History of mathematical notation back to any school or period before that of the Ionian Greeks, but the subsequent history may be divided into periods, the distinctions between which are tolerably well marked. Greek mathematics, which originated with the study of geometry, tended from its commencement to be deductive and scientific. Since the fourth century AD, Pythagoras has commonly been given credit for discovering the Pythagorean theorem, a theorem in geometry that states that in a right-angled triangle the area of the square on the hypotenuse (the side opposite the right angle) is equal to the sum of the areas of the squares 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