e (mathematical constant)

mathematical constant

e is a number, about 2.71828. It is an important mathematical constant. e has other names, like Euler's number (the Swiss mathematician Leonhard Euler), or Napier's constant (the Scottish mathematician John Napier). It is equally important in mathematics as π and i.

e is an irrational number. This means it is impossible to write as a fraction with two integers. A longer sequence, like 2.71828182845904523536, comes close to the true value. The true value of e is a number that never ends. Euler himself gave the first 23 digits of e.[1]

The number e has great importance in mathematics,[2] as do 0, 1, π, and i. All five of these numbers are important and occur again and again in mathematics. The five constants appear in one formulation of Euler's identity. Like the constant π, e is also irrational (it cannot be represented as a ratio of integers) and transcendental (it is not a root of any non-zero polynomial with rational coefficients).

The number e is very important for exponential functions. For example, the exponential function applied to the number one, has a value of e.

e was discovered in 1683 by the Swiss mathematician Jacob Bernoulli while he was studying compound interest. [3]

Magical heiroglyphsEdit

The area shown in blue (under the graph of the equation y=1/x) stretching from 1 to e is exactly 1.

There are many different ways to define e. Jacob Bernoulli, who discovered e, was trying to solve the problem:


In other words, there is a number that the expression   approaches as n becomes larger. This number is e.

Another definition is to find the solution of the following formula:


The first 200 places of the number eEdit

The first 200 digits after the decimal point are:



  1. Euler, Leonhard (1748). Introductio in analysin infinitorum. M. M. Bousquet. p. 90.
  2. Howard Whitley Eves (1969). An Introduction to the History of Mathematics. Holt, Rinehart & Winston. ISBN 978-0-03-029558-4.
  3. J J O'Connor; E F Robertson. "The number e". St Andrews University.