$17.76 with 64 percent savings

List Price: $49.95

Get Fast, Free Shipping with Amazon Prime

FREE delivery Tuesday, May 19 on orders shipped by Amazon over $35

Or Prime members get FREE delivery Tomorrow, May 15. Order within 7 hrs 53 mins.

Only 1 left in stock - order soon.

$$17.76 () Includes selected options. Includes initial monthly payment and selected options. Details

Enhancements you chose aren't available for this seller. Details

${cardName} not available for the seller you chose

${cardName} unavailable for quantities greater than ${maxQuantity}.

Ships from

Amazon

Sold by

ifbookstore

Returns

FREE 30-day refund/replacement

Gift options

Available at checkout

Available at checkout This item is a gift. Change

Payment

Secure transaction

$6.59

Pages are clean and are not marred by notes or folds of any kind. ~ ThriftBooks: Read More, Spend Less Pages are clean and are not marred by notes or folds of any kind. ~ ThriftBooks: Read More, Spend Less See less

FREE delivery May 21 - 26. Details

In stock

$$17.76 () Includes selected options. Includes initial monthly payment and selected options. Details

Access codes and supplements are not guaranteed with used items.

Enhancements you chose aren't available for this seller. Details

${cardName} not available for the seller you chose

${cardName} unavailable for quantities greater than ${maxQuantity}.

Ships from and sold by ThriftBooks-Baltimore.

Other sellers on Amazon

New & Used (108) from $1.82 + $3.99 shipping

Image Unavailable
Image not available for
Color:

Follow the author

Paul J. Nahin

An Imaginary Tale: The Story of [the square root of minus one] First Edition

by Paul J. Nahin (Author)

(302)

Part of: Princeton Science Library (61 books)

See all formats and editions

{"desktop_buybox_group_1":[{"displayPrice":"$17.76","priceAmount":17.76,"currencySymbol":"$","integerValue":"17","decimalSeparator":".","fractionalValue":"76","symbolPosition":"left","hasSpace":false,"showFractionalPartIfEmpty":true,"offerListingId":"Rm3FPZ1Tm%2Fpkk5Idv6jIeS30kYE12AkHnUFu0li17lMfYHc6%2FSLLd5TnkGTYqI5vlJ8LkUKNh%2FbEUrrPasMUbBY53ytOXy1I9%2FRVFdKCAGblwr70WwTEEGEWm06c%2FvpCP7nUtXOySl3lwRTtwIwto4PFUs2TP8cUVEFpqcUluvRkpI911x1z4rpi8mOmST2D","locale":"en-US","buyingOptionType":"NEW","aapiBuyingOptionIndex":0}, {"displayPrice":"$6.59","priceAmount":6.59,"currencySymbol":"$","integerValue":"6","decimalSeparator":".","fractionalValue":"59","symbolPosition":"left","hasSpace":false,"showFractionalPartIfEmpty":true,"offerListingId":"Rm3FPZ1Tm%2Fpkk5Idv6jIeS30kYE12AkHKgH8%2BN4mpkYItY0FNk562Nlw4FMALTevEggaaj5sMY3eXpSu4TVqHtxH6M0gDQVyaGEZdHxGclsm4CJUmUSmrbo9TClMXNfHNAUIvavjIUa5pep8bDB%2BAkC32AGiFxAabWJWwo%2FCSg5hGM5DRZOVbUZML9U7gbgP","locale":"en-US","buyingOptionType":"USED","aapiBuyingOptionIndex":1}]}

Purchase options and add-ons

Today complex numbers have such widespread practical use--from electrical engineering to aeronautics--that few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000-year-old history of one of mathematics' most elusive numbers, the square root of minus one, also known as i. He recreates the baffling mathematical problems that conjured it up, and the colorful characters who tried to solve them.

In 1878, when two brothers stole a mathematical papyrus from the ancient Egyptian burial site in the Valley of Kings, they led scholars to the earliest known occurrence of the square root of a negative number. The papyrus offered a specific numerical example of how to calculate the volume of a truncated square pyramid, which implied the need for i. In the first century, the mathematician-engineer Heron of Alexandria encountered I in a separate project, but fudged the arithmetic; medieval mathematicians stumbled upon the concept while grappling with the meaning of negative numbers, but dismissed their square roots as nonsense. By the time of Descartes, a theoretical use for these elusive square roots--now called "imaginary numbers"--was suspected, but efforts to solve them led to intense, bitter debates. The notorious i finally won acceptance and was put to use in complex analysis and theoretical physics in Napoleonic times.

Addressing readers with both a general and scholarly interest in mathematics, Nahin weaves into this narrative entertaining historical facts and mathematical discussions, including the application of complex numbers and functions to important problems, such as Kepler's laws of planetary motion and ac electrical circuits. This book can be read as an engaging history, almost a biography, of one of the most evasive and pervasive "numbers" in all of mathematics.

