Turning a sphere inside-out: http://www.youtube.com/watch?v=BVVfs4zKrgk
And part 2: http://www.youtube.com/watch?v=x7d13SgqUXg
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!