VERY HARD Puzzle: What Is The Distance Between Two Random Points In A Square?
1,893
by Super User, 5 years ago
Blog post
http://wp.me/p6aMk4FA
Simulation
https://docs.google.com/spreadsheets/d/1ZPnDOQlncgPZsLKeYXqKDNL93RUFTqypot4EY9h61w/edit?usp=sharing
Sources and further reading
Quadruple integral
http://math.stackexchange.com/questions/1254129/averagedistancebetweentworandompointsinasquare
Difference of two uniform variables
http://www.math.wm.edu/~leemis/chart/UDR/PDFs/StandarduniformStandardtriangular.pdf
Difference of two uniform variables and solving the double integral
https://www.quora.com/HowcanIcalculatethemeandistanceoftwopointsplacedatrandominaunitsquare
Solving the double integral
http://math.stackexchange.com/questions/1294800/averagedistancebetweentworandomlychosenpointsinunitsquarewithoutcalc
Mean distance polar coordinates change
http://www.mathpages.com/home/kmath324/kmath324.htm
Integral secant cubed
https://en.wikipedia.org/wiki/Integral_of_secant_cubed
Mean distance square
http://mathworld.wolfram.com/SquareLinePicking.html
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5 years ago