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
Fermat's right triangle theorem a congruent number. Equivalently, it is impossible for a square (the geometric shape) and a right triangle to have both equal areas and all sides commensurate with each other. Yet another equivalent form of Fermat's theorem involves the elliptic curve consisting of the points whose Cartesian coordinates formula_18 satisfy the equation This equation has the obvious pairs of solutions (0,0), (1,0), and (−1,0). Fermat's theorem is equivalent to the statement that these are the only points on the curve for which both "x" and "y" are rational. During his lifetime, Fermat challenged several other mathematicians to prove the non-existence of