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An Imaginary Tale: The Story of i [the square root of minus one] (Princeton Library Science Edition) (Princeton Science Library) [Paperback]

Paul J. Nahin
3.8 out of 5 stars  See all reviews (14 customer reviews)
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Book Description

14 Mar 2010 Princeton Science Library

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.

Frequently Bought Together

An Imaginary Tale: The Story of i [the square root of minus one] (Princeton Library Science Edition) (Princeton Science Library) + "e": The Story of a Number (Princeton Science Library) + Zero: The Biography of a Dangerous Idea
Price For All Three: 26.30

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Product details

  • Paperback: 296 pages
  • Publisher: Princeton University Press; Princeton Library Science edition (14 Mar 2010)
  • Language: English
  • ISBN-10: 0691146004
  • ISBN-13: 978-0691146003
  • Product Dimensions: 23.1 x 15.2 x 2 cm
  • Average Customer Review: 3.8 out of 5 stars  See all reviews (14 customer reviews)
  • Amazon Bestsellers Rank: 176,159 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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Product Description


One of Choice's Outstanding Academic Titles for 1999

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

"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

From the Inside Flap

"Dispelling many common myths about the origin of the mystic 'imaginary' unit, Nahin tells the story of i from a historic as well as human perspective. His enthusiasm and informal style easily catch on to the reader. An Imaginary Tale is a must for anyone curious about the evolution of our number concept."--Eli Maor, author of Trigonometric Delights, e: The Story of a Number, and To Infinity and Beyond

--This text refers to an out of print or unavailable edition of this title.

Inside This Book (Learn More)
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Front Cover | Copyright | Table of Contents | Excerpt | Index
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Customer Reviews

Most Helpful Customer Reviews
21 of 22 people found the following review helpful
5.0 out of 5 stars Fantastic! Thorough, scholarly, interesting! 5 Mar 1999
By A Customer
This is an excellent, beautiful book! Just the section on Kepler's laws is worth the price of the book (hardcover to boot!)
If you like math, if you are willing to spend a bit of time understanding the wonderful results -- get it! Some calculus background needed -- nothing beyond high school.
The book goes well beyond providing a narrative on the history of "square root of -1". It actually shows in complete detail how to use "i" to do wonderful things. Along the way the author provides the important historical events and plenty of notes and references for anyone interested in getting some more. It is clear the author took his time to research and study the subject. He has presented it well, thouroghly, and in an interesting way -- without sacrificing detail!
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9 of 9 people found the following review helpful
4.0 out of 5 stars Good, but you have to work at reading it 8 Feb 2008
Format:Paperback|Verified Purchase
If I had never read any of Eli Maor's excellent books I would have scored this book as 5 stars. It is a very good book that guides you through a series of difficult mathematical concepts without being a textbook. It is very readable, but it is peppered with 'roadblocks' where you suddenly have to pay a lot more attention, and possibly re-read sections, before you can proceed. It also, despite being a new 'bugs removed' edition, has at least one grammatical error which makes a paragraph hard to follow.

Having said all that, it really is a very good book. It is just that I have been spoiled by Eli Maor's books, which cover similar ground (trigonometry, e) in a similar way (history, characters, mathematical ideas, related concepts), but manage to make it an effortless joy for the reader. This book somehow never became a joy to read.
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7 of 7 people found the following review helpful
5.0 out of 5 stars Excellent book but beware of the Kindle edition 10 Jan 2011
By Peter
Format:Kindle Edition|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.
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28 of 31 people found the following review helpful
2.0 out of 5 stars Disappointing presentation of the material 14 Oct 2002
By A Customer
I read this book on the back of having just finished Eli Maor's excellent "To infinity and beyond". Unlike Maor's book, "An imaginary tale" is poorly written and presented. While Maor has a fluid and engrossing writing style, Nahin is much less convincing. The material is all there, but it's the presentation with which I have a problem. It's not all bad -- the chapter on the geometry of i is well done, for example, but that's the exception rather than the rule. Another problem is the poor quality of the diagrams. Cubic curves are hastily drawn freehand. Right angled triangles don't always have right angles, and so on. On the whole, I came away with an impression of a book with lots of potential, but most of it left unrealised.
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4 of 4 people found the following review helpful
4.0 out of 5 stars just get past the geometry 23 April 2009
By Mitt
I imagine that quite a few people who try to read this will be put off by the first section of geometry (unless you're one of the two people into geometry). It is a bit tortuous but persevere and you will be rewarded. After this point the book really becomes excellent.

