The shape of space
著者
書誌事項
The shape of space
（Monographs and textbooks in pure and applied mathematics, 249）
M. Dekker, c2002
2nd ed
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注記
Includes bibliographical references (p. 355-360) and index
9th impression published by CRC Press
内容説明・目次
内容説明
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.
目次
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
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