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Saturday, October 28, 2017

Babylonian Trig, Part 2

A plot of the first 47 Pythagorean Triples - Jrkenti
I'm looking at the numbers from the Babylonian Cuneiform Tablet Plimpton 322 and I notice that one triangle (#11) can be scaled way down. Divide all sides of #11 by 15 and you have your basic 3, 4, 5 right triangle. Then I look at the others and I notice that one side of every triangle can be factored using only the numbers, 2, 3 and 5. Well, all except #3. All the rest are prime numbers. This leads me to Euclid's formula for generating Pythagorean Triples. Working backwards I figure out what the values are for l and m, and factored them, and what do you know? The only factors of l and m are 2, 3  and 5, well, except for #3. I don't know if this proves anything, except maybe that Oswald killed Kennedy, or maybe it proves the reverse. In any case figuring this all out kept me entertained for a couple of hours. The spreadsheet has three pages. The first is the original data, the second converts the numbers to decimal and verifies some obscure mathematical assertion that some other egghead figured out, and the third contains the triples and their factors.

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