When I look at the Taylor series for $e^x$ and the volume formula for oriented simplexes, it makes $e^x$ look like it is, at least almost, the sum of simplexes volumes from $n$ to $\infty$. Does anyone know of a stronger relationship beyond, "they sort of look similar"?
Here are some links:
Volume formula
http://en.wikipedia.org/wiki/Simplex#Geometric_properties
Taylor Series
http://en.wikipedia.org/wiki/E_%28mathematical_constant%29#Complex_numbers