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> Pythagorean triples to measure right angles ... But that's not a theorem, just an observation. It becomes a theorem when you prove (i.e. explain why) this rel
by fsckboy 3y ago
> Pythagorean triples to measure right angles ... But that's not a theorem, just an observation. It becomes a theorem when you prove (i.e. explain why) this relationship always holds, based on more evident things. The Babylonian tablet mentioned in the article doesn't seem to do anything like that
according to the article, this Babylonian tablet does come closer to theorem than you are suggesting. They weren't using Pythagorean triples, rather they figured out that the diagonal of a unit square is the square root of 2, and knew how to calculate that:
1 + 24/60 + 51/602 + 10/603 = 1.414213
- hyperthesis 3y agoAgree it's closer but still an instance.
- fsckboy 3y agodepends on the method they used to come up with the formula. It's not obvious that the sum of a "more complicated than you can do in your head" series of fractions would be either the square root of two or the the diagonal of a square, let alone both. This is a fragment of a single clay tablet. If they had a systematic method of coming up with this convergent series, there might have been a stack of tablets showing square root of three, five, etc. It seems pretty highly suggestive to me.
- ssener2001 3y agoI agree.Obtaining this formula by observing is more difficult than obtaining it by proving it. Besides, it is an issue that is already needed in field work. If you have pen, paper and a good number system, it shouldn't be too difficult to find the formula with shapes.
- posterboy 3y agoProof by construction, the Curry-Howard correspondance.