical
conductor carrying one ampere within one second.)
ELECTRON CHARGE/MASS RATIO
1.75881962 x 10^11 coulombs/kilograms
(The importance of the chargetomass ratio, according to classical
electrodynamics, is that 2 particles with the same chargetomass ratio
move in the same path in a vacuum when subjected to the same electric
and magnetic fields.)
ELECTRON COMPTON WAVELENGTH
2.42631058 X 10^12 meters
(A compton wavelength of a particle is equal to the wavelength of a
photon whose energy is the same as the mass of the particle. The
compton wavelength of an electron is the characteristic length scale of
quantum electrodynamics. It is the length scale at which relativistic
quantum field theory becomes crucial for its accurate description.)
ELECTRON MAGNETIC MOMENT
9.2847701 x 10^24 joules/tesla
(The electron is a charged particle of 1e, where e is the unit of
elementary charge. Its angular momentum comes from 2 types of
rotation: spin and orbital motion.)
ELECTRON MAGNETIC MOMENT IN BOHR MAGNETONS
1.00159652193
(Bohr magneton is a physical constant and natural unit for expressing the
magnetic moment of an electron caused by either its orbital or spin
angular momentum. The electron magnetic moment, which is the
electron’s intrinsic spin magnetic moment, is approximately one Bohr
magneton.)
ELECTRON MAGNETIC MOMENT/PROTON MAGNETIC MOMENT
658.21068801
ELECTRON REST MASS
9.1093897 x 10^31 kilograms
ELECTRON REST MASS/PROTON REST MASS
5.44617013 x1 0^4
This is how much less mass the electron is as compared to the proton.
(1,836.21 times lighter than proton)
FARADAY CONSTANT
9.6458309 x 10^4 coulombs/mole
(The magnitude of electric charge per mole of electrons.)
FINE STRUCTURE CONSTANT
.00729735308
(The strength of the electromagnetic interaction between elementary
particles.)
GAS CONSTANT
8.3144710 x 10^joules/(mole x kelvin)
(A physical constant which is featured in many fundamental equations
in the physical sciences, such as the ideal gas law and the Nernst
equation.)
GRAVITATIONAL CONSTANT
6.67206 x 10^11 newtons x meters^3/(kilograms*second^2)
Denoted by letter G, it is an empirical physical constant involved
in the calculation of gravitational effects.
IMPEDENCE IN VACUUM
3.767303134 x 10^2 ohms
(The waveimpedence of a plane wave in free space. Electric field
strength divided by the magnetic field strength.)
SPEED OF LIGHT
299,792,458 meters/second
SPEED OF LIGHT IN A VACUUM SQUARED
89,875,517,873,681,764 meters^2/seconds^2
MAGNETIC FLUX QUANTUM
2.06783383 x 10^15 webers
(The measure of the strength of a magnetic field over a given area
taken perpendicular to the direction of the magnetic field.)
MOLAR IDEAL GAS VOLUME
22.41410×10^3 meters^3/moles
(As all gases that are behaving ideally have the same number density,
they will all have the same molar volume. It is useful if you want to
envision the distance between molecules in different samples.)
MUON REST MASS
1.8835327×10^28 kilograms
(A muon is an elementary particle similar to an electron, with an electric
charge of 1 and a spin of 1/2, but with a much greater mass.)
NEUTRON COMPTON WAVELENGTH
1.31959110 x 10^15 meters
(Explains the scattering of photons by electrons. The compton
wavelength of a particle is equal to the wavelength of a photon
whose energy is the same as the mass of the particle.)
NEUTRINO REST MASS
3.036463233*10^35 kilograms
NUCLEAR MAGNETON
5.0507866 X 10^27 Henry/meters
(A physical constant of magnetic moment. Using the mass of a proton,
rather than the electron, used to calculate the Bohr magneton. unit of
magnetic moment, used to measure proton spin and approximately
equal to 1.1,836 Bohr magneton.)
PERMEABILITY CONSTANT
12.5663706144 x 10^7 Henry/meters
(Magnetic constant, or the permeability of free space, is a measure of
the amount of resistance encountered when forming a magnetic field
in a classical vacuum.)
PERMITTIVITY CONSTANT
8.854187817 x 10^12 farad/meters
(A constant of proportionality that exists between electric displacement
and electric field intensity in a given medium.)
PLANCK’S CONSTANT
6.6260755×10^34 joules/hertz
6.62607004×10^34 meters^2 x kilograms/seconds
(This constant links the about of energy a photon carries with the
frequency of its electromagnetic wave.)
PROTON COMPTON WAVELENGTH
2.4263102367 x 10^12 meters
(The compton wavelength is a quantum mechanical property of a
particle. A convenient unit of length that is characteristic of an elementary
particle, equal to Planck’s constant divided by the product of the particles
mass and the speed of light.)
PROTON MAGNETIC MOMENT
1.41060761 x 10^26 joules/tesla
(The dipole of the proton. Protons and neutrons, both nucleons,
comprise the nucleus of an atom, and both nucleons act as small
magnets whose strength is measured by their magnetic moments.)
PROTON MAGNETIC MOMENT IN BOHR MAGNETONS
1.521032202 x 10^3
(A physical constant and the natural unit for expressing the magnetic
moment of an electron caused by either its orbit or spin angular
momentum.
PROTON MASS/ELECTRON MASS
1,836.152701
PROTON REST MASS
1.6726231 x 10^27 kilograms
RYDBERG CONSTANT
1.0973731534 x 10^7/meters
(A physical constant relating to atomic spectra, in the science of
spectroscopy. Appears in the Balmer formula for spectral lines of the
hydrogen atom.)
RYDBERG ENERGY
13.6056981 electronvolts
(It corresponds to the energy of the photon whose wavenumber is the
Rydberg constant, I.e. the ionization of the hydrogen atom. It describe
the wavelengths of spectral lines of many elements.)
STEFANBOLTZMANN CONSTANT
5.67051 x 10^8 weber/(meters^2 x kelvin^4)
(The power per unit area is directly proportional to the 4th power of the
thermodynamic temperature. It is the total intensity radiated over all
wavelengths as the temperature increases, of a black body which is
proportional to to 4th power of the thermodynamic temperature.)
Table of physical constants
Universal constants
Value
Quantity Symbol
299 792 458 m⋅s−1defined Newtonian constant of gravitation G
Relative standard uncertainty
speed of light in vacuum c
6.67408(31)×10−11 m3⋅kg−1⋅s−2. Planck constant h
6.626 070 040(81) × 10−34 J⋅s. reduced Planck constantħ=h/2π
1.054 571 800(13) × 10−34 J⋅s.
4.7 × 10−5 1.2 × 10−8
1.2 × 10−8
Electromagnetic constants Quantity
Symbol
Value (SI units)
Relative standard uncertainty
magnetic constant (vacuum permeability)μ0
4π × 10−7 N⋅A−2 = 1.256 637 061… × 10−6 N⋅A−2defined
electric constant (vacuum permittivity)ε0=1/μ0c2 8.854 187 817… × 10−12 F⋅m−1defined
characteristic impedance of vacuumZ0=μ0c
376.730 313 461… Ωdefined
Coulomb’s constant ke=1/4πε0
8.987 551 787 368 176 4 × 109 kg⋅m3⋅s−4⋅A−2defined
elementary charge e
1.602 176 6208(98) × 10−19 C.
Bohr magneton μB=eħ/2me 9.274 009 994(57) × 10−24 J⋅T−1.
conductance quantum
7.748 091 7310(18) × 10−5 S.
inverse conductance quantum
G0−1=h/2e2
12 906.403 7278(29) Ω 2.3 × 10−10
Josephson constant
KJ=2e/h
4.835 978 525(30) × 1014 Hz⋅V−1 6.1 × 10−9
magnetic flux quantum
φ0=h/2e
2.067 833 831(13) × 10−15 Wb 6.1 × 10−9
nuclear magneton
μN=eħ/2mp
5.050 783 699(31) × 10−27 J⋅T−1 6.2 × 10−9
von Klitzing constant
RK=h/e2
25 812.807 4555(59) Ω 2.3 × 10−10
6.1 × 10−9
6.2 × 10−9 2.3 × 10−10
Atomic and nuclear constants Quantity
Symbol
Value (SI units)
Relative standard uncertainty Bohr radius
a0=α/4πR∞
5.291 772 1067(12) × 10−11 m 2.3 × 10−9
classical electron radius
re=e2/4πε0mec2m_
2.817 940 3227(19) × 10−15 m 6.8 × 10−10
electron mass
me
9.109 383 56(11) × 10−31 kg 1.2 × 10−8
Fermi coupling constant
GF/(ħc)3
1.166 3787(6) × 10−5 GeV−2 5.1 × 10−7
finestructure constant
α=μ0e2c/2h=e2/4πε0ħc
7.297 352 5664(17) × 10−3 2.3 × 10−10
Hartree energy
Eh=2R∞hc
4.359 744 650(54) × 10−18 J 1.2 × 10−8
proton mass
mp
1.672 621 898(21) × 10−27 kg 1.2 × 10−8
quantum of circulation
h/2me
3.636 947 5486(17) × 10−4 m2 s−1 4.5 × 10−10
Rydberg constant
R∞=α2mec/2h
10 973 731.568 508(65) m−1 5.9 × 10−12
Thomson cross section
(8π/3)re2
6.652 458 7158(91) × 10−29 m2 1.4 × 10−9
weak mixing angle
sin2θW=1−(mW/mZ)2 0.2223(21)
9.5 × 10−3
Efimov factor
22.7
Physicochemical constants Quantity
Symbol Relative standard uncertainty
Value[23][24] (SI units)
Atomic mass constant
mu=1u
1.660539040(20)×10−27 kg 1.2×10−8
Avogadro constant
NA,L
6.022140857(74)×1023 mol−1 1.2×10−8
Boltzmann constant
k=kB=R/NA
1.38064852(79)×10−23 J⋅K−1 5.7×10−7
Faraday constant
F=NAe
96485.33289(59) C⋅mol−1 6.2×10−9
first radiation constant
c1=2πhc2
3.741 771 790(46) × 10−16 W⋅m2 1.2 × 10−8
for spectral radiance
c1L=c1/π
1.191 042 953(15) × 10−16 W⋅m2⋅sr−1 1.2 × 10−8
Loschmidt constant
atT = 273.15 K and p = 101.325 kPa
n0=NA/Vm
2.686 7811(15) × 1025 m−3 5.7 × 10−7
gas constant
R
8.3144598(48) J⋅mol−1⋅K−1 5.7×10−7
molar Planck constant
NAh
3.990 312 7110(18) × 10−10 J⋅s⋅mol−1 4.5 × 10−10
molar volume of an ideal gas
atT = 273.15 K and p = 100 kPa
Vm=RT/p
2.271 0947(13) × 10−2 m3⋅mol−1
5.7 × 10−7
at T= 273.15 K and p= 101.325 kPa2.241 3962(13) × 10−2 m3⋅mol−1 5.7 × 10−7
Sackur–Tetrode constant
at
T= 1 K and p= 100 kPa S0/R=52/R=+ln[(2πmukT/h2)3/2kT/p]
−1.151 7084(14)1.2 × 10−6at T= 1 K and p = 101.325 kPa −1.164 8714(14)1.2 × 10−6
second radiation constant
c2=hc/k
1.438 777 36(83) × 10−2 m⋅K 5.7 × 10−7
Stefan–Boltzmann constant
σ=π2k4/60ħ3c2
5.670367(13)×10−8 W⋅m−2⋅K−4 2.3×10−6
Wien displacement law constant
b energy=hck−1/=hck^ 4.965 114 231…
2.8977729(17)×10−3 m⋅K
5.7×10−7
Wien’s entropy displacement law constant
b entropy=hck−1/=hck^ 4.791 267 357…
3.002 9152(05) × 10−3 m⋅K 5.7 × 10−7
Adopted values Quantity
Symbol
Value (SI units)
Relative standard uncertainty conventional value of Josephson constant
KJ−90
4.835 979 × 1014 Hz⋅V−1
0 (defined)
conventional value of von Klitzing constant
RK−90
25 812.807 Ω
0 (defined)
constant
Mu=M(12C)/12
1 × 10−3 kg⋅mol−1 0 (defined)
of carbon12
M(12C)=NAm(12C)
1.2 × 10−2 kg⋅mol−1 0 (defined)
molar mass
standard acceleration of gravity (gee, freefall on Earth) gn
9.806 65 m⋅s−20 (defined) standard atmosphere
atm
101 325 Pa 0 (defined)
ATOMIC MASS UNITS
1.6605402 x 10^27 kilograms
(1/12 0f the mass of an atom of carbon12)
AVOGADRO NUMBER
6.0221367 x 10^23/moles
(mole=number of elementary entities that are in carbon12 atoms in exactly 12 grams of carbon12)
BOHR’S MAGNETON
9.2740154 x 10^24 joules/tesla
(The magnetic moment of an electron caused by either its orbital
or spin angular momentum. Magnetic moment is a quantity that determines the torque it will experience in an external magnetic
field. Torque is rotational force. A joule is equal to the work done on an object when a force of 1 newton acts on the object in the direction of motion through a distance of 1 meter: kilograms x meters^2/ seconds^2. A joule is also equal to 10 million ergs. A Tesla is a derived unit of the strength of a magnetic field: kilograms/(seconds^2 x amperes.)
BOHR RADIUS
5.29177249 x 10^11 meters
(The mean radius of an electron around the nucleus of a hydrogen atom at its ground state.)
