History of Math Test 2

Fibonacci

(1179-1250) Leonardo of Pisa, Italian Mathematician. As a youth traveled widely with father throughout the mediterannean region and beyond. Wrote Liber Abaci which helped to popularize Hindu-Arabic numbrical system in Europe: included 'zephirum' for zero, horizontal bar for division, rhetorical algebra. Three math challed problems discussed in Liber Quadratorum an Practica Geometrica. Fibonacci independently discovered the sum of two square identity. Also wrote Flos- includes rabbit problem with Fibonacci sequence, and a division of figure which included a theorem on the medians of triangles.

Gerolamo Cardano

(1501-1576) Italian mathematician, physician, astrologer, gambler. Chief mathematical work is his Ars Magna which was a full exposition of algebra known at the time using a superior notation and containing many original proofs. It included the general solution of the cubic equation with credit given to Tartaglia. Also included proof of the quartic equation due ot his student Ferrari. Cardano was a controversial figure who spent much of his time embroiled in controversies with many of his contemporaries. Predicted date of his own death and so killed himself on that day.

Francois Viete

(1540 - 1603) French mathematician, lawyer, member of French parliament. Deciphered Spanish code with 400 characters. Developed much algebraic symbolism and sometimes called the "father of modern algebraic notion," wrote on geometry, arithmetic, algebra, and trigonometry. Used all six main trig functions, derived value of pi to 10 decimal places by using a polygon with 6 x 2^16 sides. Derived an infinite product for 2/pi. Worked on three geometric problems of antiquity, wrote Introduction to the Analytical Art, Mathematical Laws Applied to Triangles, and many other works. His Isagoge (Introduction) includes consonants for known and vowels for unknowns.

John Napier

(1550-1617) Scottish nobleman (Baron of Merchiston) and mathematician. Main interest was astrology and providing that the pope was the Anti-Christ. Created the idea of logarithms or 'ratio numbers' (much admired by Henry Briggs and other). Did some work in spherical geometry and trigonometry. Also developed Napier's bones used for basic arithmetic.

Rene Descartes

(1596 - 1650) French mathematician, rationalist philosopher, aristocrat. Traveled a good deal as a soldier and spent much time in Holland and Sweden (last year of his life). Wrote La Monde (left unpublished) and philosophical tract "A Discorse of the Method... " (1637) which included three appendices including "La Geometrie" where his new methods of analytic geometry are developed (the geometry is in symbolic form). Interpreted x^2, x^3, etc. as line segments rather than as areas and volumes hence removed artificial use of dimension considerations in the arithmetic of numbers. Also wrote on optics, rainbows, "Snell's" law of refraction, Descartes' rule of signs, analytical methods for drawing tangents and normals to curves, studied many cases of cubic equations in two variables, discovered Euler-Descartes formula for convex polyhedra: v+f=e+2, found a new amicable pair, gave example of an odd number that "almost" perfect.

Pierre de Fermat

(1601 - 1655) French divorce lawyer and judge. "Prince of Mathematical Amateurs." Developed analytic geometry independent of Descartes. Developed much of differential calculus, tangents and normals to curves, function optimization, developed methods for finding areas under curves. Created probability theory with Pascal, developed method of infinite descent. Did significant work in number theory - Fermat's little Theorem, stated Fermat's last Theorem and proved n = 4 case, some work on "elliptic" functions. Made several conjecture - many proved (and others disproved) by Euler and others.

Blaise Pascal

(1623-1662) French mathematician, philosopher and religious zealot. Child prodigy who rediscovered much of Euclid's Elements - wrote on conics, mystic hexagram theorem, developed probability theory studying "problem of the points" with Fermat. Sometimes called "greatest might have been" in mathematics. Studied the cycloid and Archimedean spiral, developed method of mathematical induction, used the arithmetical (Pascal's) triangle for combinatorial problems. Father Etienne Pascal named the limacon (polar equation that looks like a snail).

Isaac Newton

(1642 - 1727) English mathematician and natural philosopher, alchemist, and religious scholar. Student of Isaac Barrow and Cambridge until Barrow relinquished his Lucasian Chair of Newton. Considered one of the greatest 3 or 4 mathematicians of all time. Co-inventor of calculus, proved fundamental theorem of calculus, generalized binomial theorem for fractional exponents, stated three law of motion (fundamental laws of physics), formulated universal law of gravitation and derived Kepler's Laws based on them. Contributed to fields of numerical analysis and calculus of variations. Derived Newton's method for finding roots, Newton's Law of Cooling. Wrote Optics and Principia Mathematica. Held many prominent posts including Master of the Mint and President of the Royal Society. Buried with much fanfare in Westminster Abbey.

