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The Shape of Space: 2nd Edition (Hardback) book cover

The Shape of Space

2nd Edition

By Jeffrey R. Weeks

CRC Press

408 pages

Purchasing Options:$ = USD
Hardback: 9780824707095
pub: 2001-12-12
$41.95
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eBook (VitalSource) : 9780429223280
pub: 2001-12-12
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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.

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

About the Series

Chapman & Hall/CRC Pure and Applied Mathematics

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Subject Categories

BISAC Subject Codes/Headings:
MAT000000
MATHEMATICS / General
MAT012000
MATHEMATICS / Geometry / General