The expected distance $d$ of randomly selected points within a unit square to the square's center is
$d = \frac{1}{6} P$
where P is the universal parabolic constant
$P = \sqrt{2} + \ln{(1+\sqrt{2})} = 2.2955871 \dots $
see
- http://mathworld.wolfram.com/SquarePointPicking.html
- http://mathworld.wolfram.com/UniversalParabolicConstant.html
Is this a mere coincidence or is there an (intuitive) reason why this constant shows up in the solution to this problem?
