Shadows from Higher Dimensions

  • George K. Francis


A hemispherical bowl has a single, circular edge. So does a disc. If you sew the disc to the hemisphere you obtain a closed, two-sided surface; it has an inside and an outside. Topologists still call this a sphere, and it could be inflated back to a geometrical sphere if you like. Now take a long, narrow strip of paper, give it a half twist and glue the ends together. The resulting surface is not only one sided, it has but a single, closed edge. What happens if this edge is sewn to the rim of a disc?


Projective Plane Triple Point Elliptical Generation Klein Bottle Picture Plane 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 2007

Authors and Affiliations

  • George K. Francis
    • 1
  1. 1.Department of MathematicsUniversity of Illinois at Urbana-ChampaignUrbanaUSA

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