BOLTZMANN CONSTANT
1.3806513 x 10^23 joules/kelvin
(A physical constant relating the average kinetic energy of particles in a gas with the temperature of the gas. Kelvin temperature scale is the primary unit of temperature measurement in the physical sciences, but is often used in conjunction with the celsius degree, which is of the same magnitude absolute zero in kelvin is equal to 273.15 degrees celsius.)
COSMOLOGICAL CONSTANT
R=1/2Rg=8 x pi x 6.67 x 10^11 x T
(T=energymomentum tensor)
The constant is a homogeneous energy density that causes the expansion of the universe to accelerate.
ELECTRON CHARGE
1.60217733 x 10^19 coulombs
(Charge carried by a single electron. The coulomb is the quantity of charge that has passed through the cross section of an electrical conductor carrying one ampere within one second.)
ELECTRON CHARGE/MASS RATIO
1.75881962 x 10^11 coulombs/kilograms
(The importance of the chargetomass ratio, according to classical electrodynamics, is that 2 particles with the same chargetomass ratio move in the same path in a vacuum when subjected to the same electric and magnetic fields.)
ELECTRON COMPTON WAVELENGTH 2.42631058 X 10^12 meters
(A compton wavelength of a particle is equal to the wavelength of a photon whose energy is the same as the mass of the particle. The compton wavelength of an electron is the characteristic length scale of quantum electrodynamics. It is the length scale at which relativistic quantum field theory becomes crucial for its accurate description.)
ELECTRON MAGNETIC MOMENT 9.2847701 x 10^24 joules/tesla
(The electron is a charged particle of 1e, where e is the unit of elementary charge. Its angular momentum comes from 2 types of rotation: spin and orbital motion.)
ELECTRON MAGNETIC MOMENT IN BOHR MAGNETONS 1.00159652193
(Bohr magneton is a physical constant and natural unit for expressing the magnetic moment of an electron caused by either its orbital or spin angular momentum. The electron magnetic moment, which is the electron’s intrinsic spin magnetic moment, is approximately one Bohr magneton.)
ELECTRON MAGNETIC MOMENT/PROTON MAGNETIC MOMENT 658.21068801
ELECTRON REST MASS
9.1093897 x 10^31 kilograms
ELECTRON REST MASS/PROTON REST MASS 5.44617013 x1 0^4
This is how much less mass the electron is as compared to the proton. (1,836.21 times lighter than proton)
FARADAY CONSTANT
9.6458309 x 10^4 coulombs/mole
(The magnitude of electric charge per mole of electrons.)
FINE STRUCTURE CONSTANT .00729735308
(The strength of the electromagnetic interaction between elementary particles.)
GAS CONSTANT
8.3144710 x 10^joules/(mole x kelvin)
(A physical constant which is featured in many fundamental equations in the physical sciences, such as the ideal gas law and the Nernst equation.)
GRAVITATIONAL CONSTANT
6.67206 x 10^11 newtons x meters^3/(kilograms*second^2)
Denoted by letter G, it is an empirical physical constant involved in the calculation of gravitational effects.
IMPEDENCE IN VACUUM
3.767303134 x 10^2 ohms
(The waveimpedence of a plane wave in free space. Electric field strength divided by the magnetic field strength.)
SPEED OF LIGHT
299,792,458 meters/second
SPEED OF LIGHT IN A VACUUM SQUARED 89,875,517,873,681,764 meters^2/seconds^2
MAGNETIC FLUX QUANTUM
2.06783383 x 10^15 webers
(The measure of the strength of a magnetic field over a given area taken perpendicular to the direction of the magnetic field.)
MOLAR IDEAL GAS VOLUME 22.41410×10^3 meters^3/moles
(As all gases that are behaving ideally have the same number density, they will all have the same molar volume. It is useful if you want to envision the distance between molecules in different samples.)
MOLAR MASS CONSTANT 1×10^3 kilograms/moles (relates relative atomic mass and molar mass)
MOLAR MASS OF CARBON12— 1.2×10^2 kilograms/moles (relates atomic mass of carbon12 and molar mass)
MUON REST MASS
1.8835327×10^28 kilograms
(A muon is an elementary particle similar to an electron, with an electric charge of 1 and a spin of 1/2, but with a much greater mass.)
NEUTRON COMPTON WAVELENGTH 1.31959110 x 10^15 meters
(Explains the scattering of photons by electrons. The compton wavelength of a particle is equal to the wavelength of a photon whose energy is the same as the mass of the particle.)
NEUTRINO REST MASS 3.036463233*10^35 kilograms
NUCLEAR MAGNETON
5.0507866 X 10^27 Henry/meters
(A physical constant of magnetic moment. Using the mass of a proton, rather than the electron, used to calculate the Bohr magneton. unit of magnetic moment, used to measure proton spin and approximately equal to 1.1,836 Bohr magneton.)
PERMEABILITY CONSTANT
12.5663706144 x 10^7 Henry/meters
(Magnetic constant, or the permeability of free space, is a measure of the amount of resistance encountered when forming a magnetic field in a classical vacuum.)
PLANCK CHARGE 1.875545956×10^18 coulombs (a quantity of electric charge)
PERMITTIVITY CONSTANT
8.854187817 x 10^12 farad/meters
(A constant of proportionality that exists between electric displacement and electric field intensity in a given medium.)
PLANCK’S CONSTANT
6.6260755×10^34 joules/hertz
6.62607004×10^34 meters^2 x kilograms/seconds
(This constant links the about of energy a photon carries with the frequency of its electromagnetic wave.)
PLANCK CONSTANT (REDUCED) 6.582119514×10^16 eVseconds
(hbar, in which h equals h divided by 2pi, is the quantization of angular momentum.)
PLANCK’S LENGTH 1.616229X10&35 meters
(the scale at which classical ideas about gravity and spacetime cease to be valid, and quantum effects dominate.)
PLANCK MASS 2.17647X10^8 kilograms
(derived approximately by setting it as the mass whose compton wavelength and schwarzschild radius are equal.)
PLANCK TIME 5.3916×10^44 seconds
(time needed for light to travel 1 planck length in a vacuum.)
PLANCK TEMPERATURE 1.416808×10^32 degrees kelvin
(if an object were to reach this temperature, the radiation it would emit would have a wavelength of 1.616×10^35 meters, Planck’s length, at which point quantum gravitational effects become relevant.)
PROTON COMPTON WAVELENGTH 2.4263102367 x 10^12 meters
(The compton wavelength is a quantum mechanical property of a particle. A convenient unit of length that is characteristic of an elementary particle, equal to Planck’s constant divided by the product of the particles mass and the speed of light.)
PROTON MAGNETIC MOMENT
1.41060761 x 10^26 joules/tesla
(The dipole of the proton. Protons and neutrons, both nucleons, comprise the nucleus of an atom, and both nucleons act as small magnets whose strength is measured by their magnetic moments.)
PROTON MAGNETIC MOMENT IN BOHR MAGNETONS 1.521032202 x 10^3
(A physical constant and the natural unit for expressing the magnetic moment of an electron caused by either its orbit or spin angular momentum.
RYDBERG CONSTANT
1.0973731534 x 10^7/meters
(A physical constant relating to atomic spectra, in the science of spectroscopy. Appears in the Balmer formula for spectral lines of the hydrogen atom.)
RYDBERG ENERGY
13.6056981 electronvolts
(It corresponds to the energy of the photon whose wavenumber is the Rydberg constant, I.e. the ionization of the hydrogen atom. It describe the wavelengths of spectral lines of many elements.)
STANDARD ACCELERATION ON EARTH BY GRAVITY 9.80665 meters/seconds^2
STANDARD ATMOSPHERE 101.325 pascals
(pressure, temperature, density, and viscosity of the earth’s atmosphere.)
STEFANBOLTZMANN CONSTANT
5.67051 x 10^8 weber/(meters^2 x kelvin^4)
(The power per unit area is directly proportional to the 4th power of the thermodynamic temperature. It is the total intensity radiated over all wavelengths as the temperature increases, of a black body which is proportional to to 4th power of the thermodynamic temperature. This constant is used to link a star’s temperature to the amount of light it emits.)
MAGNETIC CONSTANT (VACUUM PERMIABILITY) 1.256637061X10^6 NEWTONS/AMPERES^2
ELECTRIC CONSTANT (VACUUM PERMITTIVITY) 8.854187817X10^12 FARAD/METER
CHARACTERISTIC IMPEDANCE OF VACUUM 376.730313461 OHMS
COULOMB’S CONSTANT
8.9875517873881764X10^8 KILOGRAMS METERS^3/
SECONDS^4XAMPERES^2
ELEMENTARY CHARGE
1.6021766208X10^19 COULOMBS
CONDUCTIVE QUANTUM
7.748091731X10^8 SECONDS
INVERSE CONDUCTIVE QUANTUUM 12.9064037278 OHMS
JOSEPHSON CONSTANT
4.835978525X10^14 HERTZ/VOLTS
MAGNETIC FLUX QUANTUM 2.067831X10^15 WEBERS
NUCLEAR MAGNETON
5.050783699X10^27 JOULES/TESLAS
VON KILTZING CONSTANT 258.12807557 ohms
CLASSICAL ELECTRON RADIUS 2.8179403227X10^15 METERS
ELECTRON MASS
9.10938356×10^31 kilograms
FERMI COUPLING CONSTANT 1.1663787X10^5 GeV^2
FINESTRUCTURE CONSTANT 7.2972525664X10^3
HARTREE ENERGY
4.35974465X10^18 JOULES
PROTON MASS
1.6726219×10^27 kilograms
QUANTUM OF CIRCULATION
3.6369475486X10^4 METERS^2/SECONDS
THOMSON CROSS SECTION 6.6524587158X10^29 METERS^2
WEAK MIXING ANGLE .2223
EFIMOV FACTOR 22.7
FIRST RADIATION CONSTANT
3.74177179X10^16 WEBERMETERS^2
FIRST RADIATION CONSTAnt (for spectral radiance) 1.191042953×10^16 webersmeters^2seconds/radius
Loschmidt constant
2.6867811×10^25 /meters^3
Molar planck constant
3.990312711×10^10 joulesseconds/moles
Molar volume of an ideal gas (at t=273.15 k and p=100 kpa) 2.2710947×10^2meters^3/moles
Molar volume of an ideal gas (at t=273.15 k and p=101.325 kpa) 2.2413962×10^2 meters^3/moles
Sackertetrode constant (at t=273.15 k and p=100 kpa) 1.1517084
Sackertetrode constant (at t=273.15 k and p=101.325 kpa) 1.1648714
Second radiation constant
1.438777×10^2 meters kelvin
Wien displacement law constant 2.8977729×10^3 meters kelvin
Wien entropy displacement constant 3.0029152×10^3 meters kelvin
Conventional value of Josephson constant 4.835979×10^14 hertz/volts
Conventional value of von Klitzing constant 25812.807 ohms
2 PARAMETERS OF THE HIGGS FIELD POTENTIAL V(H)=lambda*(R^2v^2)=lambda*H^42*v^2*H^2*lambda*v^4
(H is the higgs field)
the higgs field is an energy field that is thought to exist everywhere in the universe. the field is accompanied by a fundamental particle called the higgs boson, which the field uses to continuously interact with other particles. the process of giving a particle mass is known as the higgs effect.
