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Pythagoras
By Ranjiz on June 8, 1998:

What are Pythagoras's contributions to mathematics ???

By Richard Dwight (rpd25) on Tuesday, September 12, 2000 - 12:52 pm:

Dear Ranjiz,

I think the best way to answer this question is to refer you to other sources on the history of maths. There is an interesting site on the web that has already been mentioned in ask nrich. This is an extract from the biography of Pythagoras found there:-

"Pythagoras of Samos was a Greek philosopher responsible for important developments in mathematics, astronomy and the theory of music. He left Samos because of the tyrant who ruled there and went to southern Italy about 532 BC. He founded a philosophical and religious school in Croton that had many followers.

Although the theorem now known as Pythagoras's theorem was known to the Babylonians 1000 years earlier he may have been the first to prove it.

Of his actual work nothing is known. His school practised secrecy and communalism making it hard to distinguish between the work of Pythagoras and that of his followers. His school made outstanding contributions to mathematics.

Pythagoreans believed that all relations could be reduced to number relations. This generalisation stemmed from observations in music, mathematics and astronomy.

The Pythagoreans noticed that vibrating strings produce harmonious tones when the ratios of the lengths of the strings are whole numbers, and that these ratios could be extended to other instruments.

The most important discovery of this school was the fact that the diagonal of a square is not a rational multiple of its side. This result showed the existence of irrational numbers. Not only did this disturb Greek mathematics but the Pythagoreans' own belief that whole numbers and their ratios could account for geometrical properties was challenged by their own results.

In astronomy Pythagoras taught that the Earth was a sphere at the centre of the Universe. He also recognised that the orbit of the Moon was inclined to the equator of the Earth and he was one of the first to realise that Venus as an evening star was the same planet as Venus as a morning star. "

There is some more on Pythagoras at
http://www-history.mcs.st-and.ac.uk/~history.
Go to the search menu and search for "pythagoras". Hope this answers your question.

Best wishes,

Richard.