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Pythagoras of Samos (c.569–c.500 BC)

Greek philosopher, mathematician, and astronomer who founded a secretive philosophical and religious school – the Pythagorean school – in Croton, southern Italy. Pythagoras left no writings and virtually nothing is known about him as an individual, so it is almost impossible to disentangle the beliefs and discoveries of the "Pythagoreans" from those of their leader.

To the Pythagoreans "everything is number" and every number was supposed to be a quantity that could be expressed as the ratio of two integers. Such a number we now call a rational number. The Pythagoreans used music as an example of the perfection and harmony of numbers that can be expressed as ratios. They showed that pitch could be represented as a simple ratios that came from the length of equally tight strings that could be plucked.

Perhaps the most famous of the Pythagoreans' mathematical results is Pythagoras's theorem. Then the sky fell in on the Pythagoreans' world-view. Using their very own theorems they showed that not all numbers are rational. Their discovery that the square root of 2 (the length of the hypotenuse of a triangle with sides one and one) can't be expressed as ratio of two whole numbers was to have been kept a closely guarded a secret, but was later revealed by one of the cult's members.

Pythagoras believed that Earth was a sphere at the center of the universe, and correctly realized that the morning star and the evening star were the same object (Venus). He was also the first to teach that the Earth was a sphere rotating around a central "fire."

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