## An Imaginary Tale: The Story of √-1Today 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 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 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. Some images inside the book are unavailable due to digital copyright restrictions. |

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### Contents

The Puzzles of Imaginary Numbers | 8 |

A First Try at Understanding the Geometry of 87301 | 31 |

The Puzzles Start to Clear | 48 |

Using Complex Numbers | 84 |

CHAPTER FIVE More Uses of Complex Numbers | 105 |

CHAPTER SIX Wizard Mathematics | 142 |

The Nineteenth Century Cauchy and the Beginning of Complex Function Theory | 187 |

APPENDIXES A The Fundamental Theorem of Algebra | 227 |

APPENDIXES C 87301sup87301to 135 Decimal Places and How It Was Computed | 235 |

APPENDIXES D Solving Clausens Puzzle | 238 |

APPENDIXES E Deriving the Differential Equation for the PhaseShift Oscillator | 240 |

APPENDIXES F The Value of the Gamma Function on the Critical Line | 244 |

Notes | 247 |

261 | |

265 | |

Acknowledgments | 269 |

### Other editions - View all

An Imaginary Tale: The Story of [the Square Root of Minus One] Paul J. Nahin No preview available - 2006 |

An Imaginary Tale: The Story of i [the square root of minus one]: The Story ... Paul J. Nahin No preview available - 2010 |