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Simple English

e is a mathematical constant. It also has other names, like Euler's number (because of the Swiss mathematician Leonhard Euler), or Napier's constant (because of the Scottish mathematician John Napier). It is an important number in mathematics, like π and i. It is an irrational number, which means it is impossible to write as a fraction with two integers; but some numbers, like 2.71828182845904523536 come close to the real value.

The number e is very important for exponential functions. For example, an exponential function becomes bigger by a factor e in the same time that a linear function (one that looks like a straight line) becomes bigger by a factor 2.

Definitions

File:Hyperbola
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:

\lim_{n\to\infty} \left(1+\frac{1}{n}\right)^n.

In other words, there is a number the expression \left(1+\frac{1}{n}\right)^n approaches if n is made very big. This number is e.

The true value of e is a number that never ends,

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

2+\cfrac{2}{2+\cfrac{3}{3+\cfrac{4}{4+\cfrac{5}{5+\cfrac{6}{\ddots\,}}}}}

The first 200 places of the number e

The first 200 digits after the decimal point are:

e=2{.}71828\;18284\;59045\;23536\;02874\;71352\;66249\;77572\;47093\;69995
\;95749\;66967\;62772\;40766\;30353\;54759\;45713\;82178\;52516\;64274
\;27466\;39193\;20030\;59921\;81741\;35966\;29043\;57290\;03342\;95260
\;59563\;07381\;32328\;62794\;34907\;63233\;82988\;07531\;95251\;01901\,\ldots.


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