Hasn't this been known for decades now?<p>'According to (Hayashi 2005, p. 363), the Śulba Sūtras contain "the earliest extant verbal expression of the Pythagorean Theorem in the world, although it had already been known to the Old Babylonians.'<p><a href="https://en.wikipedia.org/wiki/Indian_mathematics" rel="nofollow">https://en.wikipedia.org/wiki/Indian_mathematics</a><p>I remember being taught that pythagoras probably got his math from the indians who possibly got it from mesopotamia.
Great talk for those interested in clay tablets and technology: <a href="https://www.youtube.com/watch?v=s_fkpZSnz2I" rel="nofollow">https://www.youtube.com/watch?v=s_fkpZSnz2I</a><p>In my opinion, I would bet that those old civilizations had more technology that we give them credit for. The only thing they lacked was to have a long lasting medium to share that knowledge. Whimsical stories or songs could've been a way to share advances. We're lucky to have one civilization picking clay tablets as a medium and luckier that those survived (some even by accident - fires destroying houses but cooking those tablets and burying them), who knows maybe we were writing on leather for centuries before that have all disintegrated by now (we hunted, we had access to paint, we naturally don't want to waste scarce resources).
Although this archeological find relates to Pythagorean Triples, my take is that one of the most basic concepts in carpentry, the "3-4-5" rule for finding right angles, which is described by Euclid and is certainly related to the Pythagorean theorum, now would logically seem to have been used much earlier. The 3-4-5 rule holds that a right angle is deduced by marking 3 equal units on the x axis, then drawing a wide arc of 4 of the same units somewhat orthogonally (appearing to go both plus and minus) from point 0 of the x axis, then marking the point from the top of the x axis to the point on the arc at which the gap is exactly 5 of the same units. The result is a right angle. By using a plumb bob to create a vertical x axis in the first place, the resulting y axis is thus horizontal. The 3-4-5 rule is and was essential in structural work, so I'm suggesting that meaningful contributions to architecture and other pursuits were made using the 3-4-5 rule long before the use of trigonometry as we know it from Pythagorus, so any move of the Pythagorean Triples timeframe would thus apply to the timeframe of the 3-4-5 rule. I hope someone will correct any errors/delusions in my summary.
Actual source: [Mansfield, D. F. (2020). <i>Perpendicular Lines and Diagonal Triples in Old Babylonian Surveying</i>. Journal of Cuneiform Studies, 72, 87–99. doi:10.1086/709309](<a href="https://sci-hub.se/http://dx.doi.org/10.1086/709309" rel="nofollow">https://sci-hub.se/http://dx.doi.org/10.1086/709309</a>). The "Si." is short for [Sippar](<a href="https://en.wikipedia.org/wiki/Sippar" rel="nofollow">https://en.wikipedia.org/wiki/Sippar</a>).<p>From a quick skim, this seems to indeed bolster Wildberger's theory about the Babylonians' use of Pythagorean triples (actually the theory predates Wildberger, but he is its main proponent). This theory claims that the triples were used as a proto-trigonometric table, a ready-made set of rational-sided right-angled triangles, as irrationals were not expressible in Babylonian numerals. (Of course, Wildberger draws motivation for his "rational trigonometry" from this, although it is a mathematical theory that needs no historic motivation.) In contrast, the more mainstream theory is that the Pythagorean triples were a product of "scribal training" or mathematical puzzle-solving (like the Japanese sangakus). This mainstream theory, despite sounding like a cop-out, still has a lot speaking for it (see [Eleanor Robson, <i>Neither Sherlock Holmes nor Babylon: a reassessment of Plimpton 322</i>, Historia Mathematica, Volume 28, Issue 3, August 2001, Pages 167-206](<a href="https://ora.ox.ac.uk/objects/uuid:e3d8eedb-e745-45b3-8612-71f8951599aa" rel="nofollow">https://ora.ox.ac.uk/objects/uuid:e3d8eedb-e745-45b3-8612-71...</a>), particularly pp. 183--185, for some rather convincing context). But the two can in fact be combined: who said puzzles cannot be built out of applied problems? (Many a math contest problem arose this way.)
This was "discovered" some time ago : <a href="https://en.wikipedia.org/wiki/Plimpton_322" rel="nofollow">https://en.wikipedia.org/wiki/Plimpton_322</a>