## √π sqrt[pi]

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.

$\dpi{300} \bg_white \int e^{-x^2} = \sqrt{\pi}$

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)

35 notes

1. janopult answered: Well, if you put it in the simplest of terms…it means the area under a bell curve.
2. sovietskunk answered: Woah! Math is mind blowing <3
3. sleepisoverated reblogged this from proofmathisbeautiful
4. dashdotdashbackslash answered: Pi isn’t the distance around a circle. It’s the ratio of a circle’s circumference to its diameter.
5. teknomadiq answered: More fascinating is whether sqrt(pi) is hardwired into our brains…we often impose the normal curve on phenomenon that aren’t normal…why?