The Naperian or natural base to logarithms; Naperian does not refer to Napier having created it, in fact his concept of a logarithm is different than the modern concept, but he is credited as creating logarithms, hence this extremely useful number is identified with him. e is approximately 2.718281828459045 to fifteen digits, and can be expressed in many ways:
it is the limit of the slowly converging function
       /     1  \
 lim  |  1 + -   | ^ n
n->oo  \     n  /
or the more quickly converging series
 oo
---
\     1
 |   ---
/     n!
---
n=0
or as the number satisfying d/du (e^u) = (e^u). Euler gave this number the letter it is associated with; some say it is because e is the first letter of his name, but Euler said that all others were taken up to e. Euler discovered the relationship e^(i*theta) = cos(theta) + i*sin(theta), which is one of the most important formulas in complex analysis, and is responsible for the amazing relationship between the five most important numbers in mathematics: e^(i*pi) + 1 = .