Table of Contents
(NOTE:
Each chapter concludes with Exercises.)
1. Euclid's Elements.
2. Axiomatic Systems.
3. Theorems, Proofs, and Logic.
4. Set Theory and Real Numbers.
5. The Axioms of Plane Geometry.
6. Neutral Geometry.
7. Euclidean Geometry.
8. Hyperbolic Geometry.
9. Area.
10. Circles.
11. Constructions.
12. Transformations.
13. Models.
14. The Geometry of the Real World.
Appendix A: Euclid's Book I.
Definitions. Postulates. Common Notions. Propositions.
Appendix B: Other Systems of Axioms for Geometry.
Hilbert's Axioms. Birkhoff's Axioms. SMSG Axioms. UCSMP Axioms.
Appendix C: The Postulates Used in this Book.
The Undefined Terms. The Postulates of Neutral Geometry. The Parallel Postulates. The Area Postulates. The Reflection Postulate. Logical Relationships.
Appendix D: The Van Hiele Model of the Development of Geometric Thought.
Appendix E: Hints for Selected Exercises.
Bibliography.
Index.