E
Related Category: Mathematics
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
;e13;none;1;e13;;;block;;;;no;1;4224n;90919n;;;;;eq13;comptd;;center;stack;;;;;
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
ei&pgr;=−1, where
i=
−1, thus expressing the relationship between the numbers
e, i, and &pgr;. 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).