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The Geometry Center (Click image or here for video) Mathematicians are awesome. Don't believe me? Check out this 1994 animation, Outside In (I'd never seen it), which shows how to "evert" a sphere, or turn it inside out without tearing, pinching or creasing it. Letting it pass through itself is allowed. Click here for a history of sphere eversions and their visualizations, in which you'll discover that the Outside In method is actually more elaborate than necessary. (Gratuitous plug: The cover of the October 1993 SciAm depicted a step in the eversion process.) via John Baez by way of Scott Aaronson