Last edited 14aug00

Forty Years of Sphere Eversions

George Francis

For more than forty years descriptive topologists have drawn pictures, built models, programmed computers and made videos of how to turn a sphere inside out. We trace the evolution and revolution in graphical techniques invented to render the sphere eversions of Arnold Shapiro, Tony Phillips, Bernard Morin, Charlie Pugh, Nelson Max, John Hughes, Francois Apery, Bill Thurston, and John Sullivan. Videos, still pictures and real-time interactive computer animations will illustrate my story.