Pythagorean theorem Pythagoras personally, [...] one can safely assume that it belongs to the very oldest period of Pythagorean mathematics." Around 400 BC, according to Proclus, Plato gave a method for finding Pythagorean triples that combined algebra and geometry. Around 300 BC, in Euclid's "Elements", the oldest extant axiomatic proof of the theorem is presented. Pythagorean theorem In mathematics, the Pythagorean theorem, also known as Pythagoras' theorem, is a fundamental relation in Euclidean geometry among the three sides of a right triangle. It states that the square of the hypotenuse (the side opposite the right angle) is equal to the sum of
Fermat's theorem on sums of two squares version of the statement (in which he also gave the number of possible expressions of the powers of "p" as a sum of two squares) in a letter to Marin Mersenne dated December 25, 1640: for this reason this version of the theorem is sometimes called "Fermat's Christmas theorem." Since the Diophantus identity implies that the product of two integers each of which can be written as the sum of two squares is itself expressible as the sum of two squares, by applying Fermat's theorem to the prime factorization of any positive integer "n", we see that if all the