E: The Story of a Number

1. John Napier, 1614
2. Recognition
3. Financial Matters
4. To the Limit, If It Exists
5. Forefathers of the Calculus
6. Prelude to Breakthrough
7. Squaring the Hyperbola
8. The Birth of a New Science
9. The Great Controversy
10. e[superscript x]: The Function That Equals its Own Derivative
11. e[superscript theta]: Spira Mirabilis
12. (e[superscript x] + e[superscript -x])/​2: The Hanging Chain
13. e[superscript ix]: "The Most Famous of All Formulas"
14. e[superscript x + iy]: The Imaginary Becomes Real
15. But 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.