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 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