An Imaginary Tale

Author(s): Paul J. Nahin

Science

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 colourful 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.

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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"

Runner-up for Choice Magazine Outstanding Reference/Academic Book Award 1999 and AAP/Professional and Scholarly Publishing Awards: Mathematics and Statistics 1998.

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

Paul J. Nahin is the author of many best-selling popular math books, including "Digital Dice, Chases and Escapes, Dr. Euler's Fabulous Formula, When Least Is Best, Duelling Idiots and Other Probability Puzzlers," and "Mrs. Perkins's Electric Quilt" (all Princeton). He is professor emeritus of electrical engineering at the University of New Hampshire.

List of Illustrations Ch. 1 The Puzzles of Imaginary Numbers Ch. 2 A First Try at Understanding the Geometry of [the square root of] -1 Ch. 3 The Puzzles Start to Clear Ch. 4 Using Complex Numbers Ch. 5 More Uses of Complex Numbers Ch. 6 Wizard Mathematics Ch. 7 The Nineteenth Century, Cauchy, and the Beginning of Complex Function Theory App. A The Fundamental Theorem of Algebra App. B The Complex Roots of a Transcendental Equation App. C ([the square root of] -1)[superscript [square root of] -1] to 135 Decimal Places, and How It Was Computed Notes Name Index Subject Index Acknowledgments

General Fields

  • : 9780691127989
  • : PUP
  • : UNKNOWN
  • : 0.428
  • : 02 January 2007
  • : 229mm X 152mm X 20mm
  • : United States
  • : books

Special Fields

  • : Paul J. Nahin
  • : Paperback
  • : New edition
  • : 515.9
  • : 296
  • : 47 line illus, 1 halftone