The moment of proof: mathematical epiphanies PDF
Preview The moment of proof: mathematical epiphanies
The Moment of Proof The Moment of Proof Mathematical Epiphanies Donald C. Benson OXFORD UNIVERSITY PRESS OXFORD UNIVERSITY PRESS Oxford New York Athens Auckland Bangkok Bogota Buenos Aires Calcutta Cape Town Chennai Dar es Salaam Delhi Florence Hong Kong Istanhu] Karachi Kuala Lumpur Madrid Melbourne Mexico City Mumbai Nairobi Paris Sao Paulo Shanghai Singapore Taipei Tokyo Toronto Warsaw and associated companies in Berlin Ibadan Copyright © 1999 by Oxford University Press First published by Oxford University Press, Inc., 1999 First issued as an Oxford University Press paperback, 2000 198 Madison Avenue, New York, New York 10016 Oxford is a registered trademark of Oxford University Press All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording, or otherwise, without the prior permission of Oxford University Press. Figure 15.9 on page 226 courtesy of B. B. Mandelbrot, The Fractal Geometry tif Nature (W.H. Freeman, 1982). Library of Congress Cataloging-in-Publication Data Benson, Donald The moment of proof: mathematical epiphanies / by Donald Benson p. cm. Includes bibliographical references and index. ISBN 0-19-511721-2 (Cloth) ISBN 0-19-513919-4 (Pbk.) 1. Proof theory—Popular works. I.Title. QA9.54.B46 1999 511.3—dc21 97-52139 10 987654 3 21 Printed in the United States of America on acid-free paper Contents Acknowledgments, vii Introduction, I I RECALLING / Reflections, 5 2 Hand in Hand, 13 3 Further Progression, 23 II COUNTING 4 Interesting Numbers, 41 5 Tenpins, and Counting, 57 6 Order and Reorder, ji 7 Outcast, 89 8 The Power of Two, 101 9 Divide and Conquer, 123 10 Set and Match, 137 11 Chance Encounter, 149 III BALANCING 12 Cutouts, 167 13 Seesaw, Marjorie Daw, 185 14 Two Pearls, 797 IV NUMBERING 75 New Numbers for Old, 209 16 Prime News, 227 77 The Unknown Division, 237 18 Secret Messages, 259 V WINNING 79 Be Wise, Optimize, 277 20 The Play's the Thing, 293 Notes, 311 References, 319 Index, 323 This page intentionally left blank Acknowledgments I would like to acknowledge the loving encouragement and assistance of my dear wife Dorothy. Without her help, this book would never have been written. I wish to thank her especially for reading and rereading the manuscript and making suggestions and criticisms from the point of view of a mathematical novice as well as for her many invaluable stylistic insights. I would like to thank Ned Black for reading the entire manuscript and offering many valuable suggestions. I would also like to acknowledge the assistance and encouragement of Kirk Jensen at Oxford Uni- versity Press and the helpful suggestions of Henry Alder, Eric Benson, and Sherman Stein. This book, apart from the frontmatter, was typeset by the author using IffljiX.. This page intentionally left blank The Moment of Proof This page intentionally left blank
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