Outside in

© 1994 by The Geometry Center. All rights reserved. For further information, or permission to duplicate, please contact:
The Geometry Center
1300 South Second Street, Suite 500
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Jpeg Image (16 Ko)



Video(s) and extracted images: 320*240

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Jpeg Images -> (2 Ko) (2 Ko)


Outside In illustrates an amazing mathematical discovery made in 1957: you can turn the surface of a sphere inside out without making a hole, if you think of the surface as being made of an elastic material that can pass through itself. Communicating how this process of eversion can be carried out has been a challenge to differential topologists ever since. Computer graphics helps to explain as well as present the visual elegance of this process.

Technical Information

  • Software: Custom, RenderMan, Softimage, Mathematica, Geomview, Perl
  • Hardware: Silicon Graphics

More Information...

  • Bibliography :

  • Abstract :

    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. With 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 -- by discussing the related case of closed curves (which generally cannot be turned inside out) and by using everyday analogies such as train tracks, belts, smiles and frowns -- all richly animated and complete with sound effects.

  • Some external links :

  • Some more Comments :

    If you have any questions about this information, please contact: Carol Scheftic at The Geometry Center (telephone: 612-626-8325).

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