Shape of Space: How to Visualize Surfaces and Three-Dimensional Manifolds / Edition 2

Shape of Space: How to Visualize Surfaces and Three-Dimensional Manifolds / Edition 2

by Jeffrey R. Weeks, Weeks R. Weeks
     
 

ISBN-10: 0824707095

ISBN-13: 9780824707095

Pub. Date: 12/12/2001

Publisher: Taylor & Francis

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

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Overview

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.

Product Details

ISBN-13:
9780824707095
Publisher:
Taylor & Francis
Publication date:
12/12/2001
Series:
Chapman & Hall/CRC Pure and Applied Mathematics Series, #249
Edition description:
REV
Pages:
408
Sales rank:
449,702
Product dimensions:
6.10(w) x 9.00(h) x 1.00(d)

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

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