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
becomes infinitely large, or
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 e i π
=−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 © 2012, Columbia University Press. All rights reserved.
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