scientific formulas, beautiful math formulas, universal physical constants
9/6/17; 9/14/17; 10/29/17; 11/11/17; finished 12/11/17
SCIENTIFIC FORMULAS—
MATHEMATICS
PHYSICS
ASTRONOMY
ROCKET SCIENCE
Capital  Lowcase  Greek Name  English 
Alpha  a  
Beta  b  
Gamma  g  
Delta  d  
Epsilon  e  
Zeta  z  
Eta  h  
Theta  th  
Iota  i  
Kappa  k  
Lambda  l  
Mu  m 
Nu n Xi x Omicron o
Lambda l Mu m
Nu  n  
Xi  x  
Omicron  o  
Pi  p  
Rho  r  
Sigma  s  
Tau  t  
Upsilon  u  
Phi  ph  
Chi  ch  
Psi  ps  
Omega  o 
POWERS tera=10^12 giga=10^9 mega=10^6 myria=10^4 kilo=10^3 hecto=10^2
icosa=20 quindeca=15 hendeca=11 dec=10 non=9 octo=8 hepta=7 hexa=6 penta=5 tetra=4
tri=3
bi=2
uni=1
semi=.5
deci=10^1
centi=10^2
milli=10^3
micro=10^6
nano=10^9
pico=10^12
femto=10^15
atto=10^18
PRACTICAL MATHEMATICS FORMULAS PLATONIC SOLIDS—
1. Tetrahedron
Surface area=Sqrt3 x edge length^2 Volume=sqrt2/12 x edge length^3 2. Cube
Surface area=6 x edge length^2 volume=edge length^3
3. Octahedron
Surface area=2 x sqrt3 x edge length^2
volume=sqrt2/3 x edge length^3
4. Dodecahedron
Surface area=3 x sqrt(25+10 x sqrt5) x edge length^2 volume=(15+7 x sqrt5)/4 x edge length^3
5. Isocahedron
Surface area=5 x sqrt3 x edge length^2
volume=(5 x (3+sqrt5))/12 x edge
length^3
CIRCLE
Diameter D = 2 x Radius
Circumference C = 2 x Pi*Radius
area A = Pi x Radius^2
SPHERE
Surface area. A = 4 x Pi x Radius^2
volume V = 4/3 x Pi x Radius^3
Diameter of a sphere. d=cuberoot(3/4 x Pi x volume) x 2 SQUARE, RECTANGLE, PARALLELOGRAM
Area A=side 1 x side 2
VOLUME OF SQUARE, RECTANGLE, PARALLELOGRAM V=side 1 x side 2 x side
PYRAMID
Surface area=base area+.5 x slant length
Volume=base x depth x height/3
CYLINDER
Surface area=2 x pi x radius x (radius+height)
Volume=PI X radius^2 x length
CONE
Surface area=pi x radius x (radius+base to apex length) Volumes=Pi x radius^2 x height/3
TORUS
Surface area=4 x pi^2 x radius torus x radius of solid part volume=2 x pi^2 x radius torus x radius solid part^2 PYTHAGOREAN THEORM
a^2+b^2=c^2
a=length of one right angle’s leg
b=length of other right angle’s leg
c=length of hypotenuse
LAW OF SINES
a/sinA=b/sinB=c/sinC=2 x R=a x b x c/2 x area of triangle R=(a x b x c)/(squareroot((a+b+c) x (a+bc) x (b+ca)) Area of triangle=1/2 x a x b x sinC
LAWS OF COSINE
c^2=a^2+b^22 x a x b x cosC
cosC=(a^2+b^2+c^2)/2 x a x b
AREA OF A TRIANGLE
area=base x height x 1/2
AREA OF AN EQUILATERAL TRIANGLE area=(length of a side )^2 x SQRT(3)/4 AREA OF A TRAPEZOID
A=(top side+bottom side) x height/2
HERON’S FORMULA (area of any triangle) area=SRQT(s x (sside 1) x (sside 2) x (sside 3)) s=1/2 x (a + b + c)
SLOPE
m=(yy1)/(xx1)
(Y1 and x1 are locations on coordinate plane) POINT SLOPE EQUATION OF A LINE
Y y1=slope(xx1)
(Y1 and x1 are locations on coordinate plane) SLOPE INTERCEPT FORM FOR A LINE y=slope(x)+(y intercept)
DISTANCE FORMULA
distance=square root((xx1)^2+(yy1)^2+(zz1)^2)) (z1, y1, and x1 are locations on coordinate system) ALGEBRA FORMULAS
(a+b)^2=a^2+2 x a x b+b^2
(ab)^2=a^22 x a x b+b^2
x^2a^2=(x+a) x (xa)
x^3a^3=(xa) x (x^2+a x x+a^2) x^3+a^3=(x+a) x (x^2a x x+a^2) a/b+c/d=(a x d+b x c)/b x d) a/bc/d=(a x db x c)/b x d
a/b x c/d=a x c/b x d
CONIC SECTIONS
Circle (xg)^2+(yh)^2=radius^2
(g=x coordinate, h=y coordinate) Parabola
y^2+/4ax
(a=x coordinate)
x^2=+/4ay
(a=y coordinate)
ellipse
x^2/a^2+y^2/b^2=1,
(a=x, b=y coordinates, or a=y, b=x coordinates) Hyperbola
x^2/a^2y^2/b^2=1,
(a=x, b=y coordinates, or a=y, b=x coordinates) QUADRATIC EQUATION x=(b+/squareroot(b^24ac))/2a
LAWS OF EXPONENTS
a^x x a^y=a^(x+y)
a^x/a^y=a^(xy)
(a^x)^y=a^(X x Y) (a*b)^x=a^x x b^x a^0=1
a^1=a
LAWS OF LOGARITHMS
log(base a)(M x N)=log(base a)(M)+log(base a(N) log(base a)(M/N)=log(base a)Mlog(base a)(N) logM^r=r X x logM
log(base a)(M)=logM/loga
TRIGONOMETRY
sineo/h
cosine=a/h
tangent=o/a
cosecant=h/o
secant=h/a
cotangent=a/o
(a=adjacent side of right triangle)
(o=opposite side of right triangle)
(h=hypotenuse of right triangle)
Pythagorean identities
sin^2(x)cos^2(x)=1
sec^2(x)tan^2(x)=1
csc^2cos^2(x)=1
Product relations
Sinxtanx x cosx
cosx=cotx x sinx
tanx=sinx x secx
cotx=cosx x cscx
Secxcscx x tanx
cscx=secx x cotx
Trigonometry functions
sinx=xx^3/3!+x^5/5!x^7/7!
cosx=1x^2/2!+x^4/4!x^6/6!
Inverse trigonometry functions
sin1x=x+(1/2 x 3) x x^3+(1 x 3/2 x 4 x 5) x x^5+(1 x 3 x 5/2 x 4 x 6 x 7) x x^7+… cos1x=pi/2(x+(1/2 x 3) x x^3+(1 x 3/2 x 4 x 5) x x^5+(1 x 3 x 5/2 x 4 x 6 x 7) x x^7+… tan1x=xx^3/3+x^5/5x^7/7+…
cot1x=pi/2x+x^3/3x^5/5+x^7/7…
Hyperbolic functions
sinhx=x+x^3/3!+x^5/5!+x^7/7!+…
coshx=1+x^2/2!+x^4/4!+x^6/6!+…
Inverse hyperbolic functions
sinh1x=x(1/2 x 3) x x^3+(1 x 3/2 x 4 x 5) x x^5(1 x 3 x 5/2 x 4 x 6 x 7) x x^7+… tanh1x=x+x^3/3+x^5/5+x^7/7+…
Nth TERM OF AN ARITHMETIC SEQUENCE Nth term=a+(number of terms1)*d
(a=1st term, d=common difference)
SUM OF n TERMS OF AN ARITHMETIC SERIES Sumn/2 x (a+nth term)
(a=1st term, d=common difference)
Nth TERMS OF A GEOMETRIC SEQUENCE
a(n)=a x r^(n1), (r cannot equal 0.)
(a=1st term, r=common ratio)
SUM OF THE n TERMS OF A GEOMETRIC SEQUENCE s=a x ((1r^n)/(1r))
(r cannot equal 0, 1)
(n=number of terms, r=common ratio)
SUM OF AN INFINITE SERIES
s=n/(1r)
(If absolute value of r<1)
(n=number star with)
(r=how much keep multiplying x with forever) (s=sum of infinite series)
COMBINA TIONS
C(n,r)=n!/r!(nr)!
PERMUT A TIONS
P(n,r)=n!(nr)!
BINOMIAL FORMULA
(a x xb)^n
CALCULUS (DIFFERENTIATION)
d/dx (x^n)=n x x^(n1)
d/dx sinx= cost
d/dx cosx= sinx
d/dx tanx=sec^2(x)
d/dx cotx=csc^2(x)
d/dx sexsecs x tanx
d/dx cscx= cscx x cotx
d/dx e^x=e^x
d/dx lnx=1/x
d/dx (u+v)=du/dx+dv/dx
d/dx(c x u)=c x du/dx
dy/dx=dy/dx x du/dx
(chain rule)
d/dx (u x v)=(v x (du/dx)(u x (dv/dx)
(product rule)
d/dx(u/v)=(v x du/dxu x dv/dx/)v^2
(quotient rule)
du=du/dx(dx)
CALCULUS (INTEGRATION)
The definite integral of t from a to b for definite integral f(t)=F(b)F(a)
Indefinite integral of x^r dx=x^(r+1)/(r+1)+c, (r cannot equal 1)
Indefinite integral of 1/x dx=ln(absolute value (x))+c
Indefinite integral of sinx dx=cosx+c
Indefinite integral of cosx dx=sinx+c
Indefinite integral of e^x dx=e^x+c
Indefinite integral of (f(x)+g(x))dx=indefinite integral f(x)+indefinite integral g(x) Indefinite integral of c x f(x) dx=c x (indefinite integral f(x))
indefinite integral of (u)dv=u x vindefinite integral (v)du
(integration by parts)
CENTER OF MASS
Center of mass (x)=((mass1) x (center of mass1)+(mass2) x (center of mass x 2))/ (mass1+mass2)
(A point representing the mean position of the matter in a body of system.) VECTOR ANALYSIS
Norm (magnitude of a vector)=sqrt(x^2+y^2+z^2)
Dot product u (dot) v=(u1) x (v1)+(u2) x (v2)+(u3) x (v3)=u v cos(theta)
(theta is the angle between u and v, 0<=theta<=Pi)
Cross productÂ u x v=((u2) x (v3)(u3) x (v2))i((u1) x (v3)(u3) x (v1))j+((u1) x (v2)
(u2) x (v1))k
u x v=u x v sin(theta)
(Theta is angle between u and v, 0<=theta<=Pi)
2 vectors orthogonal if their dot product v and u=0 or transpose vector v and vector u=0.
Exponential growth and decay—
y=A exp^k*t
A=starting number of for example bacteria, t=length of growth time, k=constant, y=number of bacteria after t time
OUTLINE OF PHYSICS FORMULAS
*** Straight line motion ***
Velocity (meters/second)=distance (meters)/time (seconds) v=d/t (constant velocity)
v=2 x d/t (accelerating)
Distance (meters)=velocity (meters/second) x time (seconds) d=v x t
time (seconds)=distance (meters)/velocity (meters/second) t=d/v
t=sqrt(2 x distance/acceleration)
Acceleration (meters/second^2)=
((meters/second (end)meters/second (start)/)time (seconds))/2 a=(d2/td1/t)/2
Acceleration (meters/second^2)=2 x distance (meters)/time (second)^2 a=2 x d/t^2
Final velocity (meters/second)=initial velocity (meters/second)+ acceleration (meters/second^2 x time (seconds)
v(f)=v1+a x t
velocity^2=initial velocity+2 x acceleration x distance
v^2=v1+2 x a x d
Average velocity (meters/second)=initial velocity+final velocity/time v(average)=(v1+v2)/t
Average velocity=initial velocity+1/2 x acceleration x time v(average)=v1+1/2 x a x t
Distance (meters)=initial velocity x time+1/2 x acceleration x time^2 d=v1+1/2 x t x a x t^2
Distance=acceleration x time^2/2
d=a x t^2/2
Newton’s 2nd law of motion
Force (newtons)=mass (kilograms) x acceleration (meters/second^2) Fm x a
Falling bodies
velocity=gravity (9.81 meters/second^2 for the earth) x time
v=g x t
How far fallen in meters=1/2 x gravity x time^2 d=1/2 x g x t^2
Time fallen=sqrt(2 x height/gravity)
t=sqrt(2 x h/g)
velocity=sqrt(2 x gravity x height) v=sqrt(2 x g x h)
*** Circular motion *** Uniform circular motion
Moment of inertia=mass x distance from axis^2
m(inertial)=m x d^2
Angular velocity=angular displacement/change in timeÂ (radians/second) v(angular)=d/t
Angular momentum=moment of inertia x angular velocity m(angular)=m(inertial) x v(angular)
Centripedal acceleration
Centripedal acceleration=velocity^2/radius of path (radians/second^2) a(centipedal)=v^2/r
Torque (newtonsmeter)
Centripetal force
Centripetal force=mass x velocity^2/radius of path
f(centripedal)=m x v^2/r
Gravitation
gravitation (newtons)=G x (mass(1) x mass(2))/radius^2
(G=6.67 x 10^11)
f=G x (m1 x m2)/r^2
Fundamental forces in nature— strong
W eak
Electromagnetic
Gravity
*** Energy ***
work
work (joules)=force (newtons) x distance (meters)
w=f x d
work=work output/work input x 100%
w=w(o)/w(i) x 100
Power
Power (watts)=work (joules)/time (seconds)
p=w/t
horsepower=746 watts
weight=mass x gravity
w=m x g
momentum=mass (kilograms) x velocity (meters/second) momentum=m x v
Energy
kinetic energy
KE (joules)=1/2 x mass (kilograms)x velocity (meters/second)^2 ke=1/2 x m x v^2
Potential energy
PE (joules)=mass x gravity (9.81 meters/second^2) x height (meters)
pe=m x g x h
Rest energy
Rest energy (joules)=mass x 300,000,000^2
Conservation of energy
MomentumÂ (kilogramsmeters/second)
Linear momentum
L. momentum=mass (kilograms)x velocity (meters/second) m(momentum)=m x v
Conservation laws
Conservation of massenergy
Conservation of linear momentum
Angular momentum
Conservation of angular momentum
Conservation of electric charge
Conservation of color charge
Conservation of weal isospin
Conservation of probability
Conservation of rest mass
Conservation of baryon number
Conservation of lepton number
Conservation of flavor
Conservation of parity
Invariance of charge conjugation
Invariance under time reversal
CP sysmetry
Inversion or reversal of space, time, and charge
(there is a onetoone correspondence between each of the conservation laws and a differentiable symmetry in nature.)
Impulse
impulse=force (newtons) x time (seconds)
i=f x t
*** Relativity ***
special relativity
Lorentz transformation
*** Fluids ***
Density
Specific gravity
kilograms/meter^3
Pressure
pressure=force/area
pressure=newtons/meters^3
p=f/d^3
Pressure in a fluid
pressure=density (kilograms/meters^3) x depth (meters) x weight (kilograms) p=d(density) x d(depth) x w
p=kg/d^3 x d x m
Archimede’s principlethe upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces.
Bernoulli’s principlesan increase in the speed of a fluid occurs
simultaneously with a decrease in pressure or a decrease in the fluid’s potential energy.
v^2/2+gz+p/Ï=constant
v is the fluid flow speed at a point on a streamline,
g is the gravitational acceleration
z is the elevation of the point above a reference plane,
with the positive zdirection pointing upward so in the direction
opposite to the gravitational acceleration,
p is the pressure at the chosen point, and
Ï is the density of the fluid at all points in the fluid.
