3Blue1Brown | Using topology for discrete problems | The Borsuk-Ulam theorem and stolen necklaces @3blue1brown | Uploaded 5 years ago | Updated 2 hours ago
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: 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: 3blue1brown.com
Want more fair division math fun? Check out this Mathologer video
youtu.be/7s-YM-kcKME
(Seriously, Mathologer is great)
These videos are supported by the community.
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
youtu.be/csInNn6pfT4
EE Paper using ideas related to this puzzle
dl.acm.org/citation.cfm?id=802179
I first came across this paper thanks to Alon Amit's answer on this Quora post
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:
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: 3blue1brown.com
Twitter: twitter.com/3blue1brown
Reddit: reddit.com/r/3blue1brown
Instagram: instagram.com/3blue1brown_animations
Patreon: patreon.com/3blue1brown
Facebook: facebook.com/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: 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: 3blue1brown.com
Want more fair division math fun? Check out this Mathologer video
youtu.be/7s-YM-kcKME
(Seriously, Mathologer is great)
These videos are supported by the community.
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
youtu.be/csInNn6pfT4
EE Paper using ideas related to this puzzle
dl.acm.org/citation.cfm?id=802179
I first came across this paper thanks to Alon Amit's answer on this Quora post
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:
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: 3blue1brown.com
Twitter: twitter.com/3blue1brown
Reddit: reddit.com/r/3blue1brown
Instagram: instagram.com/3blue1brown_animations
Patreon: patreon.com/3blue1brown
Facebook: facebook.com/3blue1brown
