The Shape of Space

The Shape of Space

Hardback Pure and Applied Mathematics (M. Dekker)

By (author) Jeffrey R. Weeks

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  • Publisher: MARCEL DEKKER INC
  • Format: Hardback | 408 pages
  • Dimensions: 168mm x 241mm x 30mm | 612g
  • Publication date: 12 December 2001
  • Publication City/Country: New York
  • ISBN 10: 0824707095
  • ISBN 13: 9780824707095
  • Edition: 2, Revised
  • Edition statement: 2nd Revised edition
  • Illustrations note: index, bibliography
  • Sales rank: 169,391

Product description

Maintaining the standard of excellence set by the previous edition, this textbook covers the basic geometry of two- and three-dimensional spaces 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. 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.

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Table of contents

SURFACES AND THREE-MANIFOLDS Flatland Gluing Vocabulary Orientability Connected Sums Products Flat Manifolds Orientability vs. Two-Sidedness GEOMETRIES ON SURFACES The Sphere The Hyperbolic Plane Geometries on Surfaces The Gauss-Bonnet Formula and the Euler Number GEOMETRIES ON THREE-MANIFOLDS Four-Dimensional Space The Hypersphere Hyperbolic Space Geometries on Three-Manifolds I Bundles Geometries on Three-Manifolds II THE UNIVERSE The Universe The History of Space Cosmic Crystallography Circles in the Sky Appendix A Answers Appendix B Bibliography Appendix C Conway's ZIP Proof Index