i’m so bad at billiards that i ended up in the hyperbolic plane

🌏 Upgrade your online protection with an all-in-one security app! ➵ https://nordvpn.com/twoswap It’s risk free with Nord’s 30 day money-back guarantee!✌ Sources and footnotes: Professor Schwartz's paper treating the penrose kite, shown in the video: https://arxiv.org/abs/math/0702073 Dr. Lael Edwards-Costa's Interactive Demo: https://lael.dev/billiards His paper on outer length billiards, a variation of the rules discussed in the video: https://arxiv.org/pdf/2510.11869 His blog post about Outer Billiards which inspired this video: https://structures.uni-heidelberg.de/blog/posts/2024_01_costa/index.php [1] Tabachnikov (1995), establishing self-similar structure of outer billiards on the regular pentagon: https://www.math.brown.edu/reschwar/M272/advances.pdf [2] Hughes (2014), on the behavior of regular polygonal tables: https://arxiv.org/pdf/1311.6763 Hughes also provides this website with many beautiful pictures of billiards maps on the regular polygons: https://www.dynamicsofpolygons.org/ This video was inspired by David J. Romano. He's got something cool in the works for y'all in a few months...! Check him out: https://davidromano.dev If you liked this, please support me on Patreon! https://www.patreon.com/c/2swap Check out 6884's other music here! https://6884.bandcamp.com/ Or support him on Kofi: https://ko-fi.com/iam6884 This video was animated using SwapTube! https://github.com/2swap/swaptube