Up: Geometry Center Video Productions

Outside In

The computer animation 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. Along the way, the narrators discuss the related case of closed curves and why they generally cannot be turned inside out. Everyday analogies such as train tracks, belts, smiles and frowns are used throughout, all richly animated and complete with sound effects.

Outside In is 22 minutes long and was produced at the Geometry Center under the direction of Silvio Levy, Delle Maxwell and Tamara Munzner. The 48-page, full-color book, Making Waves, introduces more precisely the mathematical ideas behind Outside In and develops them further.

Both the video and the companion book are available from A.K. Peters.

About Sphere Eversions:

Graphics from Outside In:

About the video Outside In:

Software for everting spheres:

You can download the C++ program, written by Nathaniel Thurston and used by the developers of Outside In. It will generate a representation of the everting sphere at any stage in terms of polygons or bicubic patches.

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