Thursday, January 15, 2015

Chinese proved Pythagorean Theorem

I thought that the ancient Greeks invented the mathematical proof. Euclid's Elements gives an axiomatization of geomety, and proves the Pythagorean Theorem. But now I read this:
The Pythagoras theorem 'should either be an Egyptian theorem if you look at the standard of just having an idea about it, an Indian theorem if you're looking for a complete statement of it, or a Chinese theorem if you're looking for the proof of it,' Fields Medal winner and Princeton University Professor Dr Manjul Bhargava tells P Rajendran/ ...

"The Shuba Sutras do contain proofs in some special cases and contain numerical proofs in general, but the first actual rigorous proof of the Pythagorean theorem that's on record originates in China -- after the Shuba Sutra."

"So in China in school textbooks they often call it the Gougu theorem. And that was first given in a Chinese manuscript some years later (the Zhou Bi Suan Jing, the material for which dates back to sometime between the 1046 BC and 256 BC)."

"So maybe the statement of the theorem went from India to China, but the actual proof -- the complete, rigorous proof -- was given in China, at least as far as written records go. That's why the Chinese ... (named) the Pythagorean theorem after the person who first proved it (and) who was in China."
He sounds as if he knows what he is talking about, but the Chinese proof given on Wikipedia is only for the 3-4-5 triangle. I would not call that a complete rigorous proof. I also do not see any evidence that the Chinese even had an understanding of what a proof is. Yes, it appears that the diagram can be easily adapted to other right triangles, but a lot of things are easy in retrospect.

Proving a theorem requires postulates and logical deductions.

The zero is obvious in retrospect, and so are a lot of other math concepts. So is heliocentrism, and conservation of energy. There is often someone claiming in Wikipedia that some particular ancient civilization had these concepts. There is almost never clear-cut evidence of the concept. Euclid very clearly had the concept of a geometrical proof. It is doubtful that any previous civilization did.

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