*** Heat ***
internal heat
Temperature
Heat
1 kilocalorie=3.97 british thermal units (BTU)
1 BTU=.252 kilocalories
Specific heat capacity
Heat transferred=mass (kilograms) x specific heat capacity x temperature change (kelvin)
h=m x h x t
change of state
Heat of fusion
Heat of vaporization
pressure and boiling point
*** Kinetic theory of matter ***
Ideal gases
Boyle’s law
pressure(1) x volume(1)=pressure(2) x volume(2)
(temperature constant)
P1 x v1=p2 x v2
Absolute temperature scale
Temperature kelvin=temperature (celsius)+273.15
Charlie’s law
volume(1)/temperature(1)=volume(2)/temperature(2)
(pressure constant)
v1/t1=v2/t2
Ideal gas law
pressure(1) x volume(1)/temperature(1)=pressure(2) x volume(2)/temperature(2) P1 x v1/t1=p2 x v2/t2
Kinetic energy of gases
Molecular energy
KE (joules)=3/2 x K x temperature (kelvin)
(K=boltzmann’s constant=1.38 x 10^23 joules/kelvin
ke=3/2 x k x t
solids and liquids
Atoms and molecules
*** Thermodynamics ***
3 laws of thermodynamics
The four laws of thermodynamics are:
Zeroth law of thermodynamics: If two systems are in thermal equilibrium with a third system, they are in thermal equilibrium with each other.
This law helps define the notion of temperature.
1st law of thermodynamics: When energy passes, as work, as heat, or with matter, into or out from a system, the system’s inertial energy changes in accord with the law of conservation of energy. Equivalently, Perpetual motion machines of the 1st kind (machines that produce work without the input of energy) are impossible.
2nd law of thermodynamics: In a natural thermodynamic process, the sum of the entropies of the interacting thermodynamic systems increases. Equivalently, perpetual motion machines of the 2nd kind (machines that spontaneously convert thermal energy into mechanical work) are impossible.
3rd law of thermodynamics: The entropy of a system approaches a constant value as the temperature approaches absolute zero. With the exception of noncrystalline solids (glasses) the entropy of a system at absolute zero is typically close to zero, and is equal to the logarithm of the product of the quantum ground states.
entropy
The entropy of a system approaches a constant value as the temperature
absolute zero.
Mechanical equivalent of heat
Mech. Equiv. heat=4,185 x joules/kilocalories Mech. Equiv. heat=778 x footpounds/BTU
Heat engines
Engine efficiency
efficiency=1heat temperature absorbed/heat temperature given off eff=1h(temp. Absorbed)/h(temp. Given off)
Conduction
Convection
Radiation
*** Electricity ***
Electric charge
Charge of proton=1.6 x 10^19 coulombs
Charge of electron= 1.6 x 10^19 coulombs
Electric charge=current (amperes) x time taken (seconds)
Coulomb’s law
Electric force (newtons)=K x charge1 (coulombs) x charge2 (coulombs)/ distance (meters)^2
(K=9 x 10^9 newtonmeter^2/coulomb^2)
F=KÂ x c1 x c2/d^2
Atomic structure
Mass of proton=1.673 x 10^27 kilograms
Mass of neutron=1.675 x 10^27 kilograms Mass of electron=9.1 x 1031 kilograms Ions
Electric field
Electric field (newton/coulomb)=force (newtons)/charge (coulombs) E=f/c
force=charge x electric field
Electric lines of force
Potential difference
volts=work/charge
(1 volt= 1 joule/coulomb)
volt=electric field (newtons/coulomb)x distance (meters)
v=E x d
Electric field (newtons/coulombs)=volts/distance
E=v/d
Potential Difference=current (amperes)x resistance (ohms)=
energy transferred/charge (coulombs)
pd=I x r=e/c
Electric current
Electrical energy=voltage (volts)x current (amperes)x time taken (seconds) e=v x I x t
Electric current
Electric current (amperes)=charge (coulombs)/time interval (seconds)
(1 ampere=1 coulomb/second)
I=c/t
Electrolysis
Ohm’s law
Electric current (amperes)=volts/resistance (ohms)
(resistance (1 ohm))=1 volt/ampere)
I=v/r
resistance (ohms)=voltage (volts)/current (amperes)
r=v/I
voltage (volts)=current (amperes)x resistance (ohms)
v=I x r
Resisters in series
resistance=resistance(1)+resistance(2)+resistance(3)
R=r1+r2+r3
Resisters in parallel 1/resistance=1/resistance(1)+r1/resistance(2)+1/resistance(3) 1/R=1/r1+1/r2+1/r3
Kirchoff’’s law
current law=Summation (current)=0
Voltage law=summation (voltage)=0
Capacitance
1 farad=1 coulomb has 1 volt between plates
capacitance (farad)=charge (coulombs)/voltage (volts)
Work stored=work (charging)=1/2 x capacitance x voltage^2
W=w=1/2 x C x v
electric power
power (watts)=work done per unit time (joules)=voltage (volts)x charge
(coulombs)/time (seconds)
p=w=v x c/t
Power (watts)=current (amperes) x voltage (volts)=current (amperes)^2
x resistance (ohms)=voltage (volts)^2/resistance (ohms)
p=i x pd=i^2 x r=pd^2/r
Alternating current
power (watts)=1/2 x peak voltage x peak current x
cos (phase angle between current and voltage sine waves)
p=1/2 x v x I x cos(theta)
*** Magnetism ***
Magnetic field
1 tesla=1 newton/amperemeter
(tesla=weber/meter^2)
(1 gauss=10^4 teslas)
B (magnetic field)=K x I (straight line current)/distance (meters)
(K=2 x 10^7 newton/amperes^2
B=K x I/d
Magnetic field on a moving charge
Magnetic field on a current
B=Pi(3.14) x K x I/r
F=I x L x B
Magnetic field of solenoid
B=2 x Pi x K x N (number of turns)/L (length of solenoid) x I (current amperes) Forces between 2 currents
(K=2 x 10^7 newton/amperes^2
F/L=K x I(1) x I(2)/d
Lorentz force
F=charge x electric field+charge x velocity (cross product) magnetic field F=qE+qv x B
*** electromagnetism ***
Maxwell’s equations
Maxwell’s equations are a set of partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, and electric circuits.
*** Electromagnetic induction *** Generator
Motors
Alternating current
I=I (max)/sqrt(2)=.707 I (max)
V=I (max)sqrt(2)=.707 V (max)
Transformer
Primary voltage/secondary voltage=primary turns/secondary turns Primary current/secondary current=secondary turns/primary turns DC circuits
*** Waves ***
Frequency
1 hertz=1 cycle/second
W avelength
wave velocity (meters/second)=frequency (hertz) x wavelength (meters)
v=f x w
Acoustics
Optics
Electromagnetic waves
Velocity of light=c=3 x 10^8 meters/second=186,282 miles/second
Doppler effect
Frequency found by observer with respect to sound=frequency produced by source x (velocity sound+velocity observer)/(velocity soundvelocity source) f(o)=f(s) x (v+v(o))/(vv(s))
Frequency found by observer with respect to light=frequency produced by source x sqrt((1+relative velocity/c)/(1relative velocity/c))
f(o)=f(s) x sqrt((1+v/c)/(1v/c))
reflection and refraction of light
Index refraction=n=c/velocity in medium (meters/second)
r=c/v
Interference, diffraction, polarization
Particles and waves
*** Quantum physics ***
Uncertainty principlethe velocity of an object and its position
cannot both be measured exactly, at the same time, even in
theory.
The Schrodinger equation is used to find the allowed energy levels of quantum mechanical systems (such as atoms, or transistors). The associated wave function gives the probability of finding the particle at a certain position. … The solution to this equation is a wave that describes the quantum aspects of
a system.
The Pauli exclusion principle—
Quantum theory of light
Quantum energy=E=h x f
Planck’s constant=h=6.63 x 10^34 joulessecond
Xrays
Electron volt=planck’s constant x frequency
eV=h x f
Electron KE=xray photon energy
f=eV/h
momentum=kinetic energy (joules)/speed of light^2 (meters/second) p=ke/c^2
Kinetic Energy=planck’s constant x frequency=
planck’s constant x speed light/wavelength
ke (joules)=6.63 x 10^34 joulessecond x frequency hertz(meter/second)=
The Pauli exclusion principle is the quantum
mechanical
principle which states that two or more identical fermions (particles with
halfinteger spin)
cannot occupy the same quantum state within a quantum system
simultaneously.
6.63 x 1^34 x 300,000,000 meters/f (meters) joules=h x f=h x c/lambda
Electron volt
1 eV=1.6 x 10^19 joules
1 KeV=10^3 eV
1 MeV=10^6 eV
1 GeV=10^9 eV
Kinetic energy=1/2 x mass x velocity^2=
planck’s constant x frequencyelecton volts
ke (joules)=1/2 x m x v^2=6.63 x 10^34 joulessecond x feV Matter waves
De Broglie wavelength=lambda=h/m x v (momentum=m x v)
wavelength=planck’s constant/(mass x meters/second) lambda=h/m x v
Solid state physics
***Nuclear and atomic physics ***
Nucleus
Mass (proton)=1.673 x 10^27 kilograms=1.007277 u
Mass (neutron)=1.675 x 10^27 kilograms=1.008665 u Nuclear structure
Binding energy
Mass defect= change m=((number protons x mass hydrogen)+ (number neutrons x mass neutrons))m
(mass hydrogen=1.007825 u)
Fundamental forces
Gravity
Electromagnetic
Weak interaction
Strong force
Fission and fusion
Radioactivity
Alpha particle=helium nuclei
Beta particle=electron
Gamma rays=high energy photons with frequencies greater than xrays neutron>proton+electron
proton>neutron+positron Radioactive decay and halflife Elementary particles and antimatter
ASTRONOMY FORMULAS
1. How to find the DISTANCE in parsecs to a star distance=10^((apparent magnitudeabsolute magnitude+5)/5) 2. APPARENT magnitude
apm=log d x 55+abm
apparent=log(distance) x 5 – 5 + absolute magnitude
3. How do you calculate the absolute magnitude of a star abm=((log L/log 2.516)4.83)
Absolute magnitude=((log(number of sun’s luminosity of star)/ log2.516)4.83
abm=(5 x log d5apm)
Absolute magnitude= (5 x log(distance parsecs)5apparent magnitude)
4. To find brightness of a star/number of suns
L=10^((abm4.83) x (log 2.516))
LUMINOSITY of star=10^((absolute magnitude of star4.83)*(log2.516))
luminosity increase=2.512^([magnitude increase]+4.83)
luminosity=mass^3.5Â (for main sequence stars)
Luminosity (watts)=4 x pi x radius(meters)^2 x temperature (kelvin)^4 x
5.67 x 10^8 watts maters^2 kelvin^4
5. Mass binary system
Suppose in an example, we calculate the masses of 2 stars in a binary star system: if the period of star a is 27 years and its distance from the common center of mass is 19 AUs, the
Distance^3/period^2=19^3/27^2=6859/729=9.4 solar masses for the total mass of the 2 stars.
The velocity of star a is 30,000 km./second and star b is 10,000 km/second, so 30,000/10,000=3.
The mass of star b is 9.4/(1+3)=2.25 solar masses.
The mass of star a is 9.42.25=7.15 solar masses.
So star a is 7.15 solar masses, and star b is 2.25 solar masses, and both added up equals 9.4 solar masses, the combined mass of the 2 stars.
6. Radius of a star
radius=(temperature sun (kelvin)/temperature star (kelvin))^2 x (2.512^(absolute magnitude sunabsolute magnitude star)^1.2)
7. size of star/orbit/object
size object miles=arcseconds size object x distance parsecs x 864,000
8. LT=10^10 x m(star)/m(sun)^2.5
lifetime=(10^10) x (mass of star/mass of sun)^2.5
9. To find ARC SECOND measurement of object size from parsec DISTANCE and visa versa and SIZE of an object–
SIZE OF STAR IN ARCSECONDS–arcseconds=1/d (parsecs) x number of suns size ARCSECONDS– parallax=1/distance parsecs
DISTANCE (parsecs)– d=1/arcseconds
10. Galaxy distance in millions of light years
d=13,680 x rsh+8.338
distance (millions of light years)=13,680 x red shift+8.336
11. velocity of galaxy in kilometers/second
v=300,000 x rsh
velocity (kilometers per second)=300,000 x redshift
11.5. approximate number of stars in a galaxy=luminosity in number of suns galaxy/.02954
12. redshift
Rsh=mly8.338/13,680
redshift=(light years (millions)8.336)/13,680
13. Volume of a galaxy=4/3 x Pi x a x b^2
a=major axis, b=minor axis, (for elliptical galaxies)
14. Number of stars=volume/distance between stars^3
15. Average Distance between stars in light years=cube root(volume/number of stars) 16. Number of stars span across longest axis of galaxy=
(3/4 x volume)/(Pi x b^2 x n^3)
b=minor axis length light years, n=distance between stars light years
17. Escape velocity from a galaxy meters/second=
Mass galaxy kilograms x 1.989 x 10^30/(number of stars x
4,827,572.324)^2
18. Surface gravity
gravity(meters/second^2)=mass of star number of suns x 1.99 x
10^30 x 6.67 x 10^11/(size of star number of suns x 864000000 x 1.62/2)^2 19. Titusbode law
Distance (astronomical units)=3*2^n+4/10
(n=infinity, 0, 1, 2, 3, â€¦)
Mercury=infinity
Venus=0
earth=1
mars=2
Asteroid belt=3
jupiter=4
Etc
20. kepler’s 3 laws of planetary motion
1. Planets travel in elliptical orbits.
2. Equal areas are covered in in equal times in the elliptical orbit.
3. The distance in astronomical units to the 3rd power equals the time to travel one complete orbit in years to the 2nd power.
