An Imaginary Tale: The Story of

An Imaginary Tale: The Story of "i" [the square root of minus one] / Edition 1

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by Paul J. Nahin
     
 

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

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Overview

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.

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Product Details

ISBN-13:
9780691127989
Publisher:
Princeton University Press
Publication date:
01/02/2007
Edition description:
With a New preface by the author
Pages:
296
Product dimensions:
6.10(w) x 9.10(h) x 0.80(d)

Table of Contents

List of Illustrations
Preface
Introduction3
Ch. 1The Puzzles of Imaginary Numbers8
Ch. 2A First Try at Understanding the Geometry of [the square root of] -131
Ch. 3The Puzzles Start to Clear48
Ch. 4Using Complex Numbers84
Ch. 5More Uses of Complex Numbers105
Ch. 6Wizard Mathematics142
Ch. 7The Nineteenth Century, Cauchy, and the Beginning of Complex Function Theory187
App. AThe Fundamental Theorem of Algebra227
App. BThe Complex Roots of a Transcendental Equation230
App. C([the square root of] -1)[superscript [square root of] -1] to 135 Decimal Places, and How It Was Computed235
Notes239
Name Index251
Subject Index255
Acknowledgments259

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