this post was submitted on 19 May 2025
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AFAIK the Chinese knew that the value between that of the encompassing shape that meets the circle at tangeants to the inscribed shape whose edges meet the same equidistant points gives us the approximation of pi. So did archimedes, and maybe even the babylonians.
So while a triangle yields about 3 and satisfies the theorem, you could also theoretically draw a 96 gon and 192 gon like Liu Hui for an accuracy of 9x10^5.
Personally I just memorize 22/7 or use the Leibniz infinite series if I have to.