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An Imaginary Tale: The Story of [the square root of minus one] Hardcover – 1998

ISBN-13: 978-0691027951 ISBN-10: 0691027951 Edition: 1st

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Product Details

  • Hardcover: 257 pages
  • Publisher: Princeton University Press; 1st edition (1998)
  • Language: English
  • ISBN-10: 0691027951
  • ISBN-13: 978-0691027951
  • Product Dimensions: 9.6 x 6.4 x 1 inches
  • Shipping Weight: 1.2 pounds
  • Average Customer Review: 3.8 out of 5 stars  See all reviews (77 customer reviews)
  • Amazon Best Sellers Rank: #305,966 in Books (See Top 100 in Books)

Editorial Reviews Review

At the very beginning of his book on i, the square root of minus one, Paul Nahin warns his readers: "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.... 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.... 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."

Nahin is a professor of electrical engineering at the University of New Hampshire; he has also written a number of science fiction short stories. His style is far more lively and humane than a mathematics textbook while covering much of the same ground. Readers will end up with a good sense for the mathematics of i and for its applications in physics and engineering. --Mary Ellen Curtin


Honorable Mention for the 1998 Award for Best Professional/Scholarly Book in Mathematics, Association of American Publishers

One of Choice's Outstanding Academic Titles for 1999

"A book-length hymn of praise to the square root of minus one."--Brian Rotman, Times Literary Supplement

"An Imaginary Tale is marvelous reading and hard to put down. Readers will find that Nahin has cleared up many of the mysteries surrounding the use of complex numbers."--Victor J. Katz, Science

"[An Imaginary Tale] can be read for fun and profit by anyone who has taken courses in introductory calculus, plane geometry and trigonometry."--William Thompson, American Scientist

"Someone has finally delivered a definitive history of this 'imaginary' number. . . . A must read for anyone interested in mathematics and its history."--D. S. Larson, Choice

"Attempting to explain imaginary numbers to a non-mathematician can be a frustrating experience. . . . On such occasions, it would be most useful to have a copy of Paul Nahin's excellent book at hand."--A. Rice, Mathematical Gazette

"Imaginary numbers! Threeve! Ninety-fifteen! No, not those kind of imaginary numbers. If you have any interest in where the concept of imaginary numbers comes from, you will be drawn into the wonderful stories of how i was discovered."--Rebecca Russ, Math Horizons

"There will be something of reward in this book for everyone."--R.G. Keesing, Contemporary Physics

"Nahin has given us a fine addition to the family of books about particular numbers. It is interesting to speculate what the next member of the family will be about. Zero? The Euler constant? The square root of two? While we are waiting, we can enjoy An Imaginary Tale."--Ed Sandifer, MAA Online

"Paul Nahin's book is a delightful romp through the development of imaginary numbers."--Robin J. Wilson, London Mathematical Society Newsletter

Customer Reviews

This is a well written interesting book.
Amazon Customer
I caught a few typos in the math equations that could confuse less astute readers and some (but not most) of the diagrams are crude, like they were drawn hastily.
book reviewer
If you like math, if you are willing to spend a bit of time understanding the wonderful results -- get it!
Guillermo D Irisarri

