Experiencing Geometry : Euclidean and non-Euclidean with History / Edition 3 by David W. Henderson | 9780131437487 | Paperback | Barnes & Noble
Experiencing Geometry : Euclidean and non-Euclidean with History / Edition 3

Experiencing Geometry : Euclidean and non-Euclidean with History / Edition 3

by David W. Henderson, Daina Taimina
     
 

ISBN-10: 0131437488

ISBN-13: 9780131437487

Pub. Date: 07/28/2004

Publisher: Pearson

The distinctive approach of Henderson and Taimina's volume stimulates readers 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, challenging problems encourage readers to gather and

Overview

The distinctive approach of Henderson and Taimina's volume stimulates readers 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, challenging problems encourage readers to gather and discuss their reasonings and understanding. The volume provides an understanding of the possible shapes of the physical universe. The authors provide extensive information on historical strands of geometry, straightness on cylinders and cones and hyperbolic planes, triangles and congruencies, area and holonomy, parallel transport, SSS, ASS, SAA, and AAA, parallel postulates, isometries and patterns, dissection theory, square roots, pythagoras and similar triangles, projections of a sphere onto a plane, inversions in circles, projections (models) of hyperbolic planes, trigonometry and duality, 3-spheres and hyperbolic 3-spaces and polyhedra. For mathematics educators and other who need to understand the meaning of geometry.

Product Details

ISBN-13:
9780131437487
Publisher:
Pearson
Publication date:
07/28/2004
Edition description:
REV
Pages:
432
Product dimensions:
6.90(w) x 9.00(h) x 1.00(d)

Table of Contents

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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