## Is it a coincidence that the universal parabolic constant shows up in the solution to square point picking?

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

Is this a mere coincidence or is there an (intuitive) reason why this constant shows up in the solution to this problem?

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