Leonhard Euler

(1707 - 1783) Swiss mathematician, most prolific - 886 books and papers, incredible computational skill, "Analysis Incarnate", introduced notations - e,i, f(x), ∑, created graph theory and beginnings of topology, differential equations, calculus of variations, combinatorics, much applied mathematics, key work in number theory, beginning of analytic number theory, light and sound studied, mechanics, p-test for infinite series, partiation function work e^9ix)=cosx+isin(x) proved Euler-Descartes formula, showed that 1 + 1/4 + 1/9+ ... = pi^(2)/6, also wrote important textbooks in algebra and differential and integral calculus.

Joseph Lous Lagrange

(1763 - 1813) French mathematician, developed calcuclus or variations, key results in algebra - Lagrange's theorem on the order of subgroups, uniform method of resolvents to solve quadratics, cubics, and quartics, mch work in number theroy - proved that every integer is the sum of four square, worked on Pell's equation, differential equations work, deduced principle of least action, college lecturer at Turin at age 19, replaced Euler at Berlin Academy, derived from of remainder for Taylor's Theorem, used notation f' for derivative of f, worked on metric system

Carl Friedrich Gauss

(1777 - 1855) German mathematician and astrophysicist at University of Gottingen, one of the deepest mathematical thinkers of all time, constructed a 17-sided regular polygon with Euclidean tools, proved fundamental theorem of algebra (4 times), formulated and proved quadratic reciprocity law (7 times), wrote groundbreaking Disquisitions Arithmeticae (1801) with 7 chapters on number theory beginning with definition of congruence and proof of fundamental theorem of arithmetic. Developed method of least squares, found path of asteroid Ceres, developed non-Euclidean geometry, proof of arithmetic-geometric mean inequality, showed every integer is the sum of three triangular numbers, worked on geodesy and co-invested electronic telegraph.

Brahmagupta

(630 C.E.) Indian Mathematician. Wrote Astronomical System of Brahma: includes rule of arithmetic for positive and negative numbers and zero. Solved linear Diophantine equation and solved many quadratic equations iwth both positive and negative roots. MEntioned that 3 is a practical apprximation to pi, but root 10 is better. Dreived formula for area of a cyclic quadrilateral. A= sqrt((s-a)(s-b)(s-c)(s-d)) where s is the semi perimeter. Knew fibonacci's two square idenity for the product of two number each expressible as the sum of two squares.

Al Khwarizmi

(825 C.E.) Arab Mathematician and astronomer, wrote about sundials and astrolabe, the world "algorithm" is derived from his name. Wrote Hisab al-jabar wa'al muqabalah and The Hindu Art of Reckoning. Used method of completing the square to solve quadratic equations, used rhetorical algebra of the Hindu Mathematicians and Greek geometric methods. No use of negative numbers or the number zero.

Mahavira

(9th Century) Mango problem: king has 1/6 of mangos, queen 1/5 of remainder, 3/4,1/3,2/3, child has 3 mangos. How many mangos are there total? Combinatorial problems: how many ways can you distinguish D,S,R,E on a circular necklace? (3!/2=3)

Aryabhata

(Born 476 C.E.) Pi=3.1416, interesting algebra, sum of an arithmetic series (f+(f+d)+(f+2d)..+(f+(n-1)d)=(n(f+l)/2) note: f= first, l=last.)

Gebert

(c. 940 - 1003) Became pope in 999.

Omar Khayam

(provided geometric solution to cubic equation)

Tartaglia

Claimed that he could solve x^3 +px^2=n and x^3+mx=n. Puzzle problems, 3 men steal a vase with 24oz of balsam, get 5,11,13 oz test tube. How do you divide up evenly? Need to kille half of pursurs? Wolves and sheep moving together?

Abraham Ibn Ezra

Combinatorics 7 Choose K

John Wallis

Cryptographer. Created infinity symbol. Used 1/infinity infintesimal. Made contributions to trig, calc, geometry. Published treatise of conic sections. Do insane calculations in his head.

