“you can completely turn that sphere inside out without creating any holes or creases[1].”
Sphere eversion without creases
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> 19. Given a solid ball in 3‑dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different way to yield two identical copies of the original ball. While you're at it, you can completely turn that sphere inside out without creating any holes or creases[1]. [1] this video
Cites itykonstantApr 2022
“Here are two classic youtube videos on the topic of sphere eversion”
Classic sphere eversion video
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Here are two classic youtube videos on the topic of sphere eversion; they mostly overlap, but I am posting both for double the hilarity in the comment sections :) (the full 21 minute one) this video (the first 10 minutes) link If I remember correctly, I think the 10 minute one has the more hilarious comment section.
Cites itgosub100Jan 2025
“here's a 20m video explaining how to invert a sphere without tearing it”
Explains turning a sphere inside out
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Sort of a tangent, but here's a 20m video explaining how to invert a sphere without tearing it: this video