Experiencing geometry : Euclidean and non-Euclidean with history

David W. Henderson, Daina Taimiņa

For junior/senior level course in Geometry. The distinctive approach of Henderson and Taimina's text stimulates students to develop a broader, deeper understanding of mathematics through active experience-including discovery, discussion, writing fundamental ideas and learning about the history of those ideas. A series of interesting problems (ranging from easy to challenging) encourage students to gather and discuss their reasonings and understanding. This is the only undergraduate text that pays attention to geometric intuition, student cognitive development, and rigorous mathematics; and that includes a broad vision of geometry that leads to discussion of four strands in the history of geometry and to an understanding of the possible shapes of the physical universe.

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[目次]

  • Preface. How to Use this Book. 0. Historical Strands of Geometry. 1. What is Straight? 2. Straightness on Spheres. 3. What Is an Angle? 4. Straightness on Cylinders and Cones. 5. Straightness on Hyperbolic Planes. 6. Triangles and Congruencies. 7. Area and Holonomy. 8. Parallel Transport. 9. SSS, ASS, SAA, and AAA. 10. Parallel Postulates. 11. Isometries and Patterns. 12. Dissection Theory. 13. Square Roots, Pythagoras and Similar Triangles. 14. Projections of a Sphere onto a Plane. 15. Circles. 16. Inversions in Circles. 17. Projections (Models) of Hyperbolic Planes. 18. Geometric 2-Manifolds. 19. Geometric Solutions of Quadratic and Cubic Equations. 20. Trigonometry and Duality. 21. Mechanisms. 22. 3-Spheres and Hyperbolic 3-Spaces. 23. Polyhedra. 24. 3-Manifolds-the Shape of Space. Appendix A: Euclid's Definitions, Postulates, and Common Notions. Appendix B: Constructions of Hyperbolic Planes. Bibliography. Index.

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この本の情報

書名 Experiencing geometry : Euclidean and non-Euclidean with history
著作者等 Henderson David W.
Taimina Daina
Taimiņa Daina
Henderson David W. (David Wilson)
出版元 Pearson Prentice Hall
刊行年月 c2005
版表示 3rd ed
ページ数 xxx, 392 p.
大きさ 24 cm
ISBN 0131437488
NCID BA7690911X
※クリックでCiNii Booksを表示
言語 英語
出版国 アメリカ合衆国
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