Section 10.3 The Pythagorean Theorem MTH 232 Section 10.3 The Pythagorean Theorem

Pythagoras Born approximately 570 B.C. on the Greek island of Samos Founded his academy approximately 518 B.C. in southern Italy. He and his followers held five basic beliefs: (1) that at its deepest level, reality is mathematical in nature, (2) that philosophy can be used for spiritual purification, (3) that the soul can rise to union with the divine, (4) that certain symbols have a mystical significance, and (5) that all brothers of the order should observe strict loyalty and secrecy.

The Theorem Because of the communal nature of the Society, it is likely that someone else “discovered” the Theorem but Pythagoras received credit for the discovery. There is evidence that the Theorem was used previously by the Babylonians, Mesopotamians, Indians, and Chinese. Pythagoras, however, is credited with providing the first mathematical proof.

a2 + b2 = c2 In a right triangle, the square of the length of the hypotenuse (the longest side of a right triangle, located directly across from the right angle) is equal to the sum of the squares of the lengths of the legs (the two sides adjacent to the right angle). The converse is also true (if the sides of a triangle satisfy the conditions of a right triangle, then the triangle is a right triangle).

Pythagorean Triples Pythagorean Triples are integers that, used as the lengths of a right triangle, satisfy the Pythagorean Theorem: 3, 4, 5 5, 12, 13 7, 24, 25 8, 15, 17 9, 40, 41