At 07:52 PM 3/6/2003, asimovd@aol.com wrote:
I forget who mentioned that e was found to be the "best" number base. I would like to know in what sense it is best -- or is this just some kind of offhand, non-rigorous comment?
The integral and derivative of e^x is e^x, and e is unique in that respect. The integral of 1/x is log(x) where log(x) is the natural (base e) log. Any other base of log introduces a constant factor, which makes the integral the natural log. The constant e has an especially simple series (implying that it is fundamental) and e^x has an especially simple power series. Also e is the limit as n->infinity of (1+1/n)^n. And e occurs naturally in many, many places Gaussian curve, Catenary, hyperbolic trig functions, ... You might be interested in the book ""e - the story of a number", by Eli Maor.