Pythagoras triangle the square of the hypotenuse is equal [to the sum of] the squares of the two other sides"—that is, formula_1. According to a popular legend, after he discovered this theorem, Pythagoras sacrificed an ox, or possibly even a whole "hecatomb", to the gods. Cicero rejected this story as spurious because of the much more widely held belief that Pythagoras forbade blood sacrifices. Porphyry attempted to explain the story by asserting that the ox was actually made of dough. The Pythagorean theorem was known and used by the Babylonians and Indians centuries before Pythagoras, but it is possible that he
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