An older 3Blue1Brown video on why topology matters, built around the inscribed rectangle problem. It walks through how tori and Mobius strips appear in the solution. The channel later replaced it with an updated version.
Why Hacker News points people here: Fans name it as a favorite 3Blue1Brown video, praising its detective-story treatment of the inscribed square and rectangle problem.
“A particular favourite is the one on the Inscribed Square Problem”HN comment, 2018
“One of my favorite videos from his channel is "Who cares about topology? (Inscribed rectangle problem)”
Elegant inscribed rectangle problem where torus and Mobius strip appear.
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3Blue1Brown explanation of eigenvectors and eigenvalues is very insightful and intuitive [1]. One of my favorite videos from his channel is "Who cares about topology? (Inscribed rectangle problem)" [2]. They way a Torus and Möbius Strip come up as solution to the problem is so elegant. [1]: link [2]: this video
Strongly recommendsrocquaAug 2017
“I'd still wholeheartedly recommend his other videos though.”
Topological result on inscribed rectangles in closed loops.
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I really like 1blue3brown, but this one didn't quite resonate with me. To me, it felt like a long winded way to make it intuitive that the point (1, 1 ... 1) has distance sqrt(n) from the origin, where n is the number of dimensions. I think there'd be move value in explaining things like 'most volume is near the edge' and 'most points are far apart'. Granted, that is less about building intuition, and more about specifically dispelling heuristics from 2 and 3 dimensions. I'd still wholeheartedly recommend his other videos though. Especially [1] where he gives a very nice topological result regarding inscribed rectangles in closed loops. In the same vein is [2] proving the borsuk-ulam theorem. [1] this video [2] link
Strongly recommendsthicknavyrainJul 2018
“A particular favourite is the one on the Inscribed Square Problem”
Detective-story style walkthrough of the inscribed square problem.
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That's really interesting. I found that I loved, similar to the occasional video numberphile does, watching Grant explain how one might realistically solve an interesting problem. A particular favourite is the one on the Inscribed Square Problem, which, although introducing some elements of topology, engages me more from the get go. He poses a problem and my curiosity keeps me engaged until the very end, it feels a bit like a detective story, I get the same satisfaction as some of the better Sherlock Holmes stories where in the course of reading I think "Damn, I could have come to that conclusion if I'd paid a bit more attention!". this video
RecommendskmillJun 2020
“Here's a nice 3blue1brown video about the easier version of the inscribed rectangle problem”
Nice treatment of the easier inscribed rectangle existence version.
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Here's a nice 3blue1brown video about the easier version of the inscribed rectangle problem, that some inscribed rectangle exists: this video And I remember thinking this was a nice overview of some aspects of the "square peg problem" (the Toeplitz conjecture): link
