Synopses & Reviews
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.
"I like the authors' writing style and I think the explanations are very clear .... I know that my students read this book, which is certainly saying something. Sometimes they think it's hard to read, but it is at least possible-and they could think it's hard to read because it might be one of the few times they have actually had to read the text .... I think the historical illustrations will be useful for creating interest with the students. This is a nice addition to this edition of the text." Barbara Edwards, Oregon State University
"I found this text to be a wonderful, fresh, and innovative treatment of geometry. The Moore method of study by doing and involving the student works very well indeed for this subject. The style of the text is very friendly and encouraging and gets the student involved quickly with a give-and-take approach. The student develops insights and skills probably not obtainable in more traditional courses. This is a very fine text that I would strongly recommend for a beginning course in Euclidean and non-Euclidean geometry." Norman Johnson, University of Iowa
"This book remains a treasure, an essential reference. I simply know of no other book that attempts the broad vision of geometry that this book does, that does it by-and-large so successfully, and that pays so much attention to geometric intuition, student cognitive development, and rigorous mathematics." Judy Roitman, University of Kansas
Table of Contents
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.
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.
22. 3-Spheres and Hyperbolic 3-Spaces.
24. 3-Manifolds—the Shape of Space.
Appendix A: Euclid's Definitions, Postulates, and Common Notions.
Appendix B: Constructions of Hyperbolic Planes.