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.

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