An Imaginary Tale: The Story of √-1
| Book | An Imaginary Tale: The Story of √-1 |
| Format | Paperback |
| Language | English |
| Copyright | 1998 |
| Author | Paul J. Nahin |
| Publisher | Princeton University Press |
| Copyright Holder | Princeton University Press |
| Cover/Jacket Design by | Carmina Alvarez-Gaffin |
| Publisher Series | Princeton Science Library |
| Format | Paperback |
| Language | English |
| Location | United States |
| Copyright | 1998 |
| First Published In Paperback | 2007 |
| This Edition Published | 2010 |
| Pages / Font | 267 pages / Times Roman |
| ISBN | 978-0-691-14600-3 |
| Barcode | 9 780691 146003 51695 |
| Chapters | List of Illustrations . . . xi
Preface to the Paperback Edition . . . xiii
Preface . . . xxi
Introduction . . . 3
Chapter One: The Puzzles Of Imaginary Numbers . . . 8
Chapter Two: A First Try At Understanding The Geometry Of √-1 . . . 31
Chapter Three: The Puzzles Start To Clear . . . 48
Chapter Four: Using Complex Numbers . . . 84
Chapter Five: More Uses Of Complex Numbers . . . 105
Chapter Six: Wizard Mathematics . . . 142
Chapter Seven: The Nineteenth Century, Cauchy, And The Beginning Of Complex Function Theory . . . 187
Appendixes . . . 227
A. The Fundamental Theorem Of Algebra . . . 227
B. The Complex Roots Of A Transcendental Equation . . . 230
C. [( √-1) to the √-1 power] To 135 Decimal Places, And How It Was Computed . . . 235
D. Solving Clausen's Puzzle
E. Deriving the Differential Equation for the Phase-Shift Oscillator
F. The Value of the Gamma Function on the Critical Line
Notes . . . 247
Name Index . . . 261
Subject Index . . . 265
Acknowledgments . . . 269 List of Illustrations . . . xi
Preface to the Paperback Edition . . . xiii
Preface . . . xxi
Introduction . . . 3
Chapter One: The Puzzles Of Imaginary Numbers . . . 8
Chapter Two: A First Try At Understanding The Geometry Of √-1 . . . 31
Chapter Three: The Puzzles Start To Clear . . . 48
Chapter Four: Using Complex Numbers . . . 84
Chapter Five: More Uses Of Complex Numbers . . . 105
Chapter Six: Wizard Mathematics . . . 142
Chapter Seven: The Nineteenth Century, Cauchy, And The Beginning Of Complex Function Theory . . . 187
Appendixes . . . 227
A. The Fundamental Theorem Of Algebra . . . 227
B. The Complex Roots Of A Transcendental Equation . . . 230
C. [( √-1) to the √-1 power] To 135 Decimal Places, And How It Was Computed . . . 235
D. Solving Clausen's Puzzle
E. Deriving the Differential Equation for the Phase-Shift Oscillator
F. The Value of the Gamma Function on the Critical Line
Notes . . . 247
Name Index . . . 261
Subject Index . . . 265
Acknowledgments . . . 269 Show all ▾ |