Probability isn’t always about randomness (#SoME2)

CORRECTION : at 3:15, the edge of lengths of the parallelotope must of course be of length less than 1 for the result to hold, my bad. vvv NO MUSIC, SCROLL DOWN FOR INFO vvv An excursion into a problem of higher-dimensional geometry and its surprising probabilistic solution. Special thanks to my brother for greatly helping me out with the audio side of this project, and to the SoME2 Discord server for being a nice community in which to have worked on this. Image credit : Photo at 06:01 : Myrabella / Wikimedia Commons / CC BY-SA 3.0 & GFDL Chapters : 00:00 Parallelotopes 05:53 Probability?? 08:34 A Monte Carlo proof 16:55 …and it works! 19:16 Tying up loose ends 20:43 Conclusion : Gratitude Music : I didn't bother adding music because the contest is really stringent when it comes to copyright, and also because it isn't that necessary. Though If you feel like silence is going to be too heavy, here's something to listen to at low volume :    • Klaus Schulze - Sequenzer (from 70 to 07)