How has Pythagoras influenced mathematics?

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Pythagoras’ influence to mathematics is really immense. He used to be fascinated with numbers and explored odd and even numbers, prime numbers, ratios, rational and irrational numbers etc. He proved a 1000 year-old Babylonian idea that parts of right triangles are related in size and put it in a theorem that famously bears his name. He made pioneering contributions on basic solid shapes, and was able to construct most of these shapes. The geometry theorem, explanation of musical harmonics in terms of numbers, harmonic progressions, correct astronomical calculations - all these are wonderful examples of pythagorean mathematical ideas successfully applied to real life phenomenon.

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