π of course is the distance around a circle. √π is the area under ∫exp (−x²), and exp (−x²) is the key ingredient in the normal distribution.
That’s more or less what √π means—the area under the Bell curve.
But what does it mean mean? I mean, if π is a distance and √ is used to turn areas into distances — is it, like, shrinking the π even one more time? Are we talking about a half-dimension here?
edit: hmm, the end of this post seems to have been deleted by the rare weirdness of tumblr’s mass editor. I’ll see if I can’t remember how it ended. Umm, something about the moment-generating function? (i.e. going around the complex unit circle)