"E", The Story of a Number

The interest earned on a bank account, the arrangement of seeds in a sun flower, and the shape of the Gateway Arch in St. Louis are all intimately connected with the mysterious number "e". In this history, Eli Maor portrays the characters and the elegant mathematics that lie behind the number.

The interest earned on a bank account, the arrangement of seeds in a sun flower, and the shape of the Gateway Arch in St. Louis are all intimately connected with the mysterious number "e". In this informal history, Eli Maor portrays the curious characters and the elegant mathematics that lie behind the number. Designed for the reader with only a modest background in mathematics and illuminates a golde era in the age of science.

Preface John Napier, 1614 2Recognition 3Financial Matters 4To the Limit, If It Exists 5Forefathers of the Calculus 6Prelude to Breakthrough 7Squaring the Hyperbola 8The Birth of a New Science 9The Great Controversy 10e[superscript x]: The Function That Equals its Own Derivative 11e[superscript theta]: Spira Mirabilis 12(e[superscript x] + e[superscript -x])/2: The Hanging Chain 13e[superscript ix]: "The Most Famous of All Formulas" 14e[superscript x + iy]: The Imaginary Becomes Real 15But What Kind of Number Is It? App. 1. Some Additional Remarks on Napier's Logarithms App. 2. The Existence of lim (1 + 1/n)[superscript n] as n [approaches] [infinity] App. 3. A Heuristic Derivation of the Fundamental Theorem of Calculus 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 App. 5. An Alternative Definition of the Logarithmic Function App. 6. Two Properties of the Logarithmic Spiral App. 7. Interpretation of the Parameter [phi] in the Hyperbolic Functions App. 8. e to One Hundred Decimal Places Bibliography Index