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So if I'm understanding correctly, this is evidence that about 300 years after the death of Pythagoras, his proof "travelled" over the silk road to China?
by elevensies 10y ago
So if I'm understanding correctly, this is evidence that about 300 years after the death of Pythagoras, his proof "travelled" over the silk road to China?
- dmoy 10y agoOr it was independently recreated.
- platz 10y agoIt could've been used without being proved also
- idreyn 10y agoThe diagrams on the pages shown basically serve as a proof.
- theoh 10y agoIt's familiar from hands-on science museums to see a particular case of the Pythagorean theorem illustrated concretely with diagrams or liquid on a rotating plexiglass panel... But surely those aren't proofs, just illustrations. A proof needs to abstract over all possible right-angle triangles.
- greglindahl 10y agoBoth diagrams are a proof over all right-angle triangles, if you know algebra. See the very first comment after the images.
- theoh 10y agoHmmm. Maybe I'm just used to the convincing generality of the similarity argument (from Euclid, via Polya): https://math.berkeley.edu/~giventh/papers/eu.pdf https://math.berkeley.edu/~giventh/papers/eu.pdf But also, we can't trust geometrical diagrams: https://en.wikipedia.org/wiki/Missing_square_puzzle https://en.wikipedia.org/wiki/Missing_square_puzzle
- jacobolus 10y agoThere’s evidence that the “Pythagorean Theorem” was known in Mesopotamia a millennium before Pythagoras. It was likely widely known in the ancient world. The Greeks wrote their mathematical ideas in a different way than other cultures, so the answers to these questions aren’t completely clear-cut.
- kobeya 10y agoBut was the theorem proved?
- jacobolus 10y agoIt’s really hard to say. Cuneiform on clay tablets was mostly records of finished computations, with the scratch work done with some kind of physical manipulation of tokens or mentally, and most of the instruction and culture transmitted orally. The Sumerian/Babylonian style of written records did not match, say, Euclid’s Elements. (They didn’t write books full of precise definitions and proofs. They didn’t leave behind textbooks, only problem sets and worked examples.) But note that neither did the style of the Pythagoreans necessarily, and the notion that Pythagoras or his disciples made a proof comes from written records from hundreds of years later.
- fuck_google 10y agoThe proof is so trivial that it is pretty much given once you discover the theorem.
- matt_wulfeck 10y agoI was thinking the same thing. It's easy to forget just how much the ancient Greeks accomplished 2,500 years ago.
- pjmlp 10y agoI always wonder myself when I get to read ancient manuscripts and get to compare with modern days. As humans we always lived a kind of ups and downs, regarding use of technology, relationships among countries, how open/closed the societies used to be, how travelling was seen and so on. For example, in the ancient world there was already a kind of Erasmus, as Greek medicine students used to spend a few years with Egyptian doctors before getting back home and start practising.
- kccqzy 10y agoFrom Wikipedia: > Mesopotamian, Indian and Chinese mathematicians all discovered the theorem independently and, in some cases, provided proofs for special cases.