A quick websearch turns up the 'Spider Theorem': Imagine a spider crawling around the polygon counterclockwise. At each vertex it makes a left turn. When it's gone around the entire perimeter, it's made one complete rotation, which must be the sum of the left turns!
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But this is another example of a slick idea that's surprisingly tricky (but productive) to pin down, and eventually leads to the idea of a 'connection': https://en.wikipedia.org/wiki/Connection_(mathematics) …
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Doesn't it suggest a proof by bijection against the angles in a parallel arrangement of lines, all concurrent? Or is that tricky to make rigorous?
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Not sure what you mean, sorry
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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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Does cutting off a corner necessarily prove it for all n+1-gons? It strikes me there could exist n+1-gons that aren't a corner cut off an n-gon, maybe hole in the induction.
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Oh, like a rectangle, yeah. You'd have to cut a 'triangle' with two right angles and a vertex at infinity. Good point. Well, the spider proof is easier anyway.
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. Banned in Sweden. SubGenius, Zhuangist, white-hat troll. Defrocked mathematician. Brain problems.