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3.7 out of 5 stars22
3.7 out of 5 stars
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on 8 February 2008
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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on 10 January 2011
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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on 5 March 1999
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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on 23 April 2009
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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on 14 October 2002
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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on 26 December 2010
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 numbers developed. Learning complex numbers at school begins with a set of basic rules and the Argand diagram then you are into routine calculations and simple functions of a complex variable.Fun... but its a bit like painting by numbers and not especially inspiring.Every mathematics student studying Further Maths, or beginning their University course would have their experience of maths richly enhanced by carefully reading this book. Nahin starts by presenting some of the earliest algebraic puzzles involving "i" , followed by an account of early attempts to give the square root of minus one a geometric underpinning. I especially loved the chapters 'The puzzles start to clear' and 'Wizard Mathematics'.Many beautiful mathematical results are demonstrated;For the average reader (prior knowledge of basic calculus, trigonometry and complex numbers)still be prepared to do a little work to get the most out of this won't be bored. Nahin's style is relaxed yet detailed in its approach but does not obfuscate the beauty and power of the results with inappropriate rigour.It is not intended to compete with textbooks.I haven't quite finished the book yet but 'The Princeton Science Library' has to be congratulated again on another gem.
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on 23 August 1999
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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on 13 January 2014
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 within the script they are almost invariably (and unnecessarily) shown as superscripts, and where they appear on separate lines they are in a small size font that is difficult to read. Secondly, there are typographical errors, the most serious of which relate to the Greek letter theta, which is used extensively as a mathematical symbol throughout the book: however, in about half of the places where the theta symbol should appear it is missing - there is a blank space, or not even a blank space. As a result the sentence or formula is incomprehensible.

The Kindle edition needs to be re-edited by someone who understands both mathematics and typography.
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on 15 June 2011
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 book progresses. I would like to give this 4 stars but I did have to force my self to read certain chapters due to the breakdown in pace.
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on 13 October 2014
This is a really tough book. I enjoyed the companion book in the same series of books on 'e' very much, but this one is at times more like a text book than a reading book. I have a first in maths from Oxford, admittedly some years ago, but I gave up before the end. You have been warned!
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