c.582-c.507 B.C., pre-Socratic Greek philosopher. We know little of his life and nothing of his writings; all of our knowledge comes from his followers, the Pythagoreans, a mystical brotherhood he founded at Crotona. Members of the order regarded Pythagoras as a demigod and attributed all their doctrines to him. They believed in the transmigration of souls, and followed moral and dietary practices in order to purify the soul for its next embodiment. Skilled mathematicians, they influenced early Euclidian geometry, e.g., through the Pythagorean theorem (which states that the square of the length of the hypotenuse of a right triangle equals the sum of the squares of the lengths of the other two sides). They were also among the first to teach that the earth is a spherical planet revolving about a fixed point. Beginning with the discovery of numerical relations between musical notes, they taught that the essence of all things was number and that all relationships-even abstract concepts like justice-could be expressed numerically. Orphism, the ancient Greek mystery religion arising in the sixth century B.C. from a synthesis of pre-Hellenic beliefs with the Thracian cult of Zagreus, soon became mingled with the Eleusinian mysteries and the doctrines of Pythagoras.¥