Sphere Eversions: from Smale through “The Optiverse”

  • John M. Sullivan
Part of the Mathematics and Visualization book series (MATHVISUAL)


For decades, the sphere eversion has been a favorite subject for mathematical visualization. The 1998 video The Optiverse shows minimax eversions, computed automatically by minimizing elastic bending energy using Brakke’s Evolver. We contrast these geometrically optimal eversions with earlier ones, including those by Morin, Phillips, Max, and Thurston.


Triple Point Soap Film Topological Event Round Sphere Quadruple Point 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • John M. Sullivan
    • 1
  1. 1.Mathematics Dept.Univ. of IllinoisUrbanaUSA

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