


An Imaginary Tale: 

Today complex numbers have such widespread practical usefrom electrical engineering to aeronauticsthat few people would expect the story behind their derivation to be filled with adventure and enigma. In An Imaginary Tale, Paul Nahin tells the 2000yearold 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 mathematicianengineer 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 rootsnow 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. "A booklength 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 nonmathematician 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! Ninetyfifteen! 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 Endorsement: Other Princeton books authored or coauthored by Paul J. Nahin:
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