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
Group of rational points on the unit circle to the two most famous Pythagorean right triangles: 3,4,5 and 5,12,13) are elements of "G", and their group product is (−33/65 + i56/65), which corresponds to a 33,56,65 Pythagorean right triangle. The sum of the squares of the numerators 33 and 56 is 1089 + 3136 = 4225, which is the square of the denominator 65. The set of all 2×2 rotation matrices with rational entries coincides with G.This follows from the fact that the circle group formula_2 is isomorphic to formula_3, and the fact that their rational points coincide. The structure of "G" is an infinite sum of cyclic