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1 Remote Warehouse Mathematics- Geometry and Trigonometry

Three Dimensional Geometry & Topolo Volume 1

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Synopses & Reviews

Publisher Comments:

This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology. Hyperbolic geometry is the star. A strong effort has been made to convey not just denatured formal reasoning (definitions, theorems, and proofs), but a living feeling for the subject. There are many figures, examples, and exercises of varying difficulty.

This book was the origin of a grand scheme developed by Thurston that is now coming to fruition. In the 1920s and 1930s the mathematics of two-dimensional spaces was formalized. It was Thurston's goal to do the same for three-dimensional spaces. To do this, he had to establish the strong connection of geometry to topology--the study of qualitative questions about geometrical structures. The author created a new set of concepts, and the expression "Thurston-type geometry" has become a commonplace.

Three-Dimensional Geometry and Topology had its origins in the form of notes for a graduate course the author taught at Princeton University between 1978 and 1980. Thurston shared his notes, duplicating and sending them to whoever requested them. Eventually, the mailing list grew to more than one thousand names. The book is the culmination of two decades of research and has become the most important and influential text in the field. Its content also provided the methods needed to solve one of mathematics' oldest unsolved problems--the Poincaré Conjecture.

In 2005 Thurston won the first AMS Book Prize, for Three-dimensional Geometry and Topology. The prize recognizes an outstanding research book that makes a seminal contribution to the research literature. Thurston received the Fields Medal, the mathematical equivalent of the Nobel Prize, in 1982 for the depth and originality of his contributions to mathematics. In 1979 he was awarded the Alan T. Waterman Award, which recognizes an outstanding young researcher in any field of science or engineering supported by the National Science Foundation.

Synopsis:

This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology. Hyperbolic geometry is the star. A strong effort has been made to convey not just denatured formal reasoning (definitions, theorems, and proofs), but a living feeling for the subject.

Table of Contents

Preface

Reader's Advisory

Ch. 1. What Is a Manifold? 3

Ch. 2. Hyperbolic Geometry and Its Friends 43

Ch. 3. Geometric Manifolds 109

Ch. 4. The Structure of Discrete Groups 209

Glossary 289

Bibliography 295

Index 301

Product Details

ISBN:
9780691083049
Editor:
Levy, Silvio
Author:
Levy, Silvio
Author:
Thurston, William P.
Publisher:
Princeton University Press
Location:
Princeton, N.J. :
Subject:
Geometry - General
Subject:
Advanced
Subject:
Three-manifolds (Topology)
Subject:
Geometry, enumerative
Subject:
Geometry, Hyperbolic
Subject:
Three-manifolds
Subject:
Mathematics
Subject:
Mathematics-Geometry and Trigonometry
Copyright:
Edition Description:
Includes bibliographical references and index.
Series:
Princeton mathematical series ;
Series Volume:
95-66935
Publication Date:
January 1997
Binding:
HARDCOVER
Grade Level:
College/higher education:
Language:
English
Illustrations:
Yes
Pages:
320
Dimensions:
9 x 6 in 21 oz

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Related Subjects

History and Social Science » World History » General
Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry
Science and Mathematics » Mathematics » Topology

Three Dimensional Geometry & Topolo Volume 1 New Hardcover
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Product details 320 pages Princeton University Press - English 9780691083049 Reviews:
"Synopsis" by , This book develops some of the extraordinary richness, beauty, and power of geometry in two and three dimensions, and the strong connection of geometry with topology. Hyperbolic geometry is the star. A strong effort has been made to convey not just denatured formal reasoning (definitions, theorems, and proofs), but a living feeling for the subject.
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