calculus - Is there a simple geometrical description of $e$?

Of course I am not looking for a definition through $\int_1^e{1\over x} \, \mathrm{d}x=1$ or that slope of $a^x$ at $x=0$ is $1$ when $a=e$. I am looking for something understandable by a kid who has begun comprehending $\pi$ as the ratio of circumference to diameter of a circle. Or perhaps by one who is a couple of years older.

(And of course there is no reason to suspect that every mathematical constant has a simple geometrical description. But a "definition" that might not be suitable for a calculus text could be suitable for introduction to laymen.)

Edit 1:

One area I would find interesting would be a definition that uses the entire hyperbola $xy=1$ instead of pieces of it. Of course both area (between hyperbola and asymptotes) and the length, measured in the usual fashion, will be infinity. I have attempted projecting the shape onto a sphere to see if I get a number similar to $e$; but with no luck.

Answer

Math is fun has a nice description: http://www.mathsisfun.com/numbers/e-eulers-number.html

If you divide up a number into $n$ parts and multiply them together, the answer is biggest when your number is cut up to a value near $e$. It represents the best sized chunks of a number to multiply together.