Geometry : From Euclid to Knots
For Junior-level courses in Geometry.Designed to prepare prospective high school mathematics instructors to teach Euclidean geometry, this text augments Euclid's 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.
- Hardback | 458 pages
- 185.4 x 241.3 x 22.9mm | 861.84g
- 01 Aug 2002
- Pearson Education (US)
- United States
Table of contents
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 Geometer's Sketchpad. Appendix B: Summary of Propositions. Appendix C: George D. Birkhoff's Axiomatization of Euclidean Geometry. Appendix D: The University of Chicago School Mathematics Project's Geometrical Axioms. Appendix E: David Hilbert's Axiomatization of Euclidean Geometry. Appendix F: Permutations. Appendix G: Modular Arithmetic. Solutions and Hints to Selected Problems. Bibliography.