CiNii 図書 - Thinking geometrically : a survey of geometries

This is a self-contained, comprehensive survey of college geometry that can serve a wide variety of courses for students of both mathematics and mathematics education. The text develops visual insights and geometric intuition while stressing the logical structure, historical development, and deep interconnectedness of the ideas. Chapter topics include Euclidean geometry, axiomatic systems and models, analytic geometry, transformational geometry, symmetry, non-Euclidean geometry, projective geometry, finite geometry, differential geometry, and discrete geometry. The different chapters are as independent as possible, while the text still manages to highlight the many connections between topics. Appendices include material from Euclid's first book, as well as Hilbert's axioms, and provide brief summaries of the parts of linear algebra and multivariable calculus needed for certain chapters.

Preface
1. Euclidean geometry
2. Axiomatic systems
3. Analytic geometry
4. Non-Euclidean geometries
5. Transformational geometry
6. Symmetry
7. Projective geometry
8. Finite geometries
9. Differential geometry
10. Discrete geometry
11. Epilogue
Appendix A. Definitions, postulates, common notions, and propositions from Book I of Euclid's Elements
Appendix B. SMSG axioms for Euclidean geometry
Appendix C. Hilbert's axioms for Euclidean plane geometry
Appendix D. Linear algebra summary
Appendix E. Multivariable calculus summary
Appendix F. Elements of proofs
Answers to selected exercises
Acknowledgements
Index.

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Thinking geometrically : a survey of geometries

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