Most Helpful Customer Reviews

175 of 179 people found the following review helpful By Jon McAuliffe on November 30, 1999
Format: Hardcover
Despite its billing as a history of science book, I would really categorize "An Imaginary Tale" as a supplemental math text with occasional historical color, much as you'll find, for example, in offset boxes of "friendly" freshman calculus treatments. The author largely concedes this in the preface. Granted, the first couple of chapters have a more historical emphasis, but by the end of chapter 3 we've largely left behind the etiology of complex analysis.
However, as long as you are aware of this going in, you'll be treated to an absolutely first-rate trip through the motivation, development and application of complex function theory, including several thoroughly worked out real-world examples. I was delighted by Nahin's painstaking efforts to build intuition about the meaning of complex algebra. If nothing else, drilling in the idea that i is a pi/2 rotation operator in the complex plane would give a conceptual toehold to thousands of high school students who never learn anything about complex algebra beyond formal symbol manipulation. One can easily imagine "An Imaginary Tale" as recommended reading for interested high school seniors, or for undergraduates looking for some background and motivation of ideas they are required to understand.
Make no mistake, when the author says he will not "fall to his knees in dumbstruck horror" at the sight of an integral, you should take him at his word --- this book is packed with integral calculus equations, and you're not going to get much out of it if you're not prepared to follow along with them. But I think Nahin has achieved the right blend of explaining each step versus leaving algebra to the reader (here I disagree somewhat with smlauer@mindspring.
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106 of 110 people found the following review helpful By Duwayne Anderson on September 22, 1999
Format: Hardcover
When I first took a copy of Nahin's book off the shelf, I expected a history book operating under the usual rules that seem to dominate easy reading books on science today - no equations. What I found instead was an unexpected surprise that immediately cemented my decision to purchase the book - it is chuck full of equations. But then, how do you write a book about mathematics without using equations? I'm glad that for this one, at least, the publishers listened to reason.
Of course, the book isn't all equations. There is some downright interesting history in it as well. For the most part, however, this is a book that illustrates the equations (or at least their modern counter parts) that led mathematicians to develop the concept of the square root of a negative number, eventually leading to the branch of mathematics we call today complex analysis. Having said that, I should point out that this is not a mathematics book on complex analysis [for that, a better choice is "Complex Variables," by Mark J. Ablowitz and Athanassios S. Fokas, Cambridge University Press, 1997]. The author does not develop theorems or proofs, and many of the demonstrations stretch the notion of mathematical proofs - but they are not intended to be mathematical proofs at all, but just that - demonstrations. Think of this book as a mathematicians leisurely romp through the mathematical history of root negative one, with an average of at least two or three equations on every page. The mathematics isn't advanced by any means. If you are reasonably grounded in algebra, geometry, trigonometry (and lots of it), and a little calculus (including a few differential equations) you should have no trouble at all. Plan on working through the equations, though, step by step.
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45 of 45 people found the following review helpful By Kevin C. on July 21, 2000
Format: Hardcover
As a few of the other reviewers have noted, this book is not for those people whose only mathematical knowledge comes from the science pages of the New York Times. For many of the chapters and proofs shown, a background consisting of at least the basics of Freshman Calculus (through power series or so) is assumed and indeed is necessary to know what is going on. If you don't have this knowledge, you'll probably become lost quite frequently. However, the fact that Nahin is writing for a more knowledgable audience is indeed quite refreshing. Because he IS willing to include the mathematics, the historical information becomes that much more interesting. Instead of just telling how imaginary numbers came about, he works through the steps of many of the exact problems that first led people to consider (and ignore) imaginary numbers. The chapter on "Wizard Mathematics" is worth the price of the book all by itself. Some of the proofs shown there are so beautiful to make one want to cry out in the joy of discovery. In addition, he includes a chapter on the applications of Complex Numbers which is also quite enlightening.
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31 of 31 people found the following review helpful By Stan Vernooy on May 24, 2000
Format: Hardcover
If all math textbooks included the kind of material and discussions in this book, students would learn better and be more interested in math. The standard math book is a continuous list of definitions and theorems, interspersed with examples of how to do certain kinds of problems. Never does anyone explain how and why people came up with the ideas in the first place, or why such and such a theorem is important, or what kinds of problems triggered the research and investigations which have been done. "Shut up and learn it!" seems to be the universal slogan. Nahin's book can't really be used as a textbook, but it provides an all-important context for the material found in various courses all the way from Intermediate Algebra to Complex Analysis. In fact, I think the primary beneficiaries of a book like this are math teachers (like me!). The material in this book will enable me to flesh out and personalize some ideas which are found in a variety of courses which I teach. When someone asks me why anyone ever thought of having a square root of negative one, or what kinds of problems it's good for, this book will enable me to give some interesting answers. And, of course, I'll pretend that I came up with those answers all by myself!
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More About the Author

Paul Nahin was born in California, and did all his schooling there (Brea-Olinda High 1958, Stanford BS 1962, Caltech MS 1963, and - as a Howard Hughes Staff Doctoral Fellow - UC/Irvine PhD 1972, with all degrees in electrical engineering). He worked as a digital logic designer and radar systems engineer in the Southern California aerospace industry until 1971, when he started his academic career. He has taught at Harvey Mudd College, the Naval Postgraduate School, and the Universities of New Hampshire (where he is now emeritus professor of electrical engineering) and Virginia. In between and here-and-there he spent a post-doctoral year at the Naval Research Laboratory, and a summer and a year at the Center for Naval Analyses and the Institute for Defense Analyses as a weapon systems analyst, all in Washington, DC. He has published a couple dozen short science fiction stories in ANALOG, OMNI, and TWILIGHT ZONE magazines, and has written 16 books on mathematics and physics, published by IEEE Press, Springer, and the university presses of Johns Hopkins and Princeton. His most recent book, INSIDE INTERESTING INTEGRALS, discussing numerous techniques for doing definite integrals (up through and including contour integration in the complex plane) that commonly occur in physics, engineering, and mathematics, was published by Springer in September 2014. His next book, IN PRAISE OF SIMPLE PHYSICS, on the application in everyday life situations of elementary mathematics (up to and including freshman calculus) and the fundamental physical laws, is under contract with Princeton University Press and will appear in early 2016. He has given invited talks on mathematics at Bowdoin College, the Claremont Graduate School, the University of Tennessee, and Caltech, has appeared on National Public Radio's "Science Friday" show (discussing time travel) as well as on New Hampshire Public Radio's "The Front Porch" show (discussing imaginary numbers), and advised Boston's WGBH Public Television's "Nova" program on the script for their time travel episode. He gave the invited Sampson Lectures for 2011 in Mathematics at Bates College (Lewiston, Maine). When he isn't writing he is battling evil-doers on his PS4 and, now and then, he even wins ("Dying Light" and all its 'undead' are my current time-wasters).

FINALLY - numerous readers have written over the years asking about the solutions manual to my Springer book, THE SCIENCE OF RADIO. Springer has kindly made it available in pdf format (3 MB), and if you write to me I'll send you a copy.