Geometry

For Junior-level courses in Geometry. Designed to prepare prospective high school mathematics instructors to teach Euclidean geometry, this text augments Euclids elegant but sparse statements with appropriate historical commentary and many exercises. It also introduces the non-Euclidean geometries, allowing students to gain perspective and enhance their appreciation of axiomatic systems.

1. Other Geometries: A Computational Introduction. 2. The Neutral Geometry of the Triangle. 3. Nonneutral Euclidean Geometry. 4. Circles and Regular Polygons. 5. Toward Projective Geometry. 6. Planar Symmetries. 7. Inversions. 8. Symmetry in Space. 9. Informal Topology. 10. Graphs. 11. Surfaces. 12. Knots and Links. Appendix A: A Brief Introduction to The Geometers Sketchpad. Appendix B: Summary of Propositions. Appendix C: George D. Birkhoffs Axiomatization of Euclidean Geometry. Appendix D: The University of Chicago School Mathematics Projects Geometrical Axioms. Appendix E: David Hilberts Axiomatization of Euclidean Geometry. Appendix F: Permutations. Appendix G: Modular Arithmetic. Solutions and Hints to Selected Problems. Bibliography.