An Imaginary Tale : : The Story of √-1 / / Paul J. Nahin.

• VerfasserIn: Nahin, Paul J.,
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2010]; ©2010
• Year of Publication: 2010
• Edition: With a New preface by the author
• Language: English
• Series: Princeton Science Library ; 74
• Physical Description: 1 online resource (296 p.) :; 1 halftone. 47 line illus.

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' mo...

Table of Contents

• Frontmatter
• A Note to the Reader
• Contents
• List of Illustrations
• Preface to the Paperback Edition
• Preface
• An Imaginary Tale
• Introduction
• CHAPTER ONE The Puzzles of Imaginary Numbers
• CHAPTER TWO. A First Try at Understanding the Geometry of √-1
• CHAPTER THREE The Puzzles Start to Clear
• CHAPTER FOUR Using Complex Numbers
• CHAPTER FIVE More Uses of Complex Numbers
• CHAPTER SIX Wizard Mathematics
• CHAPTER SEVEN The Nineteenth Century, Cauchy, and the Beginning of Complex Function Theory
• APPENDIX A. The Fundamental Theorem of Algebra
• APPENDIX B. The Complex Roots of a Transcendental Equation
• APPENDIX C. (√-1)(√-1) to 135 Decimal Places, and How It Was Computed
• APPENDIX D. Solving Clausen's Puzzle
• APPENDIX E. Deriving the Differential Equation for the Phase-Shift Oscillator
• APPENDIX F. The Value of the Gamma Function on the Critical Line
• Notes
• Name Index
• Subject Index
• Acknowledgments