Here we look at classic proof explaining the pi in a Gaussian distribution, originally due to Poisson, which is just wildly fun to animate. On its own the proof feels out of the blue, so we also delve into the Herschel-Maxwell derivation for where a Gaussian comes from in the first place, and how it makes the famous proof much more reasonable.

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Can you do a video on the connection between hyperbolic trig functions and the real exponential. If you integrate any linear exponential across a symmetric domain it converges to a sinh. Catenary curves and the drag coefficient are applications of this fact.