(time years)^2=(radius orbit astronomical units)^3
D=P^(2/3)
P=D^(3/2)
21. Velocity to achieve orbit=sqrt(G x M/distance from center of the earth) 22. Escape velocity=sqrt(G x M/r)
23. Four types of eccentric orbits
circle eccentricity=0
ellipse eccentricity= 01
parabola eccentricity=1
hyperbola eccentricity>1
24. Eccentricity=(greatest orbital distanceclosest orbital distance)/(closest orbital distance+greatest orbital distance) e=(d(greatest)d(closest))/(d(closest)+d(greatest))
25. Calculations: orbits, periods of orbits, perihelions, aphelions and eccentricities (for example a comet)
CIRCLE
Circular formula eccentricity=0
(xh)^2+(yk)^2=r^2. (#1)
(h=x coordinate and y=y coordinate ;r=radius of orbit)
period=2 x pi x sqrt(radius^3/(6.67 x 10^11 x mass of body the body is orbiting)) Velocity in orbit=sqrt(6.67 x 10^11 x
mass of body the body is orbiting/radius of orbit)
Centripetal acceleration=velocity^2/radius of orbit
ELLIPSE
Use ellipse formula x^2/a^2+y^2/b^2=1
Then calculate from 2 coordinates in AUs with formula
x^2 x b^2 + y^2 x a^2=a^2 x b^2
find a and b (the closest and furthest approaches)
Period years of orbit=distance (AU)^3/2
time=2 x pi x sqrt(a^3/G x M)
distance=period^2/3
velocity=sqrt(G x M x (2/r1/a))
eccentricity=(0<e<1)
eccentricity=sqrt(1b^2/a^2)
a (semimajor axis)=(perihelion + aphelion)/2
Semi minor axis (b)=sqrt((eccentricity^21) x a^2)
Simple way to calculate and orbit
1=X^2+Y^2. >Â 1=x^2+semimajor axis^2+y^2/semiminor axis^2
time in seconds to get to orbital position from 0 degrees going counterclockwise t=radians at current position of orbiting body/360 x sort(semi
major axis^3/6.67 x 10^11 x 1.989 x 10^30)
to find the angle at which the orbiting body is at from 0 degrees going counterclockwise x^2=p^2+1
q=sqrt(p)
r=sqrt(x)
s=q/r
arcsin(s)=angle of the orbiting body with respect to the focal body
to find distance to orbiting body from foci
x^2=p^2+p^2
cosy=x^2/P^2 x x^2
m=arccosy
cosm=1/n
q=1/cosm
q=distance to orbiting body from foci
To find formula for the orbit, use ellipse formula
x^2/a^2+y^2/b^2=1
PARABOLA
eccentricity=1
y=a x X^2+b x X +c
Calculate from 2 coordinates of the body in its orbit (a and b coordinates in
both instances)
Solve for x, then y, and will have the formula for the parabolic orbit.
Then will have the equation of the orbit like the quadratic equation above with
numerical figures for a and b.
Velocity of body in parabolic orbit
v=sqrt(2 x 6.67 x 10^11 x mass of body being orbited/radius of body)
Period of orbit does not have an orbit so undefined.
eccentricity=sqrt(1+b^2/a^2)
time in seconds to get to orbital position from 0 degrees going counterclockwise– t=radians at current position of orbiting body/360 x sqrt(semi
major axis^3/6.67 x 10^11 x 1.989 x 10^30)
to find the angle at which the orbiting body is at from 0 degrees going counterclockwise– g^2+(distance between foci/2 (‘p))^2=d^2
(d^2p^2g^2)/(2(p^2)(g^2))=cosx
cos1x=angle x
p^21^2=g^2
(1^2p^2g^2)/(2(p^2)(g^2))=cosL
cos1L=angle L
90xL=m
mx=n
n is the angle the orbiting body is at from 0 degrees going counterclockwise HYPERBOLA
eccentricity>1
x/ay/b=1. (#1)
xbya=ab.Â (#2)
Calculate from 2 coordinates of the body in its orbit (a and b coordinates in both instances) using (equation #2).
Solve for x, then y, and will have the formula (for #1 above) for the hyperbolic orbit.
Then will have the equation of the orbit like equation #1 with numerical figures for a and b.
Velocity of body at infinity in a hyperbolic orbit
velocity at an infinite distances away=sqrt(velocity^2escapevelocity^2)
Period of orbit does not have na orbit so undefined.
26. EXAMPLES OF CALCULATING ORBITS
STEPS TO CALCULATE AN ELLIPTICAL ORBIT
Suppose we measure 2 coordinates of a comet, one at (4AU,1AU) and the other at (0AU,3AU).
1) We plug in each of the coordinates, the 1st equals the x and the 2nd equals the y, each of the 2 coordinates into b^2 x x^2+a^2 x y^2=a^2 x b^2.
Then we subtract the 2 equations from each other. Next, we solve for both a and b. The resulting equation is x^2/2.376^2+y^2/1.68^2=1
and this is the equation of the orbit for the 2 given coordinates. The ellipse equation is x^2/2.376^2+y^2/1.68^2=1.
Solving for x and y gives
x=sqrt((15.65 x y^2)/2.8) and y=sqrt((12.8 x x^2/5.65).
2) perehelion=1.68AU, aphelion=2.376AU. (figures for constants a and b) 3) semimajor axis=A=(perihelion+aphelion)/2=(1.68+2.376)/2=1.9958AU 4) Semi minor axis=smaller figure of a and b=1.68AU.
5) focii=amaller figure of a and b=1.68AU.
6) distance center of ellipse to the foci=Aperihelion=.3158AU
7) period=aphelion^3/2=2.82 years (1,029.83 days)
8) eccentricity=1perihelion/A=.158
9) velocity at any instant=1.99 x 10^30 x 6.67 x 10^11 x (1/radius=1/A)=
At perihelion=20.07 miles/second, at aphelion=10.74 miles/second
10. Suppose we want to find the time from perihelion to a distance of 2 AU and its velocity there. We use the formulas
Semimajor axis^2+semimajor axis^2=x^2
cosx=x^2/2 x semimajor axis^2 x x^2; angle=arccosx
time=angle/360 x sqrt(semimajor axis^3/6.67 x 10^11 x 1.989 x 10^30)
The answer for time atÂ 2 AU=82.79/360 x sqrt(2.7186 x 10^34/1.32733 x 10^20)=
.22997 x 14311435.6=38.09 days at a velocity there at 12.995 miles/second.
HALLEY’S COMET
period=75.986 years.
focii=.6AU.
perihelion=.6AU.
aphelion=35.28AU.
Semimajor axis=17.94Au
eccentricity=.9855.
Velocity at perihelion=33.23 miles/second, aphelion=3.124 miles/second
STEPS TO CALCULATE A CIRCULAR ORBIT
Suppose 2 coordinates were recorded of a celestial body, one (3,2,646), and the other (1,3.873). It the celestial body has a circular orbit, the squares of each set of coordinates added together will equal the same defendant number. In this example,
3^2+2.646^2=15, and 1^2+3.873^2=16, so this is a circular orbit where the equation of the orbit is 4^2=x^2+y^2, where the 4 in the 4^2 is the radius of the circle, and the x and y are the
coordinates of the circular orbit. The eccentricity of of a circular orbit is equal to zero. STEPS TO CALCULATE A PARABOLIC ORBIT
Formulas
velocity=sqrt(2 x G x Mass central body/radius of orbiting body from central body) trajectory=(4.5 x G x M x Time seconds^2)^1/3
To find out whether 2 coordinates measurements of an orbiting body if a parabolic orbit, say coordinates (3,27) and (2,12), we need to set up a parabolic equation
y=b x x^2, then put into it separately the 2 coordinates. 27=b x 3^2, solve for b to arrive at equals to 3.
12=b x 2^2, b also equals 3.
Since b in both equations are equal to each other, the orbiting object is in a parabolic orbit. The equation for the orbit is y=3 x x^2. The period of orbit is infinitely long since the orbiting object never returns. The vertex of the orbit is (0,0). The foci is equal to 3/4. We arrive at this by always using 4 x p, and setting it equal to 3, the number equal to b. When 4 x p=3 is solved, p=3/4. So the focus is at (0,3/4).the velocity of the orbiting body at its closest approach to the central body is equal to 30.05 miles/second.
STEPS TO CALCULATE A HYPERBOLIC ORBIT
Suppose 2 coordinates of an orbiting celestial body are recored as being at (28.28, 10)AU and (34.64, 14.14)AU positions. We try using the hyperbolic equation
1=x^2/a^2y^2/b^2, solve for a and b, and the result equals 1, so this is a hyperbolic orbit. a=20 and b=10. The equation for the orbit is
1=x^2/20^2y^2/10^2.
Solving for x and y yields
x=sqrt(4004 x y^2), and y=sqrt(x^2/4100(.
The orbit’s eccentricity is equal to sqrt(a^2+b^2)/a=sqrt(400+100)/400=1.118, which is greater than 1, so this is a hyperbolic orbit.
For focii=sqrt(a^2+b^2)=22.33AU from the sun’s position, which is equal to 22.33 a=22.3320=20AU, which makes the focci=(20,0).
The period of this orbiting body is undefined since it will never return. To find the semimajor axis, we use the velocity formula
v=sqrt(6.67 x 10^11 x 1.99 x 10^30 x (2/r1/semimajor axis)).
r=2.33AU in meters and v=618,000 meters/second. Solving for the semimajor axis yields 1208.12.
Let us determine the velocity of the orbiting object at say 5AU from the sun.
v=sqrt(6.67 x 10^11 x 1,99 x 10^30 x (2/5AU in meters1/1208.12))=18.77 kilometers/second, or 11.64 miles/second.
If we wanted to calculate the velocity of the object when it gets as far away as the nearest star, 4.3 light years away,
it would be traveling 25.76 meter/second there.
27. Formulas to find masses, radius, and luminosities of WHITE DWARFS (mass<=.75 suns)
(radius<=.00436 suns)
(luminosity<=.00365 suns)
radius=mass^18.68 mass=radius^.052966
luminosity=mass^19.5198 mass=luminosity^.05123
luminosity=radius^1.04494 radius=luminosity^.95699
28. Formulas to find masses, radius, and luminosities of MAIN SEQUENCE stars luminosity=mass^3.5
mass=luminosity^(.2857)
radius=(temperature kelvin sun/temperature kelvin star)^2 x
(2.512^(absolute magnitude sunabsolute magnitude star)
note main sequence star’s masses can be found by knowing the star’s luminosity and its temperature.
Type star Mass radius. Temperature luminosity lifespan
O. +16. +6.6 +33,000 kelvin 55,000 to >200,000 >9.77 m/yrs
B 2.116. 1.86.6 10,00033,000 kelvin. 4224,000. 9.77 m/yrs1.57
b/yrs
A 1.42.1. 1.41.8. 7,50010,000 kelvin. 5.124. 1.57 b/yrs4.3 b/yrs F. 1.041.4. 1.151.4. 6,0007,500 kelvin. 2.45.1. 4.3 b/yrs9.07 b/yrs
G. .81.04. .961.15. 5,2006,000 kelvin .381.2. 9.07 b/yrs17.47 b/yrs K. .45.8. .7.96. 3,7005,200 kelvin. .08.38. 17.47 b/yrs73.62 b/yrs M. <=.45. <=.7. 2,0003,700 kelvin <.002.08. >73.62 b/yrs
29. Formulas to find SUBGIANT masses, radii, and luminosities MASS TO LUMINOSITY
O type subgiant stars luminosity=100,0001 million luminosity^.295=mass
luminosity^.2=radius
mass^.675=radius
B type subgiant stars luminosity=35040,000 luminosity^.245=mass luminosity^.205=radius
mass^.84=radius
A type subgiant stars luminosity=20200 luminosity^.203=mass luminosity^.256=radius
mass^1.26=radius
F type subgiant stars luminosity=8300 luminosity^.19=mass
luminosity^.37=radius
mass^1.94=radius
G type subgiant star luminosity=1.16 luminosity^.15=mass luminosity^.5=radius mass^3.57=radius
K type subgiant stars luminosity=345 luminosity^.1mass luminosity^.625=radius mass^4.15=radius
30. Masses, radius, and luminosities for GIANT stars O type giant stars luminosity=30,000 to >2 million luminosity^.27=mass
luminosity^.206=radius
mass^.756=radius
B type giant stars luminosity=33035,000 luminosity^.24=mass luminosity^.223=radius mass^.936=radius
A type giant star luminosity=108,000 luminosity^.227=mass luminosity^.244=radius mass^1.08=radius
F type giant stars luminosity=10100 luminosity^.195=mass luminosity^.363=radius mass^1.86=radius
G type giant stars luminosity=1575 luminosity^.19=mass luminosity^.57=radius mass^2.89=radius
K type giant stars luminosity=30275 luminosity^.11=mass luminosity^.625=radius mass^5.7=radius
M type giant stars luminosity=8003,700 luminosity^.098=mass luminosity^.65=radius
mass^6.7=radius
31. Masses, radius, and luminosities for BRIGHT GIANT stars O type bright giant stars luminosity=65,000320,000 luminosity^.27=mass
luminosity^.22=radius
mass^.795=radius
B type bright giant stars 25,00040,000 luminosity^.23=mass
luminosity^.3=radius
mass^1.23=radius
A type bright giant stars luminosity=3,00015,000 luminosity^.24=mass
luminosity^.37=radius
mass^1.665=radius
F type bright giant stars luminosity=5002,500 luminosity^.23=mass
luminosity^.44=radius
mass^2.1=radius
G type bright giant stars luminosity=1501,000 luminosity^.22=mass
luminosity^.4=radius
mass^2.3=radius
K type bright giant stars luminosity=2003,500 luminosity^.21=mass
luminosity^.58=radius
mass^6=radius
M type bright giant stars luminosity=60025,000 luminosity^.19=mass
luminosity^.65=radius
mass^8.1=radius
32. Finding masses, radius, and luminosities for SUPERGIANT stars Supergiant stars luminosity=120,0002 million luminosity^.213=mass
luminosity^.56=radius
mass^2.63=radius
33. Close formula for mass to radius and radius to mass of STARS MASSES 40 to GREATER THAN 200 SOLAR MASSES
(crudely estimated formulas) luminosity^.325=mass
luminosity^.519=radius
mass^1.6=radius
34. MASSES OF STARS AND THEIR FATES Masses .0710 suns white dwarf
Masses .58 suns planetary nebulas
Masses >8 suns supernovas
Masses 1029 suns neutron stars
masses>29 suns black holes
35.
