The number e and the exponential function
El número e y la función exponencial
- Date
- 1683 · confidence high
- Place
- Basel, Switzerland
- Credited to
- Jacob Bernoulli (compound interest limit); Euler (name, series and properties, 1748)
- People
- 👤 Jakob Bernoulli1655–1705
- Field
- Knowledge & symbols
What was discovered
The constant 2.71828..., which arises as the limit of (1+1/n)^n when studying continuous compound interest and is the base of the only function equal to its own derivative. Euler named it e and proved its irrationality.
The constant appears implicitly in Napier's tables (1618, appendix by Oughtred).
What it led to
- differential equations of growth and decay
- Euler's identity
- the normal distribution
- the transcendence of e (Hermite)
Built on
- Infinitesimal calculus1665-1684
- Napier's logarithms
Made possible
- Euler formula and Euler identity1748
- Radioactivity and radium1896–1898
- population growth and interest models