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

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

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:

Nice Quanta article about this result:

Timestamps:

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

All code for specific videos is visible here:

The music is by Vincent Rubinetti.

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