Topology in Discrete Math: Borsuk-Ulam & Necklaces

Solving a discrete math puzzle using topology
I was originally inspired to cover this thanks to a Quora post by Alon Amit
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Want more fair division math fun? Check out this Mathologer video
https://youtu.be/7s-YM-kcKME
(Seriously, Mathologer is great)

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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

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