Report an issue with this product or seller

ISBN-10

9780691027951
ISBN-13

978-0691027951
Edition

First Edition
Publisher

Princeton University Press
Publication date

January 1, 1998
Part of series

Princeton Science Library
Language

English
Dimensions

6.5 x 1 x 9.75 inches
Print length

257 pages

See all details

This item: An Imaginary Tale: The Story of [the square root of minus one]

$17.74

Get it as soon as Tuesday, May 26

Sold by ASYA GROUP COMPANY and ships from Amazon Fulfillment.

Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills

$29.28

Get it as soon as Friday, May 22

Sold by The Owl’s Shelf and ships from Amazon Fulfillment.

e: The Story of a Number

$51.53

Get it as soon as Wednesday, May 20

Only 1 left in stock - order soon.

Sold by waterfall media and ships from Amazon Fulfillment.

Total price: $00

To see our price, add these items to your cart.

Try again!

Details

Added to Cart

Some of these items ship sooner than the others.

Show details Hide details

Choose items to buy together.

Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills (Princeton Science Library)
Paul J. Nahin

Paperback
$13.23
Get it as soon as Tuesday, May 19
FREE Shipping on orders over $35 shipped by Amazon
Only 18 left in stock (more on the way).
e: The Story of a Number (Princeton Science Library)
Eli Maor

Paperback
$11.69
Get it as soon as Tuesday, May 19
FREE Shipping on orders over $35 shipped by Amazon
A History of Pi
Petr Beckmann

Paperback
$9.38
Get it as soon as Tuesday, May 19
FREE Shipping on orders over $35 shipped by Amazon
Zero: The Biography of a Dangerous Idea
Charles Seife

Paperback
$11.67
Get it as soon as Tuesday, May 26
Infinite Powers: How Calculus Reveals the Secrets of the Universe
Steven Strogatz

Paperback
$15.99
Get it as soon as Tuesday, May 19
FREE Shipping on orders over $35 shipped by Amazon
The Mathematical Radio: Inside the Magic of AM, FM, and Single-Sideband
Paul J. Nahin

Hardcover
$17.12
Get it as soon as Tuesday, May 19
FREE Shipping on orders over $35 shipped by Amazon

Editorial Reviews

Amazon.com 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

Review

"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

ASIN ‏ : ‎ 0691027951
Publisher ‏ : ‎ Princeton University Press
Publication date ‏ : ‎ January 1, 1998
Edition ‏ : ‎ First Edition
Language ‏ : ‎ English
Print length ‏ : ‎ 257 pages
ISBN-10 ‏ : ‎ 9780691027951
ISBN-13 ‏ : ‎ 978-0691027951
Item Weight ‏ : ‎ 1.25 pounds
Dimensions ‏ : ‎ 6.5 x 1 x 9.75 inches
Part of series ‏ : ‎ Princeton Science Library
Best Sellers Rank: #317,077 in Books (See Top 100 in Books)
- #55 in Mathematics History
- #65 in Number Theory (Books)
- #523 in Mathematics (Books)
Customer Reviews:
(302)

About the author

Follow authors to get new release updates, plus improved recommendations.

Paul J. Nahin

Brief content visible, double tap to read full content.

Full content visible, double tap to read brief content.

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 26 books on mathematics and physics, published by IEEE Press, Springer, and the university presses of Johns Hopkins and Princeton. Translations of his books in Chinese, Russian, Arabic, Greek, Korean, Spanish, Romanian, and Japanese have appeared. His book THE DELICATE ART OF BRUTE FORCE (on the development of high-speed electronic computation) was published by Princeton in March 2026, and a collection of short science fiction stories THE ART OF THE 'WHAT-IF?' was published by Springer, also in March 2026. HIs next book, FROM QUADRATIC TO QUINTIC, is under contract at the University of Chicago Press. He has given invited talks on mathematics at the Anja Greer Math and Technology Conference at Phillips Exeter Academy (twice, in 2008 and 2018), as well as 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). He received the 2017 Chandler Davis Prize for Excellence in Expository Writing in Mathematics.

Products related to this item

Related books

Page 1 of 1Start Over

Customer reviews

302 global ratings

How customer reviews and ratings work

Customers say

Customers find this book to be a great introduction to complex analysis, with one review noting how it effectively combines history and technical explanations. However, the readability receives mixed feedback, with several customers describing it as unreadable.

AI Generated from the text of customer reviews

Select to learn more

44 customers mention content, 34 positive, 10 negative

Customers find this book engaging and well-written, particularly praising its coverage of complex numbers. One customer specifically mentions enjoying the chapter on Circuits.

