George G. Szpiro - Kepler's Conjecture.pdf - Mathematics - widez2

KEPLER’S CONJECTURE

How Some of the Greatest Minds in History

Helped Solve One of the Oldest

Math Problems in the World

George G. Szpiro

John Wiley & Sons, Inc.

KEPLER’S CONJECTURE

How Some of the Greatest Minds in History

Helped Solve One of the Oldest

Math Problems in the World

George G. Szpiro

John Wiley & Sons, Inc.

This book is printed on acid-free paper.

Published by John Wiley & Sons, Inc., Hoboken, New Jersey

Published simultaneously in Canada

Illustrations on pp. 4, 5, 8, 9, 23, 25, 31, 32, 34, 45, 47, 50, 56, 60, 61, 62, 66, 68,

69, 73, 74, 75, 81, 85, 86, 109, 121, 122, 127, 130, 133, 135, 138, 143, 146, 147,

153, 160, 164, 165, 168, 171, 172, 173, 187, 188, 218, 220, 222, 225, 226, 228, 230,

235, 236, 238, 239, 244, 245, 246, 247, 249, 250, 251, 253, 258, 259, 261, 264, 266,

Photos pp. 12, 37, 54, 77, 100, 115 © Nidersächsische Staats- und Universitätsbib-

liothek, Göttingen; p. 52 © Department of Mathematics, University of Oslo; p. 92

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Library of Congress Cataloging-in-Publication Data:

Szpiro, George, date.

Kepler’s conjecture : how some of the greatest minds in history helped solve one

of the oldest math problems in the world / by George Szpiro.

p. cm.

Includes bibliographical references and index.

ISBN 0-471-08601-0 (cloth : acid-free paper)

1. Mathematics—Popular works. I. Title.

QA93 .S97 2002

510—dc21

2002014422

Printed in the United States of America

10 9 8 7 6 5 4 3 2 1

Contents

Preface

1 Cannonballs and Melons

2 The Puzzle of the Dozen Spheres

3 Fire Hydrants and Soccer Players

4 Thue’s Two Attempts and Fejes-Tóth’s Achievement

5 Twelve’s Company, Thirteen’s a Crowd

6 Nets and Knots

7 Twisted Boxes

8 No Dancing at This Congress

112

9 The Race for the Upper Bound

124

10 Right Angles for Round Spaces

140

11 Wobbly Balls and Hybrid Stars

156

12 Simplex, Cplex, and Symbolic Mathematics

181

13 But Is It Really a Proof ?

201

14 Beehives Again

215

15 This Is Not an Epilogue

229

Mathematical Appendixes

Chapter 1

234

Chapter 2

238

Chapter 3

239

Chapter 4

243

Chapter 5

247

Chapter 6

249

Chapter 7

254

Chapter 9

258

iii

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