Vega Cl Effective relative
asstemperaturechromaticity ty (D65)
[ mass
sequence radius
main seque nce stars ~0.00 003%
0.13%
0.6%
3%
7.6%
12.1%
76.45 %
Chromatici sequence
on of Hydr all
Main Main
Main
sequence luminosity ogen
Fracti
(solar (solar radii)(bolometric lines masses) )
O 30,000 K blue
B 10,00030,00blue white
blue 16
6.6 >30,000
W eak
deep blue 2.116
0K white um
A 7,50010,000white blue white 1.42.1 1.41.8 525 Stron Kg
. F 6,0007,500 yellow white K
. G 5,2006,000 yellow K
K 3,7005,200 light orange K
M 2,4003,700 orange red K
white
yellowish
white
pale yellow 0.450.8 orange
light orange 0.080.45 red
Medi um
Weak
Very weak very weak
1.041.4
1.151.4 0.961.15 0.70.96 0.7 (<)
1.55 0.61.5 0.08“0.6 <0.08
0.81.04
The Hertzsprung Russell diagram relates stellar classification with absolute magnitude, luminosity, and surface temperature.
36. DISTRIBUTION OF TYPES OF STARS IN GALAXY
Giants and supergiants .946%
O star .0000256%
B stars .1105%
A stars .51085%
F stars 2.5545%
G stars 6.446%
K stars 10.313%
M stars 65.0295%
White dwarfs 8.515%
Brown dwarfs 110% (4.98% average estimate)
Neutron stars .8515%
Black holes .08515
DRAKE EQUATION ESTIMATE OF PERCENTAGE OF ADVANCED CIVILIZATIONS OF SYSTEMS STARS
Applies to 10% of all stars
37. SEVERAL ABSOLUTE AND APPARENT MAGNITUDES WITH LUMINOSITIES LIST ABSOLUTE MAGNITUDES LIST
Gamma ray burst. 39.1 374,000 trillion suns
Quasars 33. 1,360 trillion suns
supernovas. 19.3. 4.49 billion suns
Supernova 1978a. 15.66. 157 million suns
Pistol star. 10.75 1.7 million suns
deneb 8.38. 192,424 suns
Betelgeuse. 5.5. 13,558 suns
Sun 4.83. 1 sun
Proxima centauri. 11.13. 1/331 suns
Sun in Andromeda galaxy. 29.07. 1/4.98 billion suns
Venus 29.23. 1/5.8 billion suns
Hubble telescope viewing limit. 31. 1/29.4 billion suns
James webb telescope viewing limit. 34. 1/466 billion suns
APPARENT MAGNITUDES LIST
sun. 26.72. 23.74 trillion suns
Full moon. 12.6. 9.38 million suns
Venus. 4.4. 4,922 suns
Sirius. 1.6. 373 suns
Most energetic gamma ray burst 12.2 billion light years away 3.77. (374,000 trillion suns)
Sun seen by us if it were in andromedas galaxy. 53.31 1/(2.48 x 10^19) suns
Type 2 supernova in Andromeda as seen from here— apparent magnitude— 4.94
Venus in Andromeda as seen from here— apparent magnitude— 53.47
Deneb in Andromeda as seen from here— apparent magnitude— 15.86
38. Formulas to find temperature kelvin from spectral class—
Temp.=1500 x spectral class number+10000
O0=20, O1=19,…, B9=1, A0=0
Temp.=187.27 x spectral class number+5880
A0=22, A1=21,…, G1=1, G2=0
Temp.=132.22 x spectral class number+3500
G2=18, G3=17,…, K9=1, M0=0, M1=1, M2=2,…, M9=9
Spaceflight formulas—
Meaning of variables in the formulas— v=velocity (meters/second)
vi=velocity initial (meters/second) vf=velocity final (meters/second) vexh=exhaust velocity (meters/second) isp=seconds
m=mass (kilograms)
mi=initial mass (kilograms)
mf=final mass (kilograms)
mr=mass ratio
a=acceleration (meters/second^2) f=force (newtons)
d=distance (meters)
t=time (seconds)
ke=kinetic energy (joules)
ed=energy density (joules/kilograms) p=power (watts)
spp=specific power (kilowatts/kilograms) mm=momentum (meters x kilograms) i=impulse (thrust x seconds)
fr=fuel rate (kilograms/second) mw=molecular weight texh=temperature exhaust (kelvin) eff=propulsive efficiency
r=radius (meters)
ecc=eccentricity
g=acceleration due to gravity
(9.81 meters/second^2)
Rocket equation
velocity
v=vexh x ln(mi/mf)
v=(d x 2)/t (when accellerating) v=d/t (constant velocity) v=sqrt(2 x a x d)
Velocity of exhaust vexh=v/ln*(mi/mf)Â vexh=.25 x sqrt(texh/mw)
Isp
isp=vexh/9.81
isp=f/(fr x 9.81)
isp=vf/(ln(mr) x 9.81)
Mass ratio
mr=mi/mf
mr=e^(v/vexh)
mr=e^(vf/(isp x 9.81))
Mass final
mf=mi/(e^(vf/vexh)
Mass initial
mi=mf x e^(vf/vexh)
mass
m=f/a
m=2 x ke/v^2
Force
f=m*a
f=ke/d Â
f=9.81 x isp x fr
acceleration
a=f/m
Energy
ke=1/2 x v^2 x m
ke=d x f
Energy density (rest mass energy)
ed=ke/m
Fuel flow rate
fr=f/vexh
fr=m/t
Distance â
d=v x t/2 (with respect to accelerating)
d=v x t (constant velocity)
d=ke/f
d=v^2/2 x a
Timeâ
t=(d x 2)/v (constant acceleration)
t=d/v (constant velocity)
t=((m x vf)^2/2)(m x mi)^2/2) x (1/f) x (2/vi+vf)
Power p=ke/t
p=f x d/t
Specific power
sp=(p/1000)/m
Momentum
M=v x mÂ
Impulse â
i=f x tÂ
Antimatter needed (kilograms) m=ke/1.8 x 10^16
Propulsive efficiency eff=2/(1+(vexh/vf))
eff=(vf/vexh)^2/(e^(vf/vexh)1)
(Maximum efficiency for ratio vf/vexh<1.6) eff=f x g x isp/2 x p
BEAUTIFUL FORMULAS
8/29/178/30/17;9/15/17;11/21/1711/22/17;12/25/17; 4/19/18
CONTENTS
 Dirac’s equation
 Einstein’s field equation
 Maxwell’s equations
 General relativity
 Special relativity
 Schrodinger’s equation
 Uncertainty principle
 Gibb’s statistical mechanics
 StephanBoltzmann law
 e=mc^2
 Laplace equation
 De broglie relationmatter wave
 Navierstokes equations
 Riemann zeta function
 Noether theorem
 Eulerlagrange equation
 Hamilton quanternion
 Standard model
 Lagrange formula
 cantor inequality
 Riemann hypothesis
 HawkingBekenstein entropy formula
 Heat equation
 wave equation
 poisson equation
 Waveparticle duality
 fundamental theorem of calculus
 Pythagorean theorem
 GaussBonnet theorem
 universal law of gravitation
 Newton’s 2nd law of motion
 kinetic energy
 Potential energy
 2nd law of thermodynamics
 principle of least action
 Spherical harmonics
 Cauchy residue theorem
 CallenSymanzik equation
 Minimal surface equation
 Euler 9 point center
 Mandelbrot set
 YangBaxter equation
 Divergence theorem
 Baye’s theorem
 logistic map
 Einstein’s law of velocity addition
 Photoelectric effect formula
 Faraday law
 Cauchy momentum equation
 De moivre’s theorem
 Fourier transform
 prime counting function
 Murphy’s law
 Summation formula
 Logarithmic spiral
 Heron’s formula
 Quadratic equation
 Euler line
 Pythagorean triple formula
 Euler’s formula
 Simplex method
 Proof of infinity of prime numbers
 Harmonic series
 Euler sums
 Cubic equation
 Quartic equation
 quintic equation
 Lorentz equation
 Eulerlagrange formula
 Euler product formula
 Eulermaclaurin formula
 Pi
 Exponent
 Natural logarithm
 Conic sections
 exponential growth or decay
 Calculation an orbit I.e. a comet
 interesting number idea 1
 interesting number idea 2
 interesting number idea 3
EQUATIONS
 Dirac equation
Dirac equation(original)
The Dirac differential equation from quantum mechanics was formulated in 1928 which predicted the existence of antimatter, which are particle of the same mass and spin, but have an opposite charges than their counterparts of matter.
2. Einstein field equation
The einstein field equations, or the einsteinhilbert equations is used to describe gravity in a classical way. It uses geometry to model gravity’s effects.
3. Maxwell’s equations
James clerk maxwell formulated 4 differential equations to describe how charged particles produce an electric and magnetic force. They calculate the motion of particles in electric and magnetic fields. They describe how electric charges and electric currents create electric and magnetic fields, and vice versa.
The 1st equation is used to calculate the electric field produced by a charge.
The 2nd equation is used to calculate the magnetic field.Â The 3rd equation, ampere’s law, shows how the magnetic fields circulate around electric currents and time varying electric fields. The 4th equation. Faradayâ€™s law, shows how the electric fields circulate around time varying magnetic fields.
4. General relativity
Albert einstein, in 1915, formed the general theory of relativity which deals with space and time, two aspects of spacetime. Spacetime curves when there is gravity, matter, energy, and momentum. Central the the general theory of relativity is the principle of equivalence. The theory shows that light curves in an accelerating frame of reference. It also asserts that light will bend and it will slow down in the presence of a massive amount matter.
5. SPECIAL RELATIVITY
The Lorentz Transformations (the mathematical basis for the special theory of relativity
An object at rest still has energy, called its rest mass, which is
E0=mc^2.
The special theory of relativity asserts that the speed of light is the same no matter what speed the observer travels. It also explains what is relative and what is absolute about time, space, and motion. It further describes how mass increases, length shrinks, time slows down for objects moving close to the speed of light, and that a person traveling close to the speed of light would age less than would a stationary person.
6. Schrodinger equation
This is a differential equation that is the basis of quantum mechanics. It is one of the most precise theories of how subatomic particles behave as fully as possible. This equation defines a wave function of a particle or group of particles that have a certain value at every point in space for every given time. the wave function contains all information that can be known about a particle or system. The wave function gives real values relating to physical properties such as position, momentum, energy, etc.
7. Uncertainty principle
This principle says that trying to pin a thing down to one definite position will make its momentum less well pinned down, and viceversa.
8. GIBB’S STATISTICAL MECHANICS
Statistical mechanics is a branch of theoretical physics which uses probability theory to study the average behavior of a
mechanical system, where the state of the system is uncertain.
Statistical mechanics is commonly used to explain the thermodynamic behavior of large systems.
9. Stefan Boltzmann law
R=ÏƒT^{4}
where Ïƒ is the StefanBoltzmann constant, which is equal to 5.670 373(21) x 10^{8} W m^{2} K^{4}, and where R is the energy radiated per unit surface area and per unit time. Tis temperature, which is measured in kelvin scale. this law is only usable for the energy radiated by blackbodies but is still useful none the less. In quantum physics, the StefanBoltzmann law (sometimes called Stefan’s Law) states that the black body radiation energy emitted by an object is directly proportional to the temperature of the object raised to the fourth power.
10. Mass energy equivalence
E=mc^2
In physics, mass energy equivalence asserts that anything having mass has an equivalent amount of energy and vice versa. these fundamental quantities are directly related to one another.
11. Laplace’s equation
In mathematics, Laplace’s equation is a secondorder partial differential equation. The solutions of Laplace’s equation are the harmonic functions, which are important in many fields of science, notably the fields of electromagnetism, astronomy, and fluid dynamics, because they can be used to accurately describe the behavior of electric, gravitational, and fluid potentials. In the study of heat conduction, the Laplace equation is the steadystate heat equation.
12. DE BROGLIE RELATION/Matter wave
Î»=h/mv
Where Î» is the wavelength of the object, h is Planck’s constant, m is the mass of the object, and v is the velocity of the object. An alternate but correct version of this formula is
Î»=h/p
Where p is the momentum. (Momentum is equal to mass times velocity). These equations merely say that matter exhibits a particlelike nature in some circumstances, and a wavelike characteristic at other times.
