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### Synopses & Reviews

#### Publisher Comments

The interest earned on a bank account, the arrangement of seeds in a sunflower, and the shape of the Gateway Arch in St. Louis are all intimately connected with the mysterious number *e*. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest background in mathematics, this biography of *e* brings out that number's central importance in mathematics and illuminates a golden era in the age of science.

#### Synopsis

The interest earned on a bank account, the arrangement of seeds in a sunflower, and the shape of the Gateway Arch in St. Louis are all intimately connected with the mysterious number

*e*. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest mathematical background, this biography brings out the central importance of*e*to mathematics and illuminates a golden era in the age of science.#### Synopsis

The interest earned on a bank account, the arrangement of seeds in a sunflower, and the shape of the Gateway Arch in St. Louis are all intimately connected with the mysterious number

*e*. In this informal and engaging history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for a reader with only a modest background in mathematics, this biography of*e*brings out that number's central importance in mathematics and illuminates a golden era in the age of science.### About the Author

Eli Maor is the author of "Venus in Transit", "Trigonometric Delights", "To Infinity and Beyond", and "The Pythagorean Theorem: A 4,000-Year History" (all Princeton). He teaches the history of mathematics at Loyola University in Chicago and at the Graham School of General Education at the University of Chicago.

### Table of Contents

Preface | ||

1 | John Napier, 1614 | 3 |

2 | Recognition | 11 |

3 | Financial Matters | 23 |

4 | To the Limit, If It Exists | 28 |

5 | Forefathers of the Calculus | 40 |

6 | Prelude to Breakthrough | 49 |

7 | Squaring the Hyperbola | 58 |

8 | The Birth of a New Science | 70 |

9 | The Great Controversy | 83 |

10 | e[superscript x]: The Function That Equals its Own Derivative | 98 |

11 | e[superscript theta]: Spira Mirabilis | 114 |

12 | (e[superscript x] + e[superscript -x])/2: The Hanging Chain | 140 |

13 | e[superscript ix]: "The Most Famous of All Formulas" | 153 |

14 | e[superscript x + iy]: The Imaginary Becomes Real | 164 |

15 | But What Kind of Number Is It? | 183 |

App. 1. Some Additional Remarks on Napier's Logarithms | 195 | |

App. 2. The Existence of lim (1 + 1/n)[superscript n] as n [approaches] [infinity] | 197 | |

App. 3. A Heuristic Derivation of the Fundamental Theorem of Calculus | 200 | |

App. 4. The Inverse Relation between lim (b[superscript h] - 1)/h = 1 and lim (1 + h)[superscript 1/h] = b as h [approaches] 0 | 202 | |

App. 5. An Alternative Definition of the Logarithmic Function | 203 | |

App. 6. Two Properties of the Logarithmic Spiral | 205 | |

App. 7. Interpretation of the Parameter [phi] in the Hyperbolic Functions | 208 | |

App. 8. e to One Hundred Decimal Places | 211 | |

Bibliography | 213 | |

Index | 217 |

### Product Details

- ISBN:
- 9780691141343
- Binding:
- Trade Paperback
- Publication date:
- 01/19/2009
- Publisher:
- PRINCETON UNIVERSITY PRESS
- Series info:
- Princeton Science Library
- Pages:
- 227
- Height:
- 9.50
- Width:
- 6.00
- Thickness:
- .50
- Series:
- Princeton Science Library
- Illustration:
- Yes
- Copyright Year:
- 2009
- UPC Code:
- 2800691141345
- Author:
- Media Run Time:
- B
- Subject:
- History
- Subject:
- History of Science and Medicine, Philosophy of Science
- Subject:
- History -- Philosophy.
- Subject:
- Mathematics -- History.
- Subject:
- Popular science
- Subject:
- e (The number)
- Subject:
- Mathematics