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Turning a sphere inside-out:

And part 2:

This is really, really cool. They describe things in really simple terms though (like referring to curvatures with smiles and frowns) and sometimes I wish I could connect it to the math that I know if relevant terms were brought up. The animations are simply amazing, and I can't believe this was made in 1994!

I was wondering if anyone knows if these people made other videos like this using their techniques... So cool!

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Related:… - videos for Mobius transformations, origami, the Poincare conjecture, and some other geometrically flavored topics. – anon Aug 29 '11 at 22:08
I have converted the question to community wiki, as it's asking for a list of examples and there is no single right answer. – Zev Chonoles Aug 30 '11 at 0:41
up vote 3 down vote accepted

Check out this Math Overflow thread! For instance, you may enjoy this video about the Möbius band.

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Niles Johnson at UGA recently posted this video he made illustrating the Hopf fibration:

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