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: Instead of sponsored ad reads, these lessons are funded directly by viewers: 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. The onscreen argument for why all closed nonorientable 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: . .., 3Blue1Brown, Mathematics, threeblueonebrown, 3blue1brown, 3b1b, 3brown1blue, 3brown1blue, threebrownoneblue 20241224 IQqtsmbBRU
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