References and Futher Reading

Flatland was written in 1884 by a Victorian schoolmaster named Edwin Abbott Abbott. It is a science-fiction story about an imaginary two-dimensional world. The book works on three levels. Most obviously, it is a satire on Victorian society. "Irregulars" (cripples) are put to death, women have no rights at all, and when the main character, A Square, tries to teach his fellows about the third dimension, he is imprisoned. On the second level, Flatland is scientific. Flatland's relationship to the 3rd-diminision is analogous to our relationship to the 4th-diminision. Finally, at the deepest level, A Square's trip into higher dimensions is a metaphor for the mystic's experience of higher reality. It is a short book, and a fun read.

[Health-56]: Sir T. Health. The Elements (Euclid), Dover, New York, NY (1956).

[Kedder-85]: R. M. Kedder. "How High-schooler Discovered New Math Theorem", The Christian Science Monitor, pp. 19-20, (April, 1985).

[Moise-74]: E.E. Moise. Elementary Geometry from an Advanced Standpoint, Addison-Wesley, Reading, MA (1974).

This book gives a clear, yet complete, axiomatic development of the Poincaré Model, and other geometric systems. It is easily readable by an undergraduate mathematics student.

[Rucker-84]: Rudy Rucker. The Fourth Dimension: Toward a Geometry of Higher Reality. Boston: Houghton Mifflin Company, 1984.

Rudy Rucker does an excellent job of helping the reader actually visualize the 4th-dimension. It is filled with great, cartoon drawings and thought provoking puzzles. Part III of the book is titled "How To Get There".

[Polking-98]: John Polking. The Geometry of the Sphere, Web site of the Department of Mathmatics of Rice University, http://math.rice.edu/~pcmi/sphere/.