Be aware though that this book is essentially a collection of derivations following the history of the use of i and complex numbers. As such it is very equation heavy, so if you want a popular science type book that talks about the ideas but not the nitty gritty (a la The Music of the Primes: Why an Unsolved Problem in Mathematics Matters) then look elsewhere. However, if you don't mind the equations and are prepared to put in a little mental effort then you will find many amazing results.
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3 of 3 people found the following review helpful
1.0 out of 5 stars Badly translates to Kindle 7 Aug 2013
Format:Kindle Edition|Verified Purchase
Any book about mathematics must accurately reproduce the formulae which are essential to the subject matter. I had bought the paper version of this book which I found to be excellent. That deserved at least ten stars!

I decided to also buy the Kindle version purely for convenience, and that is what I am reviewing here. What a mess it is!! The formulae are truncated at both ends so that they make no sense whatsoever and mathematical expressions which are used in the main text are extremely badly "translated" for the Kindle. Also the formulae are in a smaller typeface than the normal text and since I am visually disabled they are extremely difficult to read in the Kindle version.

Whoever converted this book to the Kindle format had no knowledge of mathematics or didn't give a damn about accurately reproducing formulae or mathematical expressions.

I would like give the Kindle version zero stars because it is so dire but I am not allowed to do that. Clearly the only way to read this book is in the paper version.
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19 of 22 people found the following review helpful
5.0 out of 5 stars Eulogy 23 Aug 1999
By A Customer
I rate this book as one of the three best general mathematical books that I have ever bought. Its style is clear and light and the scope of the mathematics is breathtaking; I learnt a great deal from it and saw explained some hard ideas in a very readable way. Not every question is answered but as the author says it isn't a text book. If you want to get into complex analysis and learn about its development and the geniuses who have been involved in it I can think of no better path to take-but you will need to work at some bits! The author avoids actually defining complex numbers in a rigorous way and I would have liked to have seen them defined somewhere as ordered pairs of reals with a reasonable definition of addition and a funny definition of multiplication, with i simply a change of notation. Not easy to fit into the historical development but worth an appendix.
Buy the book. If you don't like it I reckon the problem's with you!
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Most Recent Customer Reviews
2.0 out of 5 stars Highly Mathematical
It's not really a story in the normal sense, highly mathematical (I got lost by page 3) without an explanation to whats going on and why. Read more
Published 2 months ago by B Nic Tesla
4.0 out of 5 stars An enjoyable read
I didn't feel that I learned much that I didn't already know, but I did enjoy the text. The author is happy to present the mathematics in mathematical symbols but doesn't overload... Read more
Published 5 months ago by Albear
3.0 out of 5 stars Need for re-edit of Kindle edition
This is a fascinating book but the Kindle edition does not do it justice for two main reasons. The first concerns the presentation of mathematical formulae: where these appear... Read more
Published 7 months ago by MR MICHAEL J GREEN
5.0 out of 5 stars Very good
Very readable book going through the history of "i". Some very interesting details are given that one doesn't normally come across in textbooks or courses (given the fact... Read more
Published 14 months ago by Dr G
5.0 out of 5 stars Calling Russell Group+ Maths Uni applicants
I accept the comments from other reviewers - you do have to work through this book. Whilst with other 'wow' mathematical books (such as Derbyshire's Prime Obsession) which have a... Read more
Published 21 months ago by R Stoner
3.0 out of 5 stars Good but loses pacing
The mix of history, characters and mathematical concepts produces a fascinating read. My only complaint is that the exciting structure of the beginning gradually loses pace as the... Read more
Published on 15 Jun 2011 by RobertH
5.0 out of 5 stars Magnificent.
This book is marvellous in every way. The historical approach in the early chapters is just right and reading through them you really get a feel for how the theory of complex... Read more
Published on 26 Dec 2010 by Andi H
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