And "e" Appears from Nowhere: Quick Numerical Experiment with Clojure

This is the most interesting bit: "Select a random number between 0 and 1. Now select another and add it to the first. Keep doing this, piling on random numbers. How many random numbers, on average, do you need to make the total greater than 1? The answer is e."

The proof appears right at the bottom.

For kicks, here it is in R:

  PlusRandom <- function(initial, steps) {
    if (initial > 1) steps
    else PlusRandom(initial + urand(1), steps + 1)
  }

  mean(replicate(100000, PlusRandom(0,0))

  [1] 2.71872

I like it, although reading it at 9 AM this morning just hurt until I could think about it in more detail later.

Pretty awesome really.