The Shape of Space (3^rd Ed.) Textbooks in Mathematics Series

The 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 spaces?stretching students? 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 discussion of cosmological applications
• Intuitive examples missing from many college and graduate school curricula

About the Author:

Jeffrey R. Weeks is a freelance geometer living in Canton, New York. With support from the U.S. National Science Foundation, the MacArthur Foundation and several science museums, his work spans pure mathematics, applications in cosmology and?closest to his heart?exposition for the general public.

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

Jeffrey R. Weeks is a free-lance geometer living in Canton, New York. With support from the U.S. National Science Foundation, the MacArthur Foundation and several science museums, his work spans pure mathematics, applications in cosmology and—closest to his heart—exposition for the general public.