This is really slick, but it was a bit of a puzzle for me trying to turn it into a paper proof! After a few minutes, I realized that you can do it by induction on the number of vertices: it's trivial for n = 3, and if it holds for n - 1, slice off a corner and see what happens.https://twitter.com/ThingsWork/status/1121857148068065280 …
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Thinking about deleting the tweet because my approach was so inadequate TBH
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The animation reminds me a little of a Russian book on proving geometry results using "kinematics". From the MIR math books translated to all languages in the Soviet era. Highly coveted by Mexican math nerds.
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I forget which Soviet mathematician was very insistent that mathematics is just the part of physics one can do without experiments.
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Found it, V. I. Arnold https://www.uni-muenster.de/Physik.TP/~munsteg/arnold.html …
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I think his argument goes way too far but it's certainly true that I took years of graduate algebraic geometry without any damn idea what it was for.
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I do sometimes pick up Ravi Vakil's algebraic geometry notes. They're great. But they get really hard fast even if it's probably the friendliest intro to real alg geometry.
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I'm an algebraist and I have a decent handle on group theory, representation theory, algebraic topology etc. But I self-studied Hartshorne before my PhD program and took a lot of courses in algebraic geometry during, and never understood the point.
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. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems.