Outside In

Discusses the problem of turning a sphere inside out without creating sharp bends or creases, illustrating an application of turning points

Outside In explains the amazing discovery, made by Steve Smale in 1957, that a sphere can be turned inside out by means of smooth motions and self-intersections. Through a combination of dialogue and exposition accessible to anyone who has some interest in mathematics, Outside In builds up to the grand finale: Bill Thurston’s “corrugations” method of turning the sphere inside out.