2018-11-18

[public] 505K views, 28.6K likes, 131 dislikes audio only

3Blue1Brown

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

/youtube/video/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

/youtube/video/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

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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:

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