Autorentext

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 andclosest to his heartexposition for the general public.

Klappentext

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.

Inhalt

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