Скачать или смотреть This open problem taught me what topology is

The inscribed square/rectangle problem, solved using Möbius strips and Klein bottles.
Playlist with more neat proofs:    • Puzzles with beautiful solutions  
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This argument was originally by Herbert Vaughan, appearing for examples in this issue of the Topology Proceedings.
https://topology.nipissingu.ca/tp/rep...

The on-screen argument for why all closed non-orientable surfaces must intersect themselves in 3d is a slight variation on one I heard from Dan Asimov.

2020 Paper by Greene and Lobb:
https://arxiv.org/pdf/2005.09193

Nice Quanta article about this result:
https://www.quantamagazine.org/new-ge...

Timestamps:
0:00 - Inscribed squares
1:00 - Preface to the second edition
3:04 - The main surface
10:47 - The secret surface
16:45 - Klein bottles
22:38 - Why are squares harder?
25:10 - What is topology?

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https://github.com/3b1b/manim
https://github.com/ManimCommunity/manim/

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The music is by Vincent Rubinetti.
https://www.vincentrubinetti.com
https://vincerubinetti.bandcamp.com/a...
https://open.spotify.com/album/1dVyjw...

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