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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Draw a set of lines, each parallel to one of the polygon's sides, but all of them going through the same point (concurrent). Each exterior angle of the poly is congruent to one of the angles in that arrangement, and the latter add up to a circle "by inspection".
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Ah yeah, that sounds pretty much like the 'spider proof'
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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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. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems.