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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
Minneapolis, MN 55454 U.S.A.
1-612-626-0888 (phone)
1-612-626-7131 (fax)
permission@geom.umn.edu (email: contact this address for information on how to link to the original, definitive versions, which is encouraged; permission to make copies for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or direct commercial advantage, and that copies bear a proper Geometry Center copyright notice; other uses may be permitted, contact the address indicated for futher information)

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Description



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 :

    http://www.geom.umn.edu/locate/oi/biblio.html

  • 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 :

    (oo)
    http://www.geom.umn.edu/locate/oi
  • 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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