Product Description

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.

Product Details

• Amazon Sales Rank: #209559 in Books
• Published on: 1998-08-24
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 257 pages

Review
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 )

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 )

Review
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" )

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

Customer Reviews

Fantastic! Thorough, scholarly, interesting!
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!

Disappointing presentation of the material
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.

Eulogy
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!