Geometric analogy to the colliding blocks setup that computes π

The physics behind one of the most surprising occurrences of pi Next video on Grover's Algorithm: https://youtu.be/RQWpF2Gb-gU Instead of sponsored ad reads, these lessons are funded directly by viewers: https://3b1b.co/support An equally valuable form of support is to simply share the videos. The original paper by Gregory Galperin: https://www.maths.tcd.ie/~lebed/Galperin.%20Playing%20pool%20with%20pi.pdf Adam Brown's paper on the analogy with Grover's Algorithm: https://arxiv.org/pdf/1912.02207 Here's a lovely interactive built by GitHub user prajwalsouza after watching this video: https://prajwalsouza.github.io/Experiments/Colliding-Blocks.html Matt Parker's Pi Day video: https://youtu.be/vlUTlbZT4ig NY Times blog post about this problem: https://wordplay.blogs.nytimes.com/2014/03/10/pi/ Timestamps: 0:00 - Intro 0:48 - Recap, the surprise pi 3:58 - How to analyze the blocks 13:30 - The geometry puzzle 18:35 - Small angle approximations 23:30 - The value of pure puzzles SEV#7: https://youtu.be/RTCQYcOpmN4 The original version of this explanation (now unlisted): https://youtu.be/jsYwFizhncE ------------------ These animations are largely made using a custom Python library, manim. See the FAQ comments here: https://3b1b.co/faq#manim https://github.com/3b1b/manim https://github.com/ManimCommunity/manim/ All code for specific videos is visible here: https://github.com/3b1b/videos/ The music is by Vincent Rubinetti. https://www.vincentrubinetti.com https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. If you're reading the bottom of a video description, I'm guessing you're more interested than the average viewer in lessons here. It would mean a lot to me if you chose to stay up to date on new ones, either by subscribing here on YouTube or otherwise following on whichever platform below you check most regularly. Mailing list: https://3blue1brown.substack.com Twitter: https://twitter.com/3blue1brown Instagram: https://www.instagram.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Facebook: https://www.facebook.com/3blue1brown Patreon: https://patreon.com/3blue1brown Website: https://www.3blue1brown.com