2024-12-24

[public] 275K views, 37.7K likes, dislikes audio only

3Blue1Brown

The inscribed square/rectangle problem, solved using Möbius strips and Klein bottles.

Playlist with more neat proofs: https://www.youtube.com/playlist?list=PLZHQObOWTQDPSKntUcMArGheySM4gL7wS

Instead of sponsored ad reads, these lessons are funded directly by viewers: https://3b1b.co/support

An equally valuable form of support is to simply share the videos.

This argument was originally by Herbert Vaughan, appearing for examples in this issue of the Topology Proceedings.

https://topology.nipissingu.ca/tp/reprints/v06/tp06107.pdf

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-geometric-perspective-cracks-old-problem-about-rectangles-20200625/

Timestamps:

0:00 - Inscribed squares

1:00 - Preface to the second edition

3:04 - The main surface

10:47 - The secret surface

16:45 - Proving collision

22:38 - Why are squares harder?

25:10 - What is topology?

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These animations are largely made using a custom Python library, manim. See the FAQ comments here:

https://3b1b.co/faq#manim

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

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

All code for specific videos is visible here:

https://github.com/3b1b/videos/

The music is by Vincent Rubinetti.

https://www.vincentrubinetti.com

https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown

https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u

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