Nicdo Fontana

Cubic and Quartic Equation

Tycho Brahe

Danish Astronomer. Saved kings life after he fell into river drinking. Had a dwarf dressed in clown outfit. Married common woman. Great eye site. Had his own island.

Henry Briggs

Developed Base 10 for logarithims. Influential prof.

Abdul Wafa

Developed sine tables. Proved double and half angle formulas. Further developed trig.

Zeno's Paradoxes

Dichotomy- travelling half distances. Achilles and tortoise same. Arrow moving- arrow always at rest. stade-moving blocks. Doesn't understand that infinite sums aren't infinte.

Isacc Barrow

Discovered the FTC.

Evangelist Tarricolli

Early calc. Redification of a logarithmic spiral. example gabriels horn and find area under. Revlolign the shaded region by x axis.

Levi ben Gerson

Estimated stellar distances correctly.

Johann Widman

First person to use "+", "-"

Thabit ibn Qurra

Formula for amicable pairs: 220, 284 was known to the Greeks. Found if p,q, and r are prime and p=3*2^(n-1), q=3*2^(n)-1, r=q(2^(2n-1))-1, for fixed n>1, then 2^(n)pq and 2^nr form an amicable pair. Note: Euler found 62 more examples and Paganii discovered another. Triangle thm: for traingle(ABC) let B' and C' lie on BC such that angle(AB'B)=angle(ACC')=angle(BAC) then (AB)^2+(AC)^2=BC(BB'+CC').

Regonontus

Found the 5th perfect number.

Gilled Perssonne De Roberval

French mathematician. Chair of mathematics at royal college of France. Also worked with the method of indivisibles. Method of drawing tangents.

Bhaskara

Gave solution to Pythagorean triplet.

Robert Record

Introduced "="

Bonoventura Cavalieri

Italian Mathematician. Known for work on problems of optics and motion. Worked on indivisibles. Introduced logarithms to Italy. Developed theory of mirrors shaped in parabolas, hyperbolas and ellipses. Developed Cavalieri's quadature formula - computing areas under the curves y=x^n.

Nicolo Fontana of Brescia

Known as Tartaglia. Solution of cubic equation. Was challenged by Antonio Fior to solve cubic problems and he did. Wrote nova scienza.

Nicole Oresme

Merton Rule: A body moving with uniform acceleration will cover the same distances as a second car moving at a constant velocity at the midspeed of the other car. Proposed that the Earth Spins. Wrote Tractacus de figuratime potanitor menaram. Law of Exponents. Rectangle = area of triangle. Looked at infinite series, harmonic series, and latitude of forms.

Islam Math

Monotheistic Religion. Influence by Greece and India. House of Wisdom located in Baghdad is center of learning.

Kepler

Mystery of the Cosmos. Wrote Astronmia Nova, Harmony of the worlds. Keplers laws of motion. Heliocentric. (1. Planets move about the sun in elliptical orbits w/ the sun at one focus, the radius vector joining a planet to the sun sweeps out equal areas in equal time intervals, the square of an orbital period of a planet is proportional to the cube of the orbits average distance from the sun). Only 6 planets in line with platonic solid. Solid Geometry of wine barrles.

Gottfired Wihlem Lebniz

Notion for derivatives and integrals

Indian Math

Numerical system - 1st to include (a decimal base 10, a positional notion, a ciphered form for the #s 1,2,3,...9)

Evangelista Torricelli

Student of Gallileo. Rectification of log spiral. Invented mercury barometer. Gabriel horn cacl problem - SA is infinite but whose volume is finite. Physicist and mathematician. Studied how projectiles fly through the air.

Georg Rheticus

Studied with Copernicus

Apollonius

Study of conic sections and tangent/normal lines. Exodus/Archimedies - method of exhaustion given an r less that 1 greater than 0 there is a small quantity epsilon such that r^n is less than epsilon.

Galileo Galilei

The speed that different weight objects fall is the same. Wrote the starry messenger. Worked on telescopes. wrote the two chief systems, the two sciences (wrote both in Italian for common people). Church got mad. Found that moving bodies following parabolic paths. Spotted 4 moons of jupiter.

Copernicus

Wrote De revolutionibu arbim colestill (revolution of the heavenly spheres). Firm believer of heliocentric theory. This work also explains variation of brightness between planets.

Luca Pacioli

Wrote The Summa. First printed algebra book. Progress in such as "+" and "-"