Description
Book SynopsisThe Shape of Space, Third Edition maintains the standard of excellence set by the previous editions. This lighthearted textbook covers the basic geometry and topology of two- and three-dimensional spacesâstretching studentsâ minds as they learn to visualize new possibilities for the shape of our universe.
Written by a master expositor, leading researcher in the field, and MacArthur Fellow, its informal exposition and engaging exercises appeal to an exceptionally broad audience, from liberal arts students to math undergraduate and graduate students looking for a clear intuitive understanding to supplement more formal texts, and even to laypeople seeking an entertaining self-study book to expand their understanding of space.
Features of the Third Edition:
- Full-color figures throughout
- Picture proofs have replaced algebraic proofs
- Simpler handles-and-crosscaps approach to surfaces
- Updated discussi
Table of Contents
Part I Surfaces and Three-Manifolds
Flatland
Gluing
Vocabulary
Orientability
Classification of Surfaces
Products
Flat Manifolds
Orientability vs. Two-Sidedness
Part II Geometries on Surfaces
The Sphere
The Hyperbolic Plane
Geometries on Surfaces
Gauss-Bonnet Formula and Euler Number
Part III Geometries on Three-Manifolds
Four-Dimensional Space
The Hypersphere
Hyperbolic Space
Geometries on Three-Manifolds I
Bundles
Geometries on Three-Manifolds II
Part IV The Universe
The Universe
The History of Space
Appendix A: Answers
Appendix B: Bibliography
Appendix C: Conway’s ZIP Proof
