The Shape of Space

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.

Auteur

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.

Texte du rabat

The Shape of Space, Third Edition maintains the standard of excellence set by the previous editions. This textbook covers the basic geometry of two- and three-dimensional spaces. Bridging the gap from geometry to the latest work in observational cosmology, the book illustrates the connection between geometry and the behavior of the physical universe and explains how radiation remaining from the big bang may reveal the actual shape of the universe.

Written by a master expositor, leading researcher in the field, and MacArthur Fellow, it includes experiments to determine the true shape of the universe and contains illustrated examples and engaging exercises that teach mind-expanding ideas in an intuitive and informal way that is best intended for wider audiences, as well as mathematicians.

Features of the Third Edition:

• First new edition in nearly two decades

• Now features color images to better illustrate lessons

• Text is widely reviewed and praised

• Updated presentation and applications in cosmology

• Includes intuitive examples missing from many college and graduate school curriculum

Jeffrey R. Weeks is a mathematics author, master expositor and MacArthur Fellow. He received his Ph.D. in mathematics from Princeton University and has taught at Ithaca College and Middlebury College. His research interests lie in 3-manifolds and physical cosmology.

Contenu

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