Why is $e$ the number that it is? Why is $e$ the number that it is?  Most of the irrational number that we learn about in school have something to do with geometry, like $\pi$ is the ratio of a circle's diameter to its circumference.  Those numbers can also be derived using maths ($\pi = \lim_{n\to\infty}4\sum_{k = 1}^{n}\frac{(-1)^{k+1}}{2k - 1}$).  On the other hand, $e$ is derived only from math, and finds no other immediate geometric basis.  Why then, is $e$ the number that it is ($2.7182\ldots$) and not some other number?
EDIT: My question is more along the lines of why $e$ is $2.7182\ldots$ On an alien world where there is a different system of numbers, could there be a similar constant that has all the properties of $e$, but is not $2.7182\ldots$?

Not forget to mention:


*

*$$e^x = \sinh(x) + \cosh(x)$$ 

*$e$ is fundamental for the Theory of Representations in Group Theory, essential topic in Quantum field theory, quantum mechanics and particle physics 

*$e$ arises also from the "compound interests" problem in economics

*It's fundamental for Fourier transforms, Stirling approximation and Gaussian curves (so that it's fundamental in Data Analysis and Probability and Statistics)

