Math That Makes You Go Wow

A Multi-Disciplinary Exploration of Non-Orientable Surfaces

Written and designed by Margaret Boittin, Erin Callahan, David Goldberg, and Jacob Remes
for Math 195a at Yale University. December 1998.





Click on the Chapter or Subchapter you wish to read. 
    Preface for Teachers 
  1. Introduction to Orientability:  A Fable 
  2. The Math of Non-Orientable Surfaces 
    1. Surface and Manifold
    2. Non-Orientable Surface 
    3. Orientable Surfaces:  Sphere, Torus
    4. Möbius Band
    5. Klein Bottle 
    6. Real Projective Plane 
    7. And Beyond: 3-Manifolds 
    8. What Would it Be Like to Live on a...?
    9. Homework Exercises about Math
  3. The History and Philosophy of Non-Orientability 
    1. The Original Topological Tyrant
    2. Klein Bottles and Kant
    3. Homework Exercises about History and Philosophy
  4. Literature 
    1. "The No-Sided Professor"
    2. "A Subway Named Moebius"
    3. Extra Short Stories
    4. The Bald Soprano
    5. The Gift
    6. Homework Exercises about Literature
  5. Music
    1. Bach and Schoenberg
    2. The Moebius Strip Tease
    3. If You're Musically Inclined...
    4. Homework Exercises about Music
  6. Other Topics 
    1. Knit Hats and Scarves
    2. Fun Toys on the Internet
    3. Non-Orientable Housing
    4. The Marvelous Moebius Molecule
    5. Moebius Mistakes
    6. Non-Orientable Surfaces in Art
    7. Homework Exercises on These Topics
  7. Bibliography 
A Klein Bottle; Created by Paul Bourke,

Graphic from Paul Bourke,
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