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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.
Literature
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 VisualizationIntuitive 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).
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 PhilosophyGoedel,
Escher, and Bach by Douglas Haufsteder (Basic Books, 1979, to be rereleased
1999).
Other SectionsArchimedes’ 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). |
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The sources for individual pictures and java applets are noted on the pages they're on. |