13. Navier Stokes equations
The Navier Stokes equations describe the motion of fluids. The equations result from applying newton’s 2nd law to fluid dynamics with the belief that the fluid stress is the sum of a diffusing vicious term (in relation to the gradient of velocity), plus a pressure term. They are very useful because they describe the physics of many things. They may be used to model weather, ocean currents, water flow in a pipe, the air’s flow around a wing, and the motion of stars inside a galaxy. The Navier Stokes equations in their full and simplified forms help with the design of aircraft and cars, the study of blood flow, the design of power stations, the analysis of pollution, and many other things. Together with Maxwell’s equations they can be used to model and study magnetohydrodynamics. The Navier Stokes equations are also of great interest in a purely mathematical sense. Somewhat surprisingly, given their wide range of practical uses, mathematicians have not yet proven that in three dimensions solutions always exist (existence), or that if they do exist, then they do not contain any singularities (or infinity or discontinuity) (smoothness). These are called the navierstokes existence and smoothness problems. The Navier Stokes equations dictate not position but rather velocity. A solution of the Navier Stokes equations is called a velocity field or flow field, which is a description of the velocity of the fluid at a given point in space and time. Once the velocity field is solved for, other quantities of interest (such as flow rate or drag force) may be found. This is different from what one normally sees in classical mechanics, where solutions are typically trajectories of position of a particle or deflection of a continuum. Studying velocity instead of position makes more sense for a fluid, however for visualization purposes one can compute various trajectories.
14. Riemann zeta function
Î¶(s)=âˆ‘n=1 to âˆž 1ns, Re(s)>1.
Where
Re(s) is the real part of the complex numbers. For example, if s=a+ib, then Re(s)=a. (where i^2=â1)
Riemann zeta function Î¶(s) in the complex plane. The color of a point s shows the value of Î¶(s): strong colors are for values close to zero and hue encodes the value’s argument. The white spot at s= 1 is the pole of the zeta function; the black spots on the negative real axis and on the critical line Re(s) = 1/2 are its zeros.
In mathematics, the Riemann zeta function, is a prominent function of great significance in number theory. It is so important because of its relation to the distribution of prime numbers. It also has applications in other areas such as physics, probability theory, and applied statistics.
The riemann hypothesis is a conjecture about the distribution of the zeros of the Riemann zeta function. Many mathematicians consider the Riemann hypothesis to be the most important unsolved problem in pure mathematics.
15. Noether’s theorem
dX/dt=0
Emmy noether was an influential mathematician known for her groundbreaking contributions to abstract algebra and theoretical physics.
Noether’s theorem can be stated informally
If a system has a continuous symmetry property, then there are corresponding quantities whose values are conserved in time.
A more sophisticated version of the theorem involving fields states that:
To every differentiable symmetry generated by local actions, there corresponds a conserved current.
16. Euler Lagrange equation
In the calculus of variations, the Euler Lagrange equation, Euler’s equation, or Lagrange’s equation (although the latter name is ambiguous), is a secondorder partial differential equation whose solutions are the functions for which a given functional is stationary.
Because a differentiable functional is stationary at its local maxima and minima, the Euler Lagrange equation is useful for solving optimization problems in which, given some functional, one seeks the function minimizing or maximizing it. This is analogous to format’s theorem in calculus, stating that at any point where a differentiable function attains a local extremum its derivative is zero. In Lagrangian mechanics, because of Hamilton’s principle of stationary action, the evolution of a physical system is described by the solutions to the Euler Lagrange equation for the action of the system. In \classical mechanics, it is equivalent to newton’s law of motion, but it has the advantage that it takes the same form in any system of generalized coordinates, and it is better suited to generalizations. In classical field theory there is an analogous equation to calculate the dynamics of a field.
17. Quaternion
a + bi + cj + dk
where a, b, c, and d are real numbers, and i, j, and k are the fundamental quaternion units.
In mathematics, the quaternions are a number system that extends the complex numbers. they are applied to in 3dimensional space. A feature of quaternions is that multiplication of two quaternions is noncommutative. Hamilton defined a quaternion as the quotient of two directed lines in a threedimensional space^{]} or equivalently as the quotient of two vectors.
Quaternions find uses in both theoretical and applied mathematics, in particular for calculations involving 3dimensional rotations such as in 3dimensional computer graphics, computer vision and crystallographic texture analysis. In practical applications, they can be used alongside other methods, such as euler angles and rotation matrices, or as an alternative to them, depending on the application.
18. Standard Model (mathematical formulation) for particle physics
19. LAGRANGE FORMULA
Lagrangian mechanics is a reformulation of classical mechanics.
In Lagrangian mechanics, the trajectory of a system of particles is derived by solving the Lagrange equations in one of two forms, either the Lagrange equations of the first kind, which treat constraints explicitly as extra equations, often using Lagrange multipliers; or the Lagrange equations of the second kind, which incorporate the constraints directly by judicious choice of generalized coordinates. In each case, a mathematical function called the Lagrangian is a function of the generalized coordinates, their time derivatives, and time, and contains the information about the dynamics of the system.
20. CANTOR’S INEQUALITY/Cantor’s theorem
In elementary set theory, Cantor’s theorem is a fundamental result that states that, for any set A, the set of all subsets of A (the power sets of A, ð’«(A)) has a strictly greater cardinality than A itself. For finite sets, Cantor’s theorem can be seen to be true by simple enumeration of the number of subsets. Counting the empty subset, a set with n members has 2^{n} subsets, so that if card(A) = n, then card(ð’«(A)) = 2^{n}, and the theorem holds because 2^{n} > n is true for all nonnegative integers.
the theorem implies that there is no largest cardinal number (colloquially, “there’s no largest infinity”
21. Riemann hypothesis
The Riemann hypothesis is a mathematical conjecture. Many people think that finding a proof of the hypothesis is one of the hardest and most important unsolved problems of pure mathematics.
The hypothesis is named after Bernhard riemann. It is about a special function, the riemann zeta function. This function inputs and outputs complex numbers values. The inputs that give the output zero are called zeros of the zeta function. Many zeros have been found. The “obvious” ones to find are the negative even integers. This follows from Riemann’s functional equation. More have been computed and have real part 1/2. The hypothesis states all the undiscovered zeros must have real part 1/2.
The functional equation also says all zeros (except the “obvious” ones) must be in the critical strip: real part is between 0 and 1. The Riemann hypothesis says more: they are on the line given, in the image on the right (the white dots). If the hypothesis is false, this would mean that there are white dots which are not on the line given.
If proven correct, this would allow mathematicians to better describe how the prime numbers are placed among whole numbers. The Riemann hypothesis is so important, and so difficult to prove, that the Clay Mathematics Institute has offered $1,000,000 to the first person to prove it.
22. HAWKINGBEKENSTEIN ENTROPY FORMULA
blackhole thermodynamics is the area of study that seeks to reconcile the laws of thermodynamics with the existence of Blackhole event horizons. As the study of the statistical mechanics of blackbody radiation led to the advent of the theory of quantum mechanics, the effort to understand the statistical mechanics of black holes has had a deep impact upon the understanding of quantum gravity, leading to the formulation of the holographic principle.
The 2nd law of thermodynamics requires that black holes have entropy. If black holes carried no entropy, it would be possible to violate the second law by throwing mass into the black hole. The increase of the entropy of the black hole more than compensates for the decrease of the entropy carried by the object that was swallowed.
23. HEAT EQUATION
The heat equation is a parabolic partial differential equation that describes the distribution of heat (or variation in temperature) in a given region over time. In the heat equation in two dimensions predicts that if one area of an otherwise cool metal plate has been heated, say with a torch, over time the temperature of that area will gradually decrease, starting at the edge and moving inward. Meanwhile the part of the plate outside that region will be getting warmer. Eventually the entire plate will reach a uniform intermediate temperature.
The heat equation is of fundamental importance in diverse scientific fields. In mathematics, it is the prototypical parabolic partial differential equation. In probability theory, the heat equation is connected with the study of brownian motion via the Fokkerplanck equation.In financial mathematics, it is used to solve the blackscholes partial differential equation. The diffusion equation, a more general version of the heat equation, arises in connection with the study of chemical diffusion and other related processes.
The heat equation is used in probability and describes random walks. It is also applied in financial mathematics for this reason.
It is also important in riemannian geometry and thus topology: it was adapted by richard s. Hamilton when he defined the Ricci flow that was later used by Grigori perelmanto solve the topological poincare conjecture.
24. Wave equation
iâ„âˆ‚/âˆ‚tÎ¨(x,t)=H^Î¨(x,t)
where i is the imaginary number, Ïˆ (x,t) is the wave function, Ä§ is the reduced planck constant, t is time, x is position in space, Ä¤ is a mathematical object known as the Hamilton operator. The reader will note that the symbol âˆ‚/âˆ‚t denotes that the partial derivative of the wave function is being taken.
Equations that describe waves as they occur in nature are called wave equations. Waves as they occur in rivers, lakes, and oceans are similar to those of sound and light. The problem of having to describe waves arises in fields like acoustics, electromagnetic, and fluid dynamics.
Historically, the problem of a vibrating string such as that of a musical instruments was studied.Â In 1746, d’Alambert discovered the onedimensional wave equation, and within ten years Euler discovered the threedimensional wave equation.
In quantum mechanics, the Wave function, usually represented by Î¨, or Ïˆ, describes the probability of finding an electron somewhere in its matter wave. To be more precise, the square of the wave function gives the probability of finding the location of the electron in the given area, since the normal answer for the wave function is usually a complex number. The wave function concept was first introduced in the legendary schrodinger equation.
25. Poisson’s equation
âˆ‡^2Ï†=f.
(âˆ‚^2/âˆ‚x^2+âˆ‚^2/âˆ‚y^2+âˆ‚^2/âˆ‚z^2)Ï†(x,y,z)=f(x,y,z).
When f=0 identically we obtain laplace’s equation.
In mathematics, Poisson’s equation is a partial differential equation of elliptic type with broad utility in mechanical engineering and theoretical physics. It arises, for instance, to describe the potential field caused by a given charge or mass density distribution; with the potential field known, one can then calculate gravitational or electrostatic field. It is a generalization of laplace’s equation, which is also frequently seen in physics. Poisson’s equation may be solved using a green’s function.
26.Wave particle duality
Wave particle duality is perhaps one of the most confusing concepts in physics, because it is so unlike anything we see in the ordinary world.
Physicists who studied light in the 1700s and 1800s were having a big argument about whether light was made of particles shooting around like tiny bullets, or waves washing around like water waves. Light seems to do both. At times, light seems to go only in a straight line, as if it were made of particles. But other experiments show that light has a frequency and wavelength, just like a sound wave or water wave. Until the 20th century, most physicists thought that light was either one or the other, and that the scientists on the other side of the argument were simply wrong.
Wave particle duality means that all particles show both wave and particle properties. This is a central concept of quantum mechanics. Classical concepts like “particle” and “wave” do not fully describe the behavior of quantumscale objects.
27. Fundamental theorem of calculus
The fundamental theorem of calculus is central to the study of calculus. It is the theorem that shows the relationship between the derivative and the integral and between the definite integral and the indefinite integral. It is broken into two parts, the first fundamental theorem of calculus and the second fundamental theorem of calculus.
The first fundamental theorem of calculus states that if the function f is continuous, then
d/dxâˆ«axf(t)dt=f(x)
This means that the derivative of the integral of a function f with respect to the variable t over the interval [a,x] is equal to the function f with respect to x. This describes the derivative and integral as inverse processes.
28. Pythagorean theorem
In mathematics, the Pythagorean theorem or Pythagoras’s theorem is a statement about the sides of a right triangle.
One of the angles of a right triangle is always equal to 90 degrees. This angle is the right angle. The two sides next to the right angle are called the legs and the other side is called the hypotenuse. The hypotenuse is the side opposite to the right angle, and it is always the longest side.
The Pythagorean theorem says that the area of a square on the hypotenuse is equal to the sum of the areas of the squares on the legs. In this picture, the area of the blue square added to the area of the red square makes the area of the purple square. If the lengths of the legs are a and b, and the length of the hypotenuse is c, then,
a^2+b^2=c^2.
Pythagorean Triples
Pythagorean Triples or Triplets are three whole numbers which fit the equation
a^2+b^2=c^2.
The triangle with sides of 3, 4, and 5 is a well known example. If a=3 and b=4, then
3^2+4^2=5^2
because
9+16=25. This can also be shown as 3^2+4^2=5.
The threefourfive triangle works for all multiples of 3, 4, and 5. In other words, numbers such as 6, 8, 10 or 30, 40 and 50 are also Pythagorean triples. Another example of a triple is the 12513 triangle, because
12^2+5^2=13
29. Gauss Bonnet theorem
The Gauss Bonnet theorem or Gauss Bonnet formula in differential geometry is an important statement about surfaces which connects their geometry (in the sense of curvature) to their topology (in the sense of the euler characteristic).
30. Newton’s law of universal gravitation
Fg=Gm1m2/r2,
Newton’s universal law of gravitation is a physical law that describes the attraction between two objects with mass.
In this equation:
F_{g} is the total gravitational force between the two objects.
G is the gravitational constant.
m_{1} is the mass of the first object.
m_{2} is the mass of the second object.
r is the distance between the centres of the objects.
In SI units, F_{g} is measured in newtons (N), m_{1} and m_{2} in kilograms (kg), r in meters (m), and the constant G is approximately equal to 6.674Ã—10^{11} N m^{2} kg
31. Newton’s 2nd law of motion
F=ma.
For a particle of mass m, the net force F on the particle is equal to the mass m times the particle’s acceleration a.
32. Kinetic energy
Kinetic energy is the energy that an object has because of its motion. This energy can be converted into other kinds, such as gravitational or electric potential energy, which is the energy that an object has because of its position in a gravitational or electric field.
