Pythagorean Theorem Found On Clay Tablet 1,000 Years Older Than Pythagoras
But while Pythagoras was an important historical figure in the development of mathematics, he did not figure out the equation most associated with him (a2 + b2 = c2). In fact, there is an ancient Babylonian tablet (by the catchy name of IM 67118) which uses the Pythagorean theorem to solve the length of a diagonal inside a rectangle. The tablet, likely used for teaching, dates from 1770 BCE – centuries before Pythagoras was born in around 570 BCE.
Another tablet from around 1800–1600 BCE has a square with labeled triangles inside. Translating the markings from base 60 – the counting system used by ancient Babylonians – showed that these ancient mathematicians were aware of the Pythagorean theorem (not called that, of course) as well as other advanced mathematical concepts.
"The conclusion is inescapable. The Babylonians knew the relation between the length of the diagonal of a square and its side: d=square root of 2," mathematician Bruce Ratner writes in a paper on the topic. "This was probably the first number known to be irrational. However, this in turn means that they were familiar with the Pythagorean Theorem – or, at the very least, with its special case for the diagonal of a square (d2 = a2 + a2 = 2a2) – more than a thousand years before the great sage for whom it was named."
So why did this get attributed to Pythagoras? No original writing from Pythagoras survives. What we know of him was passed on by others, in particular the Pythagoreans – members of a school he set up in what is now modern-day southern Italy. The school, named the Semicircle of Pythagoras, was secretive, but knowledge learned there or discovered was passed on, and often attributed to the man himself.
https://www.iflscience.com/pythagorean-theorem-found-on-clay-tablet-1000-years-older-than-pythagoras-70934
I posted this in error earlier in the video forum.
= new reply since forum marked as read
of how much you need to set the next layer of blocks it to produce a stable pyramid (eg "if your block is 4 cubits high, you must set the next layer at least 3 and a quarter cubits in" or whatever).
See eg the "Bent Pyramid" from a bit earlier:
Unfortunately, the building technique that was used -a technique going back to the Step Pyramids which consisted of using inward leaning courses- did not help to stabilise this monument. Fearing that the pyramid would collapse under its own weight, its slope was lowered to 43°22' somewhere halfway up the building. It is possible that the upper part of the Bent Pyramid was continued only after finishing the Red Pyramid, which was built a couple of kilometres to the North of the Bent Pyramid. In any case, the Red Pyramid has exactly the same slope of 43°22' as the upper part of the Bent Pyramid. In its finished state, this pyramid has a base length of 188 metres and is 105 metres high.
http://www.ancient-egypt.org/history/old-kingdom/4th-dynasty/snofru/pyramids/bent-pyramid-at-dashur.html
To get the sides all to meet at a point, you just do the same thing on all 4 sides. And if they did use angles like us - measured as a fraction of a complete circle - that doesn't need Pythagoras' theorem. That only comes in when you're calculating the diagonal lengths.
