3Blue1Brown: The most unexpected answer to a counting puzzle and So why do colliding blocks compute pi? and How colliding blocks act like a beam of light…to compute pi. (YouTube, 5:12min and 15:15min and 14:40min)
The connection between the initial experiment and the calculation of π is surprising, and finding two different solutions in physics is even more astounding. The videos are extremely well done, and the presentation helps a lot with understanding the mathematical manipulations.
Link via Futility Closet.