The foundations of geometry
作者： Gerard A. Venema
DOI:
关键词: Absolute geometry 、 Foundations of geometry 、 Mathematics 、 Euclidean geometry 、 Synthetic geometry 、 Pure mathematics 、 Pasch's axiom 、 Algebra 、 Axiom 、 Point–line–plane postulate 、 Non-Euclidean geometry
摘要: (NOTE: Each chapter concludes with Exercises.) 1. Euclid's Elements. 2. Axiomatic Systems. 3. Theorems, Proofs, and Logic. 4. Set Theory Real Numbers. 5. The Axioms of Plane Geometry. 6. Neutral 7. Euclidean 8. Hyperbolic 9. Area. 10. Circles. 11. Constructions. 12. Transformations. 13. Models. 14. Geometry the World. Appendix A: Book I. Definitions. Postulates. Common Notions. Propositions. B: Other Systems for Hilbert's Axioms. Birkhoff's SMSG UCSMP C: Postulates Used in this Book. Undefined Terms. Parallel Area Reflection Postulate. Logical Relationships. D: Van Hiele Model Development Geometric Thought. E: Hints Selected Exercises. Bibliography. Index.
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