Using topology for discrete problems | The Borsuk-Ulam theorem and stolen necklaces

Video Description

Solving a discrete math puzzle using topology I was originally inspired to cover this thanks to a Quora post by Alon Amit Help fund future projects: https://www.patreon.com/3blue1brown An equally valuable form of support is to simply share some of the videos. Special thanks to these supporters: http://3b1b.co/borsuk-thanks Home page: https://www.3blue1brown.com Want more fair division math fun? Check out this Mathologer video https://youtu.be/7s-YM-kcKME (Seriously, Mathologer is great) These videos are supported by the community. https://www.patreon.com/3blue1brown The original 1986 by Alon and West with this proof https://m.tau.ac.il/~nogaa/PDFS/Publications/The%20Borsuk-Ulam%20Theorem%20and%20bisection%20of%20necklaces.pdf VSauce on fixed points https://youtu.be/csInNn6pfT4 EE Paper using ideas related to this puzzle https://dl.acm.org/citation.cfm?id=802179 I first came across this paper thanks to Alon Amit's answer on this Quora post https://www.quora.com/As-of-2016-what-do-mathematicians-on-Quora-think-of-the-3Blue1Brown-maths-videos If you want to contribute translated subtitles or to help review those that have already been made by others and need approval, you can click the gear icon in the video and go to subtitles/cc, then "add subtitles/cc". I really appreciate those who do this, as it helps make the lessons accessible to more people. Music by Vincent Rubinetti: https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown Time stamps: 0:00 - Introduction 0:36 - The stolen necklace problem 3:08 - The Borsuk Ulam theorem 9:15 - The continuous necklace problem 13:19 - The connection 17:30 - Higher dimensions ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted on new videos, subscribe: http://3b1b.co/subscribe Various social media stuffs: Website: https://www.3blue1brown.com Twitter: https://twitter.com/3blue1brown Reddit: https://www.reddit.com/r/3blue1brown Instagram: https://www.instagram.com/3blue1brown_animations/ Patreon: https://patreon.com/3blue1brown Facebook: https://www.facebook.com/3blue1brown