YouTube sadly has some horrible bits, but there’s a subset of it that
has loads of fascinating math videos. Last week there was a
great one which showed a bizarre way to calculate pi using
a physics thought experiment.
He left the actual equations that explained why this happens to
a later video. Happilly it came out today. What it boils down
to is an interaction between the equations for conservation of
energy and the conservation of momentum. If you lay out the
equations the right way you end up with a circle and a series
of points on it.