It's excellent book. Just like with any book or product, there are always ways to make them better....Read more

Very good and very interesting if you love math and its story. I believe you need some knowledge of College algebra to follow everything.Read more

...All in all a great book! I recommend it highly.Read more

...Extremely disappointing.Read more

26 customers mention informative, 23 positive, 3 negative

Customers find the book informative, particularly praising it as a great introduction to complex analysis and a good source for learning about complex math. One customer notes that it effectively combines history and technical explanations.

Very in depth book with excellent description and explanations. Very insightful and answered questions I had for a long time....Read more

...book and its sequel don't hide the math, they provide a great intro to complex analysis and its applications. I learned a lot of new stuff from them.Read more

...someone who has a BS in BioMedical Engineering; I found this book quite insightful in regards to some of the coursework I took in school....Read more

...Cogent and concise explanation of this and many related terms. The math can be daunting but the concepts are presented well....Read more

11 customers mention readability, 1 positive, 10 negative

Customers find the book difficult to read, with multiple reviews describing it as unreadable, and one customer noting that the formulas are illegible.

...Many of the often complex equations are extremely difficult to read. Extremely disappointing.Read more

...Much of it is too difficult to understand unless you have a decent background in math.Read more

...All of this makes reading the book a chore - when it could be enjoyable and instructive. Shame on you Amazon!Read more

...All the formulas are illegible!...Read more

Reviews with images

See all photos

Top reviews from the United States

There was a problem filtering reviews. Please reload the page.

David J. Lewis
Perfect enrichment for math students & teachers
Reviewed in the United States on July 21, 2008
Verified Purchase

Teaching mathematics is often an uphill battle against the forces of abstraction and dullness. This delightful book is a perfect antidote, weaving as it does the history, applications and actual mathematics surrounding the concept of "imaginary" and "complex" numbers. But don't get the wrong expectation -- it's a real math book, with equations, proofs, etc, varying in level from high-school algebra and geometry to college calculus and physics.

I myself bought it in a search for material to motivate a bright 11-year-old that I am tutoring. I introduced imaginary and complex numbers to him, but all of the actual applications seemed far out of his reach. So now when I mention imaginary numbers he screws up his face and asks for more boolean algebra instead. But with this book, I now have a number of examples and historical anecdotes to motivate and fascinate him, particularly geometric interpretations and applications.

Here, for example, is one extremely elementary application that I did not know about. Prove: the product of two sums of squares is itself the sum of two squares in two different ways. Symbolically, given any integers a, b, c, d, there are integers p, q, r, s with...

(a^2 + b^2)(c^2 + d^2) = p^2 + q^2 = r^2 + s^2

This was demonstrated by mathematicians a long time ago, but not particularly easily. Using complex numbers, it's almost trivial to see, however, certainly within reach of a student of Algebra I. (There's an even simpler version of the proof that Nahin presents, but it's a bit messy to write without properly typeset mathematics.) This also makes the important point that complex numbers are very useful to help understand non-complex mathematical phenomena, a point Nahin makes throughout the book.

This also illustrates that this is a real math book, not simply a popularization piece ~about~ mathematics and mathematicians. It's really too bad that reviewers who expected the latter are downgrading their ratings of the book, because if you understand and accept what it is trying to be, it's a gem!

Much of this material is, of course, available by searching the internet. But it's not easy to find, and of highly variable quality. So Nahin's book is a real service to teachers and students at all levels.

Read more

9 people found this helpful

Helpful

Report
Roy E. Kimbrell
Thank you Amazon!
Reviewed in the United States on April 7, 2009
Verified Purchase
Below you'll see the initial review I had written of the Kindle edition of this wonderful book. I had been sorely disappointed in its formatting (as you might see if you read what I had written). I got a notice a couple of days ago from Amazon telling me that they had reformatted the book to correct the errors. I've started rereading the book, and I am delighted! All of the magic is there. I am not a mathematician (nor do I play one on TV - old joke), but I do like math. And I do like this book. Paul Nahin tells an engrossing history of imaginary numbers, which by itself is very cool. And then he shows us all the ways it is used today. You do need a little understanding of math to really get what he says: some high school math. A little freshman college calculus wouldn't hurt as well. If you're like me, someone who likes math but isn't really a mathematician, you'll love this book.

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

This delightful book, full of really cool mathematics, was ruined by Amazon when they scanned it for distribution to Kindle users. I believe they used an optical character reader to scan a hard-copy of the book, and then didn't bother to check what they had. Quality control of this product is egregious! There are errors on nearly every page: large letter V's in the place of square root radicals. wildly varying character sizes when reproducing mathematical notation, missing parts of equations (for example, primes missing from functions indicating second derivatives), all exponents tagged as footnotes, and more.

