Turning a sphere inside out

    This video does not give a lot of specifics but it is interesting. In simple terms, the challenge is all about avoiding sharp bends while inverting a circle with the unusual characteristic of having a surface that can pass through itself.
   I urge you to watch a second video discussing the process in detail. It is presented here: "Sphere Inside Out Part II."
   You can question the exercise's relevancy, but in my opinion solving such mathematical puzzles is inherently valuable if not for exercising the human mind alone. Both the mathematical calculations needed to solve it and the animation are admirable.
   See also:

• Smale's paradox     
• The Optiverse