Stirling’s Formula in Words

 

I recently sketched a quick proof of Stirling’s asymptotic formula for the factorial. But what does this formula really mean?

Above is my favorite explanation. You can’t see the number in the words here, but it’s hiding in the formula for a Gaussian probability distribution. But what about the factorial, and the rest?

My description in words was informal. I’m really talking about a
Poisson distribution. If raindrops land at an average rate this says that after time the probability of...