Translational kinetic energy
The translational kinetic energy of an object is:
E translational=1/2mv^2
where m is the mass (resistance to linear acceleration or deceleration); v
is the linear velocity.
Rotational kinetic energy
The rotational kinetic energy of an object is:
E rotational=1/2I^2
where I is the moment of inertia (resistance to angular acceleration or deceleration, equal to the product of the mass and the square of its perpendicular distance from the axis of rotation);
Ï is the angular velocity.
33. Potential energy
Potential energy is the energy that an object has because of its position on a gradient of potential energy called a potential field.
Actual energy (E = hf) is nonzero frequency angular momentum.
Potential energy (rest mass) is zero frequency angular momentum.
The potential fields are irrotationally radial (“electric”) fluxes of the vacuum and divide into two classes:
The gravitoelectric fields;
The electric fields.
The potential energy is negative. It is not a mere convention but a consequence of conservation of energy in the zeroenergy universe as an object descends into a potential field, its potential energy becomes more negative, while its actual energy becomes more positive, and, in accordance with the 2nd law of thermodynamics, tends to be radiated away, so that the object acquires a net negative potential energy, also known as the object’s binding energy.
In accordance with the minimal total potential energy principle, the universe’s matter flows towards ever more negative total potential energy. This cosmic flow is time.
Gravitational potential energy
Self gravitating sphere
The gravitational potential energy of a massive spherical cloud is proportional to its radius and causes the sphere to fall towards its own centre.
Earth
If an object is lifted a certain distance from the surface from the earth, the force experienced is caused by weight and height. Work is defined as force over a distance, and work is another word for energy.
Electric potential energy
Electric potential energy is experienced by charges both different and alike, as they repel or attract each other. Charges can either be positive (+) or negative (), where opposite charges attract and similar charges repel.
Elastic potential energy
Elastic potential energy is experienced when a rubbery material is pulled away or pushed together. The amount of potential energy the material has depends on the distance pulled or pushed. The longer the distance pushed, the greater the elastic potential energy the material has.
34. Second law of thermodynamics
S (prime)S>=0
The second law of thermodynamics says that when energy changes from one form to another form, or matter moves freely, entropy (disorder) increases, in a closed system.
Differences in temperature, pressure, and density tend to even out horizontally after a while. Due to the force of gravity, density and pressure do not even out vertically. Density and pressure on the bottom will be more than at the top.
Entropy is a measure of spread of matter and energy to everywhere they have access.
The most common wording for the second law of thermodynamics is essentially due to Rudolf Clausius:
It is impossible to construct a device which produces no other effect than transfer of heat from lower temperature body to higher temperature body
In other words, everything tries to maintain the same temperature over time.
There are many statements of the second law which use different terms, but are all equal. Another statement by Clausius is:
Heat cannot of itself pass from a colder to a hotter body.
An equivalent statement by Lord Kelvin is:
A transformation whose only final result is to convert heat, extracted from a source at constant temperature, into work, is impossible.
The second law only applies to large systems. The second law is about the likely behavior of a system where no energy or matter gets in or out. The bigger the system is, the more likely the second law will be true.
In a general sense, the second law says that temperature differences between systems in contact with each other tend to even out and that work can be obtained from these nonequilibrium differences, but that loss of thermal energy occurs, when work is done and entropy increases. Pressure, density and temperature differences in an isolated system, all tend to equalize if given the opportunity; density and pressure, but not temperature, are affected by gravity. A heat engine is a mechanical device that provides useful work from the difference in temperature of two bodies.
Quotes
The law that entropy always increases, holds, I think, the supreme position among the laws of nature. If someone points out to you that your pet theory of the universe is in disagreement with Maxwell’s equations a then so much the worse for Maxwell’s equations. If it is found to be contradicted by observation a well, these experimentalists do bungle things sometimes. But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation.
–Sir Arthur Stanley Eddington, The Nature of the Physical World (1927)
The tendency for entropy to increase in isolated systems is expressed in the second law of thermodynamics — perhaps the most pessimistic and amoral formulation in all human thought.
—Greg Hill and Kerry Thornley. principia discordia(1965)
There are almost as many formulations of the second law as there have been discussions of it.
–Philosopher / Physicist P.W. Bridgman, (1941)
35. Principle of least action
The principle of least action a or, more accurately, the principle of stationary action â’s a variational principle that, when applied to the action of a mechanical system, can be used to obtain the equations of motion for that system. In relativity, a different action must be minimized or maximized. The principle can be used to derive newtonian, lagrangian and hamiltonian equations of motion, and even general relativity. The principle remains central in modern physics and mathematics, being applied in thermodynamics, fluid mechanics, the theory of relativity, mechanics, particle physics, and string theory and is a focus of modern mathematical investigation in morse theory. maupertuis principle and Hamilton’s principle exemplify the principle of stationary action.
36. SPHERICAL HARMONICS
In mathematics and physical science, spherical harmonics are special functions defined on the surface of a sphere. They are often employed in solving partial differential equations that commonly occur in science. The spherical harmonics are a complete set of orthogonal functions on the sphere, and thus may be used to represent functions defined on the surface of a sphere, just as circular functions (sines and cosines) are used to represent functions on a circle via fourier series. Like the sines and cosines in Fourier series, the spherical harmonics may be organized by (spatial) angular frequency. Further, spherical harmonics are basis functions for SO(3), the group of rotations in three dimensions, and thus play a central role in the group theoretic discussion of SO(3).
37. Cauchy Residue theorem
In complex analysis, a discipline within mathematics, the residue theorem, sometimes called Cauchy’s residue theorem, is a powerful tool to evaluate line integrals of analytic functions over closed curves; it can often be used to compute real integrals as well. It generalizes the cauchy integral theorem and cauchy integral formula. From a geometrical perspective, it is a special case of the generalized stoke’s theorem.
38. Callan Symanzik equation
In physics, the Callan Symanzik equation is a differential equation describing the evolution of the npoint correlation functions under variation of the energy scale at which the theory is defined and involves the betafunction of the theory and the anomalous dimensions.
39. MINIMAL SURFACE EQUATION
In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature. The term “minimal surface” is used because these surfaces originally arose as surfaces that minimized total surface area subject to some constraint. Physical models of areaminimizing minimal surfaces can be made by dipping a wire frame into a soap solution, forming a soap film, which is a minimal surface whose boundary is the wire frame. However the term is used for more general surfaces that may selfintersect or do not have constraints. For a given constraint there may also exist several minimal surfaces with different areas.
40. EULER’S 9 POINT CENTER/Ninepoint center
In geometry, the ninepoint center is a triangle center, a point defined from a given triangle in a way that does not depend on the placement or scale of the triangle. It is socalled because it is the center of the 9point circle, a circle that passes through nine significant points of the triangle: the midpoints of the three edges, the feet of the three altitudes, and the points halfway between the orthocenter and each of the three vertices.
41 MANDELBROT SETS
The Mandelbrot set is a famous example of a fractals in mathematics.The Mandelbrot set is important for the chaos theory. The edging of the set shows a selfsimilarity, which is not perfect because it has deformations.
42. Yang Baxter equation
In physics, the Yang Baxter equation (or startriangle relation) is a consistency equation which was first introduced in the field of statistical mechanics. It depends on the idea that in some scattering situations, particles may preserve their momentum while changing their quantum internal states. It states that a matrix
R, acting on two out of three objects, satisfies
(RâŠ—1)(1âŠ—R)(RâŠ—1)=(1âŠ—R)(RâŠ—1)(1âŠ—R)
In one dimensional quantum systems,
R is the scattering matrix and if it satisfies the Yang Baxter equation then the system is integrable. The Yang Baxter equation also shows up when discussing knot theory and the braid groups where
R corresponds to swapping two strands. Since one can swap three strands two different ways, the Yang Baxter equation enforces that both paths are the same.
43. DIVERGENCE THEOREM
In vector calculus, the divergence theorem, also known as Gauss’s theorem or Ostrogradsky’s theorem, is a result that relates the flow (that is, flux) of a vector field through a surface to the behavior of the vector field inside the surface. More precisely, the divergence theorem states that the outward flux of a vector field through a closed surface is equal to the volume integral of the divergence over the region inside the surface. Intuitively, it states that the sum of all sources (with sinks regarded as negative sources) gives the net flux out of a region. The divergence theorem is an important result for the mathematics of physics and engineering, in particular in electrostatics and fluid dynamics.
In physics and engineering, the divergence theorem is usually applied in three dimensions. However, it generalizes to any number of dimensions. In one dimension, it is equivalent to the fundamental theorem of calculus. In two dimensions, it is equivalent to green’s theorem. The theorem is a special case of the more general stoke’s theorem.
44. Bayes’ theorem
P(AB)=P(BA)P(A)P(B).
In probability theory and applications, Bayes’ theorem shows the relation between a conditional probability and its reverse form. For example, the probability of a hypothesis given some observed pieces of evidence and the probability of that evidence given the hypothesis.
45. Logistic map
xn+1=rxn(1xn)
where
xn
is a number between zero and one that represents the ratio of existing population to the maximum possible population.
46. EINSTEIN’S LAW OF VELOCITY ADDITION/Velocityaddition formula
In relativistic physics, a velocityaddition formula is a threedimensional equation that relates the velocities of objects in different reference frames. Such formulas apply to successive lorentz transformations, so they also relate different frames. Accompanying velocity addition is a kinematic effect known as thomas procession, whereby successive noncollinear Lorentz boosts become equivalent to the composition of a rotation of the coordinate system and a boost.
Standard applications of velocityaddition formulas include the doppler shift, doppler navigation, the aberration of light, and the dragging of light in moving water. It was observed by galilei that a person on a uniformly moving ship has the impression of being at rest and sees a heavy body falling vertically downward. This observation is now regarded as the first clear statement of the principle of mechanical relativity. The cosmos of Galileo consists of absolute space and time and the addition of velocities corresponds to composition of galilean transformations. The relativity principle is called galilean relativity. It is obeyed by newtonian mechanics.
According to the theory of special relativity, the frame of the ship has a different clock rate and distance measure, and the notion of simultaneity in the direction of motion is altered, so the addition law for velocities is changed. The cosmos of special relativity consists of Minkowski spacetime and the addition of velocities corresponds to composition of lorentz transformations. In the special theory of relativity Newtonian mechanics is modified into relativistic mechanics.
47. PHOTOELECTRIC EFFECT FORMULA
The photoelectric equation involves; h = the Planck constant 6.63 x 10^{34} J s. f = the frequency of the incident light in hertz (Hz) … E_{k} = the maximum kinetic energy of the emitted electrons in joules (J)
The photoelectric effect is the emission of electrons or other free carriers when light is shone onto a material. Electrons emitted in this manner can be called photo electrons. The phenomenon is commonly studied in electronic physics, as well as in fields of chemistry, such as quatuum chemistry or electrochemistry.
48. Faraday’s law of induction
Faraday’s law of induction is one of the basic laws of electromagnetism. The law explains the operation principles of generators, transformers and electric motors.
49. Cauchy momentum equation
The Cauchy momentum equation is a vector partial differential equation put forth by cauchy that describes the nonrelativistic momentum transport in any continuum.
50. De Moivre’s formula
The process of mathematical induction can be used to prove a very important theorem in mathematics known as De Moivre’s theorem. If the complex number z = r(cos α + i sin α), then. The preceding pattern can be extended, using mathematical induction, to De Moivre’s theorem.
51. Fourier transform
The Fourier transform is a mathematical function that can be used to show the different parts of a continuous signal. It is most used to convert from time domain to frequency domain. Fourier transforms are often used to calculate the frequency spectrum of a signal that changes over time. This kind of signal processing has many uses such as cryptography, oceanography, speech recognition, or handwriting recognition. Fourier transforms can also be used to solve differential equations.
Calculating a Fourier transform requires understanding of integration and imaginary numbers. Computers are usually used to calculate Fourier transforms of anything but the simplest signals. The Fast Fourier Transform is a method computers use to quickly calculate a Fourier transform.
52. Primecounting function
In mathematics, the primecounting function is the function counting the number of prime numbers less than or equal to some real number x. It is denoted by Ï€(x) (unrelated to the number Ï€).
Number of primes in up to the number x=x/lnx
53. MURPHY’S LAW FORMULA
Here, PM is the Murphy’s probability that something will go wrong. KM is Murphy’s constant (equal to one) and FM is Murphy’s factor, a very small number.
Murphy’s law is an adage or epigram that is typically stated as: “Anything that can go wrong will go wrong”.
54. SUMMATION FORMULA
In mathematics, summation (capital Greek sigma symbol: âˆ‘) is the addition of a sequence of numbers; the result is their sum or total. If numbers are added sequentially from left to right, any intermediate result is a partial sum, prefix sum, or running total of the summation.
The numbers to be summed (called addends, or sometimes summands) may be integers, rational numbers, real numbers, or complex numbers. Besides numbers, other types of values can be added as well: vectors, matrices, polynomials and, in general, elements of any additive group (or even monoid).
55. Logarithmic spiral A logarithmic spiral, equiangular spiral or growth spiral is a special kind of spiral spiral curve which often appears in nature. The logarithmic spiral was first described by descarte and later extensively investigated by Jakob bernoulli, who called it Spira mirabilis, “the marvelous spiral”.
Logarithmic spirals in nature
In several natural phenomena one may find curves that are close to being logarithmic spirals. Here follows some examples and reasons:
The approach of a hawk to its prey. Their sharpest view is at an angle to their direction of flight; this angle is the same as the spiral’s pitch.
The approach of an insect to a light source.