For Further Reading

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 
We are indebted to several websites and books for our understanding of non-orientable surfaces.  You may wish to look at some of these, either as part of the class or for your own interest.  Although many of these books may be found at a good library (particularly a university library), we have included links to Amazon in case you should need to buy a copy. 


"Math That Makes You Go Wow" refers to several books and short stories. The best source for mathematical short stories we have found is the classic Fantasia Mathematica by Clifford Fadiman, published first in 1958 and republished in 1997.  The reissue was published by Springer-Verlag.  It includes: 
  • "The No-Sided Professor" 
  • "A Subway Named Möbius" 
  • "A. Botts and the Möbius Strip" 
  • "The Last Magician" 
  • ". . . And He Built a Crooked House" (also online)
Other works of literature included: 
The Bald Soprano by Eugene Ionesco (in "The Bald Soprano and Other Plays," Donald M. Allen, translator; Grove Press, 1982). 

The Gift by Vladimir Nabokov (Vintage, 1991). 

Math and Visualization

Flatland by Edwin Abbott Abbott (Dover, 1992).  (Also available online.) 

Intuitive Concepts in Elementary Topology by Bradford Henry Arnold (Prentice-Hall, 1962).  (Out of print.) 

Beyond the Third Dimension, by Thomas F. Banchoff (Scientific American Library, 1996). 

How Surfaces Intersect in Space:  An Introduction to Topology, by J. Scott Carter (World Scientific Publishing, 1995)  (Out of print). 

A Topological Picture Book by George K Francis (Springer-Verlag, 1987). 

The Shape of Space by Jeffery R.Weeks (Marcel Dekker, 1985).  (There is also a movie based on the book.) 

The CRC Concise Encyclopedia of Mathematics by Eric W. Weisstein (CRC Press, 1998). 
There are also several websites that provided help and display beautiful pictures
The CRC Concise Encyclopedia of Mathematics provides wonderfully clear and beautiful discussions of many math subjects, including various non-orientable surfaces.  Unfortunately, due to copyright issues, certain pages are blocked on different days. 

Paul Bourke's site on geometry also has pictures and discriptions. 

The Geometry Center's Topological Zoo includes pages on Klein bottles and projective planes

The website for Zbigniew Fiedorowicz's Introduction to Toplogy course at Ohio State is a good beginner's resource. 

Author Jeff Weeks' website offers educational material and games based on the flat torus and Klein bottle. 

History and Philosophy

Beyond the Third Dimension, by Thomas F. Banchoff (Scientific American Library, 1996). 

Goedel, Escher, and Bach by Douglas Haufsteder (Basic Books, 1979, to be rereleased 1999). 
By far the most useful (and most often linked to) website on the history of math is the MacTutor project at St. Andrews University.  See especially the pages on August Moebius and Felix Klein

Other Sections 

Moebius and His Band edited by John Fauvel, Raymond Flood, and Robin Williams (Oxford U.P., 1993). 

Archimedesí Revenge:  The Joys and Perils of Mathematics by Paul Hoffman (Ballantine, 1989). 

"Moebius Strip Tease," by Nicolas Slonimnsky, in  Source Vol. V/1, Nov. 1971, pp. 64-66. 

Tertium Organum: the Third Canon of Thought, a Key to the Enigmas of the World, by P.D. Oupensky, revised translation by Nicholas Bessaraboff and Claude Bragdon (Knopf, 1982, 1st American Edition; reissued 1998). 

Style and Idea by Arnold Schoenberg (U.C. Press, 1989).

Who are we? 
  • MLB is Margaret Boittin, a sophomore in Ezra Stiles.  She wrote the sections on Literature and Music and coordinated the story of Thomas Tordu.
  • EEC is Erin Callahan, a junior in Jonathan Edwards.  She is responsible for the History and Philosophy section and the Introduction.
  • DLG is Trumbull College freshman David Goldberg, who wrote the math chapter.
  • JACR is Saybrook freshman Jacob Remes.  He designed and edited the site and wrote most of that which does not fall under another category and filler text (like this).

  • The sources for individual pictures and java applets are noted on the pages they're on.
     Created 981125 by jacr. Updated 981130 by jacr. URL is ./bibliography.htm