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About the Outside In Sphere Eversion

Outside In is a 22-minute computer generated video about turning a sphere inside out produced at the Geometry Center.

Overhead view of sixteen stages of the eversion
Interactive 3D (VRML/WebOOGL) demo

Distributed by

  AK Peters, Ltd.
  289 Linden Street
  Wellesley, MA  02181
  phone: (617) 235-2210
  fax:   (617) 235-2404
  email:  kpeters@math.harvard.edu

Stay tuned for more online materials...

Abstract

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. The sphere eversion has a rich history in both mathematics and computer graphics. Outside In illustrates Bill Thurston's method, invented in 1974.

We bring the sphere eversion to a general audience by using nontechnical language and exciting graphics to present a comprehensible, step-by-step exploration which retains mathematical depth. Our ground rules introduce the concept of a "regular homotopy" from topology, which is traditionally not encountered until advanced undergraduate mathematics classes. Although Outside In is accessible to a broad audience, it and its written supplement are the first public presentation of Thurston's theory of corrugations, which has wide applicability in differential topology.

Bibliography

Silvio Levy, Delle Maxwell, Tamara Munzner. Outside In. AK Peters, Ltd. 1994 (video).

Silvio Levy. Making Waves, A Guide to the Ideas behind Outside In. AK Peters, Ltd. 1995.

Anthony Phillips. Turning a surface inside out. In Scientific American, 112--120, May 1966.

Nelson Max. Turning a Sphere Inside Out. International Film Bureau, Chicago, 1977 (video).

Awards

As of March 1995 Outside In has won the following honors:

SIGGRAPH Electronic Theater 1994 (8 minute excerpt shown)
SIGGRAPH Screening Room 1994 (full version shown)
Gold LEAF Award (London Effects and Animation Festival) 1994 (1st, Education and Training category)
NICOGRAPH Award 1994 (1st, Public category)
Prix Pixel INA Imagina 1995 (2nd, Simulation-Visualization category)

The video will be part of a new exhibit on Modern Mathematics to open at the Maryland Science Center in June. It has been shown on public television in several nations, including Spain, France, and Germany. It has also been shown at other conferences which do not give out video awards, including SIAM (Society of Industrial and Applied Mathematics, San Diego) and FISEA (Fifth International Symposium of Electronic Arts, Helskinki).

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