The constant can be defined in many ways. For example, $e$ can be defined as the unique positive number $a$ such that the graph of the function $y=a^x$ has unit slope at $x=0.$ The function $f(x)~=~e^x$ is called the exponential function, and its inverse is the natural logarithm, or logarithm to base $e.$ The natural logarithm of a positive number $k$ can also be defined directly as the area under the curve $y~=~1/x$ between $x=1$ and $x=k,$ in which case, $e$ is the number whose natural logarithm is 1. There are alternative characterizations.

Sometimes called Euler's number after the Swiss mathematician Leonhard Euler, $e$ is not to be confused with $\gamma$ - the Euler-Mascheroni constant, sometimes called simply Euler's constant. The number $e$ is also known as Napier's constant, but Euler's choice of the symbol $e$ is said to have been retained in his honor. The constant was discovered by the Swiss mathematician Jacob Bernoulli while studying compound interest.

• http://en.wikipedia.org/wiki/E_(mathematical_constant)

Local neighbourhood - D3