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
Right triangle two legs (the two sides that meet at a right angle). This can be stated in equation form as where "c" is the length of the hypotenuse, and "a" and "b" are the lengths of the remaining two sides. Pythagorean triples are integer values of "a, b, c" satisfying this equation. The radius of the incircle of a right triangle with legs "a" and "b" and hypotenuse "c" is The radius of the circumcircle is half the length of the hypotenuse, Thus the sum of the circumradius and the inradius is half the sum of the legs: One of the