All of this makes reading the book a chore - when it could be enjoyable and instructive.

Shame on you Amazon!

Read more

23 people found this helpful

Helpful

Report
Jon
Welcome reading I'm an interesting path through history. the appendices need editorial review.
Reviewed in the United States on April 14, 2024
Format: eTextbookVerified Purchase
I enjoy this book and 4 stars covers that sentiment. Two things that I would have like to see improvement are, firstly, some more care in formulation: showing a bit more work; but that also reflects some of my lack of experience. Secondly, the appendices are helpful, but I feel editorial and that the slight against Bell in appendix A was based on an uncharitble, if not stark misinterpretation, of his comments about Leibniz

Read more

One person found this helpful

Helpful

Report

Top reviews from other countries

Translate all reviews to English

A user
Well researched, detailed
Reviewed in Germany on October 2, 2015
Format: eTextbookVerified Purchase

This is, of course, not just a history of i ( = sqrt(-1) ), but of many consequences that the discoveries of its properties have engendered.
Nahin's text is easily readable, and the step-by-step derivations of remarkable algebraic identities is well don. This implies, however, that the reader has experience (and knows how to) read texts that include mathematical exposes and mathematics as part of the text. If not, the text will probably be overwhelming. That said: there should be books like Nahin's, and his is an excellent one about the topic.

Read more
Report
lim_bus
no puedo opinar, me censuran los censores de amazon.es
Reviewed in Spain on November 9, 2019
Format: HardcoverVerified Purchase
no puedo opinar, me censuran los censores de amazon.es

Read more
Report
Translate review to English
Matthewie0pi
The explanation of the i (or j) operator.
Reviewed in Canada on October 22, 2016
Format: HardcoverVerified Purchase
Arrived in excellent condition. The book is accessible to those with a high school mathematics education.

Read more
Report
Vilas P. Bokil
It is great that such titles on Basics are Available...!
Reviewed in India on April 8, 2014
Verified Purchase
It is nice to see a beautifully presented actual view of an "Imaginary thing")... Sq rt of -1.
I am an mathematis amatuer interested in basics, basically a Diploma & B.E Mech ,passed out with Ranking 50 years ago
Searched throgh the Book store .I want to buy some titles which are available at pracically throw away prices ,on amezon.com but by sea-mail since I do not mind sacrificing time ,the present shipment rates are too much to bear.
Thanks a lot. Look forward to more purchases through you. Best Wishes!

Read more
Report
Peter
Excellent book but beware of the Kindle edition
Reviewed in the United Kingdom on January 10, 2011
Verified Purchase
As with most of the other reviews I found this book very interesting with lots of intriguing detail and no desire to avoid the maths.

Nahin's book "Dr Euler's Fabulous Formula" can be similarly recommended.

A word of warning. I made the mistake of buying the Kindle edition which is poorly typeset and has very low quality graphics used to render the equations. Typical of examples I have found so far are a multiplication sign replaced by a minus sign, square root symbol replaced by a "V" and so on. All of this interferes with the flow of thought while reading and I am reasonably sure does not exist in the paper version.

The 5 star rating is for the author's intended version of the book and certainly not for the Kindle production of it.

Read more
Report

See more reviews

Sorry, there was a problem.

Sorry, there was a problem.

Image Unavailable

Follow the author

An Imaginary Tale: The Story of [the square root of minus one] First Edition

Purchase options and add-ons

Frequently bought together

Customers who viewed this item also viewed

Customers also bought or read

Editorial Reviews

Amazon.com Review

Review

Review

From the Inside Flap

From the Back Cover

About the Author

Product details

Videos

About the author

Paul J. Nahin

Products related to this item

Related books

Customer reviews

Customers say

Select to learn more

Images in this review

Reviews with images

I’m enjoying this book (plus a warning).

Top reviews from the United States

There was a problem filtering reviews. Please reload the page.

5.0 out of 5 stars Perfect enrichment for math students & teachers

5.0 out of 5 stars Thank you Amazon!

4.0 out of 5 stars Welcome reading I'm an interesting path through history. the appendices need editorial review.

Top reviews from other countries

5.0 out of 5 stars Well researched, detailed

3.0 out of 5 stars no puedo opinar, me censuran los censores de amazon.es

5.0 out of 5 stars The explanation of the i (or j) operator.

4.0 out of 5 stars It is great that such titles on Basics are Available...!

5.0 out of 5 stars Excellent book but beware of the Kindle edition

Perfect enrichment for math students & teachers

Thank you Amazon!

Welcome reading I'm an interesting path through history. the appendices need editorial review.

Well researched, detailed

no puedo opinar, me censuran los censores de amazon.es

The explanation of the i (or j) operator.

It is great that such titles on Basics are Available...!

Excellent book but beware of the Kindle edition