Is it a coincidence that the universal parabolic constant shows up in the solution to square point picking? - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T22:33:16Z http://mathoverflow.net/feeds/question/37871 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/37871/is-it-a-coincidence-that-the-universal-parabolic-constant-shows-up-in-the-solutio Is it a coincidence that the universal parabolic constant shows up in the solution to square point picking? asmaier 2010-09-06T10:57:54Z 2010-09-06T10:57:54Z <p>The expected distance $d$ of randomly selected points within a unit square to the square's center is</p> <p>$d = \frac{1}{6} P$</p> <p>where P is the universal parabolic constant</p> <p>$P = \sqrt{2} + \ln{(1+\sqrt{2})} = 2.2955871 \dots$</p> <p>see</p> <ul> <li><a href="http://mathworld.wolfram.com/SquarePointPicking.html" rel="nofollow">http://mathworld.wolfram.com/SquarePointPicking.html</a></li> <li><a href="http://mathworld.wolfram.com/UniversalParabolicConstant.html" rel="nofollow">http://mathworld.wolfram.com/UniversalParabolicConstant.html</a></li> </ul> <p>Is this a mere coincidence or is there an (intuitive) reason why this constant shows up in the solution to this problem?</p>