- 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-dimension
is analogous to our relationship to the 4th-dimension. 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).

This book is a translation from Euclid's original text written in Greek over 2000 years ago. It is remarkably similar to modern high school geometry text books. The editor has added extensive, and useful commentary.

**[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 Disk Model, and other geometric systems. The only
prerequisite to this text is a solid understanding of typical high school
geometry.

**[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".
Execellent reading for the layperson and mathamatition alike.

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

**[Ramsay&Richtmyer-95]**:
Arlan Ramsay, Robert D. Richtmyer. Introduction To Hyperbolic Geometry,
Springer-Verlag, New York, Berlin, Heidelberg (1995).

This text for advanced undergraduates emphasizes the logical connections of the subject. The derivations of formulas from the axioms do not make use of models of the hyperbolic plane until the axioms are shown to be categorical; the differential geometry of surfaces is developed far enough to establish its connections to the hyperbolic plane; and the axioms and proofs use the properties of the real number system. Topics include: Axioms for Plane Geometry, some Neutral Theorems of Plane Geometry, Qualitative Description of the Hyperbolic Plane, Differential Geometry of Surfaces, Quantitative Considerations, Consistency and Categoricalness of the Hyperbolic Axioms, the Upper Half-Plane Model, Matrix Representation of the Isometry Group, Tilings, Differential and Hyperbolic Geometry in More Dimensions, and Applications to Special Relativity. Elementary techniques from complex analysis, matrix theory, and group theory are prerequisite to this text.