Pythagorean Theorem found on clay tablet 1k years older than Pythagoras (2009)

It needs to be renamed as the Tablet Theorem.

did they know about the Pythagorean theorem, or did they know about the square root of two? It seems that people did puzzle over this quantity for a while.

> Every group who ever managed to build a building with a rectangular foundation figured out the relation between the side lengths and the diagonal.

I don't see why that was necessary. You can get pretty far with eyeballing it and custom cutting to fit.

A "you" can, and many individual "you"s presumably did that, to general satisfaction. But the implicit assumption you made is that eyeballing and cutting is easy, while triangles are hard, even though it's the other way around, especially with stone age tools.

But we're talking about groups of people, "they", who all build a lot. Such groups tend to have a few people who make these observations, and then the observations proliferate, because they are both way easier to use than the alternative hack-work, and yield much more aesthetically pleasing results. Especially in the stone age when you nornally don't have easy access to anything at all with a right angle (unlike in modern construction) and you build stuff out of clay bricks, where minor inaccuracies inevitably add up and make your life much harder down the road. Tying together three pieces of string with prescribed ratios, pull it tight was a very easy way to get a right angle compared to anything that came before.

It's necessary in the sense that stone age construction is so much easier if you know about it, and so much harder if you don't. Those who didn't come up with it didn't do such construction, because doing difficult things is harder than doing easy things.

Pythagoras was specifically known for accumulating the wisdom of diverse cultures—supposedly he met Thales, was initiated as Egyptian priest in Hermopolis, spent time in Babylon after being captured, and was initiated into every mystery cult he could. And as a boy on his home island of Samos, he would have been exposed to the building of the largest stone temple in Ancient Greece (to Hera) and the incredible engineering feat of the tunnel of Eupalinos.

Iamblichus’s “life of Pythagoras” [1] is worth a read as he had access to all the old sources now lost. The relationship between math and spirituality was very strong back then!

There are lots of fun stories that may be true but no one will ever know. In Diogenes Laertius’ “Lives of the Philosophers,” it is claimed that when Pythagoras made his discovery of what we call the Pythagorean theorem, he sacrificed 100 oxen (a hecatomb) [1]. As noted by Charles Dodgson (Lewis Carrol), “that would produce an inconvenient supply of meat” [3], especially for a vegetarian. Iamblichus, on the other hand, claims it was a single ox — and made of flour!

[1] Guthrie, K. S., & Fideler, D. R. (Eds.). (1987). The Pythagorean sourcebook and library: an anthology of ancient writings which relate to Pythagoras and Pythagorean philosophy. Red Wheel/Weiser.

[2] “he sacrificed a hecatomb, when he had discovered that the square of the hypotenuse of a right-angled triangle was equal to the squares of the sides containing the right angle.” DL, found in [1]

[3] Maor, E. (2019). The Pythagorean theorem: a 4,000-year history. Princeton University Press.