I have a pi-day challenge for all the physics students among you (or anyone willing to set up an experiment). If you share your results with me by March 10th, I may feature them in a video, depending on how good the results are and how many I get.
Many years ago I made this video about how two colliding blocks on a frictionless plane can compute pi. My challenge to you is simple: Implement this in practice.
The original puzzle assumes zero friction and zero energy loss in collisions, so obviously there are limits to how far you can get. I can tell you the real limiting factor is energy lost in collisions, more so than friction.
Also, it's a wildly inefficient way to compute pi, to even get "3.14" you'd need this to work with a 10,000-to-1 mass ratio and have a way to count all 314 collisions. Matt Parker and I actually gave this a go, and the results were...okay, but could definitely have been improved :)
Note, there's no reason to restrict yourself to powers of 100. For example, you could use powers of 4 to compute pi in binary. A mass ratio of 64-to-1 should give 25 collisions, which is 11001 in binary, and pi looks like 11.001...
More generally, with a mass ratio of N-to-1, the number of collisions is around π / arctan(1 / sqrt(N)). So any big mass ratio gives you an approximation of pi by multiplying the number of collisions by arctan(1/sqrt(N))
If you do this, you can reach out to the channel via this page:
3blue1brown.com/contact
Be sure to have a link to footage of the experiment. If anyone can get it to work with 100-to-1, I'd be happy, and if anyone can do it for 10,000-to-1, I'd be both delighted and amazed.