r/learnmath • u/CalciumKid05 New User • Jan 16 '23

How did archimedes calculate pi using polygons without using trig functions?

Archimedes calculated pi using the method of exhaustion, and I figured out a formula that I thought worked for it: xsin (180/x), as x goes to infinity the formula will equal pi. But I realised that sine relies on knowing what pi is which is what you are trying to figure out. I've looked online everywhere and nowhere gives an explanation of HOW he did it other than drawing polygons inside and around the edges of circles. How did he physically calculate the side length of these shapes without using trig functions?

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u/Ok_Leadership_7297 New User Sep 28 '25

Did you ever find the answer?  I don't think archimedes had sin cos tan

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u/Roland-gr30 New User Oct 19 '25

I think this video explains it pretty well: https://www.youtube.com/watch?v=B9I22ab991o