This post contains a derivation of a recurrence relation that can be used to calculate $\pi$. While it's not useful for the purpose of calculating to any decimal place imaginable, what's notable is that it only uses the Pythagorean thereom and should therefore be easy to follow. Unsurprisingly, the recurrence relation is neither original nor unique because it falls under the category of using polygons to compute $\pi$ (attributed to Archimedes). At the end of the notebook, the derived recurrence relation is implemented in code and run.
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