# e

*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;e13;none;1;e13;;;block;;;;no;1;4224n;90919n;;;;;eq13;comptd;;center;stack;;;;;CE5In 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* = - 1art/square-root-of-negative-1.gif the square root of negative 1, 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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