Pythagoras: Encyclopedia II - Pythagoras - Pythagoreans

Pythagoras - Pythagoreans

Pythagoras' followers were commonly called "Pythagoreans." For the most part we remember them as philosophical mathematicians who had an influence on the beginning of axiomatic geometry, which after two hundred years of development was written down by Euclid in The Elements.

The Pythagoreans are known for their theory of the transmigration of souls, and also for their theory that numbers constitute the true nature of things. They performed purification rites and followed ascetic, dietary and moral rules which they believed would enable their soul to achieve a higher rank among the gods. Consequently, they expected they would be set free from the wheel of birth.

The Pythagoreans also believed that the sexes are equal. Pythagoras started a school, together with his wife Theano, built on this principle. After he died, his wife and daughters ran and taught at the school. Theano herself discovered a formula to derive the golden rectangle.

All slaves were treated humanely, and animals were respected as creatures with souls. The highest purification of the soul was "philosophy", and Pythagoras has been credited with the first use of the term. The Jains in India follow similar beliefs and practices, which leads some neo-Pythagoreans and neo-Platonic authors to believe that Pythagoras had visited India, and studied under the Jains.

It was the Pythagoreans who discovered that the relationship between musical notes could be expressed in numerical ratios of small whole numbers. The Pythagoreans elaborated on a theory of numbers the exact meaning of which is still debated among scholars. They taught that all things were numbers, that the essence of everything is a number, and that all relationships can be expressed numerically.

Adapted from the Wikipedia article "Pythagoreans", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki