e: The Story of a Number

Eli Maor is the author of Beautiful Geometry (with Eugen Jost), Venus in Transit, Trigonometric Delights, To Infinity and Beyond, and The Pythagorean Theorem: A 4,000-Year History (all Princeton).

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