Pythagoras

Little is known of the life of the ancient Greek mathematician Pythagoras. This may be due to the influence of the mystical society that he founded, since its reclusive and communal nature discouraged the release of any information about its doings. Nevertheless, the influence of Pythagoras on show more mathematics is profound because of the famous theorem that carries his name---the Pythagorean Theorem. (The theorem states that, if a and b are the lengths of the two legs of a right triangle and if c is the length of the hypotenuse, then a2 + b2 = c2.) It is unlikely that Pythagoras actually discovered the relationship that bears his name. But he may have been the first to prove it. The relationship was probably known and used by other ancients, such as the Egyptians and the Babylonians. The Pythagorean approach to the right-triangle relationship, however, is fundamentally different from that of the Babylonians and the Egyptians. They were interested in the relationship as a means of solving certain specific problems in measurement, while Pythagoras and his followers were interested in the fact that the theorem expressed a fundamental geometric relationship that was true for all right triangles. It is this attitude that characterized the Pythagoreans as mathematicians in the modern sense of the word. This mathematical attitude also can be seen in the way in which Pythagoras approached arithmetic, not as a computational skill, but as the study of the properties of numbers. From the Pythagorean point of view, the proper role of arithmetic---and also of geometry, music, and astronomy---is to help a conscientious seeker of knowledge attain a better appreciation of truth and beauty. The Pythagoreans regarded numbers, especially whole, or counting, numbers, as a supreme example of abstractions that are eternal and unchanging. This point of view is reflected in their overall mystical philosophy. (Bowker Author Biography) show less