What physical quantity gives a good sense of $1/\sqrt{\pi}$?

An example of a "physical quantity that gives a good sense" of $\pi$ would be the area of a disk with unit radius.


closed as off-topic by mrf, punctured dusk, Daniel W. Farlow, graydad, Tim Raczkowski Nov 12 '15 at 0:59

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The radius of a disk with unit area.


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