Pythagoreanism

Pythagoreanism is a philosophical and religious movement which was based on the teachings of ancient Greek philosopher Pythagoras and his followers. The Pythagoreans are best known for their mathematical ideas, especially the Pythagorean theorem, but they also made significant contributions to music, astronomy, and metaphysics.

History

Pythagoreanism originated in the 6th century BC in the Greek city of Samos, where Pythagoras was born. After travelling widely in his youth, Pythagoras established a religious community in Croton, a Greek colony in southern Italy. This community, known as the Pythagorean school, was dedicated to the study of philosophy, mathematics, and natural science.

Beliefs and Practices

The Pythagoreans believed in the transmigration of souls, or reincarnation, and practiced a form of vegetarianism. They also followed a strict code of conduct, which included rules about clothing, food, and social behavior.

In mathematics, the Pythagoreans discovered the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. They also developed the concept of mathematical proof, and made important contributions to the theory of proportions and number theory.

In music, the Pythagoreans discovered the mathematical relationships between musical intervals, which led to the development of the musical scale. They also believed in the music of the spheres, a concept that the movements of the celestial bodies produce a form of music.

In astronomy, the Pythagoreans proposed that the Earth is a sphere and that all the planets move in circular orbits around a central fire. This model, known as the Pythagorean universe, was one of the earliest attempts to explain the structure of the universe.

Influence

The ideas of the Pythagoreans had a profound influence on later Greek philosophy, especially Platonism and Neoplatonism. They also influenced the development of mathematics, music theory, and astronomy in the Western world.

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  Cropped image of Pythagoras from Raphael's School of Athens

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  Plimpton 322

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  Pythagorean theorem animation

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  Kapitolinischer Pythagoras

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  Bronnikov's "Hymn to Pythagoras"

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  Archytas curve

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  First six triangular numbers

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  Pythagoras and Philolaus