Just dumb luck, I think. In general, anything that depends essentially on working in base 10 tends to be just coincidence :-). If you compute some more places,

Just dumb luck, I think. In general, anything that depends essentially on working in base 10 tends to be just coincidence :-). If you compute some more places, you get 1.0000000271816967980437100574683393 so the digits of e don't continue for very long. The thing that's more surprising on the face of it is that the result is so close to 1. Let's rearrange it a little: exp(s3 gg) ~= exp(1) s3 gg which I prefer to write as exp(s3 gg - 1) ~= 1 + (s3 gg - 1) because the series for exp looks like exp(x) = 1 + x + ... -- so what gives you the value close to 1 is that s3 gg - 1 is rather close to 0, so that the first couple of terms of the series are close to the actual value of exp(); in other words, that gg is close to 1/s3. So far as I know, this too is just a coincidence. (There are lots of simple-ish constants between, say, 0.1 and 10; it's not really that surprising to find a pair that are approximately reciprocals.) The e-like digits that follow amount (after a little simple algebra) to the fact that (s3 gg - 1)^2/2 ~= e/10^8 or, if you prefer, 1 - s3 gg ~= sqrt(2e)/10^4. Which smells very, very coincidental to me. It's a basically random smallish number; why shouldn't it be close to sqrt(2e) / a power of 10?