How to derive a formula for π

A link to the full video is at the bottom of the screen.
Or, for reference: https://youtu.be/NaL_Cb42WyY

That video explores how this question leads to a quandary on prime numbers, and how a pattern in primes allows for a clean final answer.

Editing from long-form to short by Dawid Kołodziej
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https://www.youtube.com/watch?v=R1e7aHBKLnM