Encyclopediae,
e, in mathematics, irrational number occurring widely in mathematics and science, approximately equal to the value 2.71828; it is the base of natural, or Naperian, logarithms. The number e is defined as the limit of the expression (1+1/n)n as n becomes infinitely large, or
| e = | lim
n =>infinty | (1 + 1/n)n |
In 1873 the French mathematician C. Hermite proved that
e was transcendental, i.e., not a
root of any algebraic equation; this proof constituted a great contribution to the growth of mathematics. The number
e is also known as Euler's number, for Leonhard Euler, who discovered the famous formula
eiπ=-1, where
i=
, thus expressing the relationship between the numbers
e, i, and π. The exponential function e
x, often written exp(
x), occurs in various applications ranging from statistics to nuclear physics.
See study by E. Maor (1994).
The Columbia Electronic Encyclopedia, 6th ed. Copyright © 2007, Columbia University Press. All rights reserved.
See more Encyclopedia articles on: Mathematics
