## √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. sleepisoverated reblogged this from proofmathisbeautiful
3. dashdotdashbackslash answered: Pi isn’t the distance around a circle. It’s the ratio of a circle’s circumference to its diameter.
4. 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?
5. xpalright answered: Of course, you can think about pi instead as the area of a circle instead of its circumference, if that helps your thought process.
6. mydigiverse answered: π is NOT a distance, it is ratio of two distances (circumference and diameter). Therefore π is a dimensionless constant (as well as √π is)..
7. bparramosqueda reblogged this from proofmathisbeautiful
8. divide-by-zero answered: Pi is a NUMBER, not a distance. The R in 2pi*R gives the units of distance around a circle. Pi has no intrinsic units :)
9. hildapermatas reblogged this from proofmathisbeautiful
10. theshoutingendoflife reblogged this from proofmathisbeautiful and added:
PI IS A FUCKING NUMBER. IT ARISES NATURALLY MANY TIMES IN REAL AND COMPLEX ANALYSIS WITHOUT THE REQUIREMENT OF GEOMETRY...
11. proofmathisbeautiful reblogged this from isomorphismes
12. gaberoo answered: Yo Chris! So I guess you’ve moved on to serious things!! :)
13. davidaedwards answered: sum(1/n^2,n,1,infinity)=(pi)^2/6; So? Such things don’t require geometric reasons!
14. isomorphismes posted this