Foundations of Plane Geometry
For junior/senior-level courses in Geometry.Ideal for students who may have little previous experience with abstraction and proof, this text provides a rigorous and unified-yet straightforward and accessible-exposition of the foundations of Euclidean, hyperbolic, and spherical geometry. Unique in approach, it combines an extended theme-the study of a generalized absolute plane from axioms through classification into the three fundamental classical planes-with a leisurely development that allows ample time for students' mathematical growth. It is purposefully structured to facilitate the development of analytic and reasoning skills and to promote an awareness of the depth, power, and subtlety of the axiomatic method in general, and of Euclidean and non-Euclidean plane geometry in particular.
- Hardback | 298 pages
- 160 x 236.2 x 20.3mm | 544.32g
- 01 Nov 2002
- Pearson Education (US)
- United States
Table of contents
0. The Question of Parallels. 1. Five Examples. 2. Some Logic. 3. Practice Proofs. 4. Set Terminology and Sets of Real Numbers. 5. An Axiom System for Plane Geometry: First Steps. 6. Betweenness, Segments and Rays. 7. Three Axioms for the Line. 8. The Real Ray Axiom and Its Consequences. 9. Antipodes and Opposite Rays. 10. Separation. 11. Pencils and Angles. 12. The Crossbar Theorem. 13. Side-Angle-Side. 14. Perpendiculars. 15. The Exterior Angle Inequality and Triangle Inequality. 16. Further Results on Triangles. 17. Parallels and the Diameter of the Plane. 18. Angle Sums of Triangles. 19. Parallels and Angle Sums. 20. Concurrence. 21. Circles. 22. Similarity. Appendix I. Definitions and Assumptions from Book I of Euclid's Elements. Appendix II. The Side-Angle-Side Axiom in the Hyperbolic Plane. Bibliography. Index.