580 BCE Samos was Thales' student.
discovered pythagorean theorem. discovered quantities that are not numerically computable. Founded a school. most notable success was explanation of musical harmony in term of whole-number ratios.
300 BCE taught in Alexandria.
the "Elements" was the base of mathematical education for 2000 years.
constructed math by deduction from axioms.
proved that there were infinitely many prime numbers by contradiction.
contains constructions by ruler and compass only.
250 CE in Alexandria.
general formula for generating Pythagorean triples: ax + by = c.
found methods to solve quadratic and cubic equations. Equations for which rational solutions are sought are called Diophantine - one relation in all equations.
1800 BCE may have known the pythagorean theorem before Pythagoras, found it on a clay tablet known as "Plimpton 322."
1619 wanted to explain the planets and their distance. discovery was ruined when they discovered Uranus was a planet.
1882 proved that not only is pi irrational but it is also transcendental. there is no polynomial in which pi is the solution.
1700 found a factorization for h=5,
p_5_ = 2^32 + 1 is not a prime number.1700 found a factorization for h=5, p5=232+1 is not a prime number
200 BCE Syracus. enraged a soldier by saying "stay away from my diagram!" and was murdered. his reputation rested on his mechanical inventions. found the area of a parabolic segment, which relied on an infinite process, the summation of an infinite geometric series.
400 BCE theory of proportions, "method of exhaustion" - Book XII; theory of irrationals - book V
integer triples (a,b,c) satisfying 1, such that
a^2 + b^2 = c^2, for example (3,4,5) (5,12,13) (8,15,17)
a solid that is convex and has congruent shapes on each side, there are only five.
a quantity that is not the root of any polynomial equation with rational coefficients
a method for finding the greatest common divisor of two natural numbers, book VII
an integer of the form 2m, where m is an integer. can be divided easily into groups of two