An Imaginary Tale: The Story of i the square root of minus one

297 Pages·1998·2.53 MB·English

by  Paul J. Nahin

An Imaginary Tale

An Imaginary Tale
THE STORY OF 2-1
With a new preface by the author
Paul J. Nahin
PRINCETON UNIVERSITY PRESS
PRINCETON AND OXFORD
Copyright ©1998 by Princeton University Press
Published by Princeton University Press, 41 William Street,
Princeton, New Jersey 08540
In the United Kingdom: Princeton University Press, 3 Market Place,
Woodstock, Oxfordshire OX20 1SY
All Rights Reserved
Fifteenth printing, and first paperback printing,
with a new preface and appendixes by the author, 2007
Paperback ISBN-13: 978-0-691-12798-9
Paperback ISBN-10: 0-691-12798-0
The Library of Congress has cataloged the cloth edition of this book as follows
Nahin, Paul J.
An imaginary tale : the story of [the square root of minus one] / Paul J. Nahin.
p. cm.
On t.p. “[the square root of minus one]” appears as
a radical over “–1”.
Includes bibliographical references and indexes.
1. Numbers, Complex. I. Title.
QA255.N34 1998
ISBN 0-691-02795-1 (cloth : alk. paper)
515'.9—dc21 97-52082
British Library Cataloging-in-Publication Data is available
This book has been composed in Times Roman
Printed on acid-free paper. ∞
pup.princeton.edu
Printed in the United States of America
15 16 17 18 19 20
DEDICATED TO MY MOTHER
KATHERINE DOROTHY MARKFELDER
AND TO THE MEMORY OF
MY FATHER
PAUL GILBERT NAHIN
(1916–1990)
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A Note to the Reader
AN IMAGINARY TALE has a very strong historical component to it, but that does
not mean it is a mathematical lightweight. But don’t read too much into that
either. It is not a scholarly tome meant to be read only by some mythical, elite
group, such as the one described in the 1920s fable that claimed there were
only twelve people in the world who really understood Einstein. ˇ21 has
long labored under a similar false story of unfathomable mystery. The French
philosophical genius of the Enlightenment, Denis Diderot, wrote of mathe-
maticians that they “resemble those who gaze out from the tops of high moun-
tains whose summits are lost in the clouds. Objects on the plain below have
disappeared from view; they are left with only the spectacle of their own
thoughts and the consciousness of the height to which they have risen and
where perhaps it is not possible for everyone to follow and breathe [the thin
air].” Well, in this book the air is almost always at sea-level pressure. Large
chunks of this book can, in fact, be read and understood by a high school
senior who has paid attention to his or her teachers in the standard fare of pre-
college courses. Still, it will be most accessible to the million or so who each
year complete a college course in freshman calculus. It is not a textbook, but I
do think it could be profitably read by students as a supplement to the more
standard presentations of mathematics. I am an electrical engineer, not a mathemati-
cian, and the style of the writing reflects the difference. Indeed, I have taken
advantage of my freedom from the usual dictates of textbook pedagogy—
which in its worst form can be pedantic—to write in a casual and, I hope,
entertaining style. But when I need to do an integral, let me assure you I have
not fallen to my knees in dumbstruck horror. And neither should you. The
power and beauty of complex numbers and functions, and the amazing story
of their discovery, will amply repay any extension of concentration that the
relatively harder parts may demand.
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