Pi: A Biography of the World's Most Mysterious Number

327 Pages·2004·5.85 MB·English

by  Alfred S. Posamentier

A Biography of the World's
Most Mysterious Number
At.fred S. Posamentier
& Ingmar Lehmann
Afterword by Dr. Herbert A. Hauptman,
Nobel. Laureate
Prometheus Books
59 John Glenn Drive
Amherst, New York 14228-2 197
Published 2004 by Prometheus Books
Pi: A Biography of the World's Most Mysterious Number. Copyright © 2004 by Alfred S.
Posamentier and Ingmar Lehmann. 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, dig-
ital, electronic, mechanical, photocopying, recording, or otherwise, or conveyed via the
Internet or a Web site without prior written permission of the publisher, except in the case
of brief quotations embodied in critical articles and reviews.
Inquiries should be addressed to
Prometheus Books
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Amherst, New York 14228—2197
VOICE: 716—691—0133, ext. 207
FAX: 716—564—2711
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Library of Congress Cataloging-in-Publication Data
Posamentier, Alfred S.
Pi : a biography of the world's most mysterious number / Alfred S. Posamentier
and Ingmar Lehmann.
p. cm.
Includes bibliographical references and index.
ISBN 1—59102—200—2 (hardcover: alk. paper)
1. Pi. I. Lehmann, Ingmar. II. Title.
QA484.P67 2004
51 2.7'3—dc22
2004009958
Printed in the United States of America on acid-free paper
Contents
Acknowledgments 7
Preface 9
Chapter 1 What Is it? 13
Chapter 2 The History of it 41
Chapter 3 Calculating the Value of it 79
Chapter 4 it Enthusiasts 117
Chapter 5 it Curiosities 137
Chapter 6 Applications of it 157
Chapter 7 Paradox in it 217
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Contents
Epilogue 245
Afterword by Dr. Herbert A. Hauptman 275
Appendix A A Three-Dimensional Example of a
Rectilinear Equivalent to a Circular
Measurement 293
Appendix B Ramanujan's Work 297
Appendix C Proof That > iCe 301
Appendix D A Rope around the Regular Polygons 305
References 309
Index 313
Acknowledgments
The daunting task of describing the story of it for the general reader
had us spend much time researching and refreshing the many tidbits
of this fascinating number that we encountered in our many decades
engaged with mathematics. It was fun and enriching. Yet the most
difficult part was to be able to present the story of it in such a way
that the general reader would be able to share the wonders of this
number with us. Therefore, it was necessary to solicit outside opin-
ions. We wish to thank Jacob Cohen and Edward Wall, colleagues at
the City College of New York, for their sensitive reading of the entire
manuscript and for making valuable comments in our effort to reach
the general reader. Linda Greenspan Regan, who initially urged us to
write this book, did a fine job in critiquing the manuscript from the
viewpoint of a general audience. Dr. Ingmar Lehmann acknowledges
the occasional support of Kristan Vincent in helping him identify the
right English words to best express his ideas. Dr. Herbert A.
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Acknowledgments
Hauptman wishes to thank Deanna M. Hefner for typing the after-
word and Melda Tugac for providing some of the accompanying fig-
ures. Special thanks is due to Peggy Deemer for her marvelous copy-
editing and for apprising us of the latest conventions of our English
language while maintaining the mathematical integrity of the manu-
script.
It goes without saying that the patience shown by Barbara
and Sabine during the writing of this book was crucial to its suc-
cessful completion.
Preface
Surely the title makes it clear that this is a book about it, but you
may be wondering how a book could be written about just one
number. We will hope to convince you throughout this book that it
is no ordinary number. Rather, it is special and comes up in the
most unexpected places. You will also find how useful this number
is throughout mathematics. We hope to present it to you in a very
"reader-friendly" way—mindful of the beauty that is inherent in the
study of this most important number.
You may remember that in the school curriculum the value that
it took on was either 3.14, 3 or For a student's purposes, this
was more than adequate. It might have even been easier to simply
use it = 3. But what is it? What is the real value of it? How do we
determine the value of it? How was it calculated in ancient times?
How can the value be found today using the most modern tech-
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