[1] What is the mean distance between two random points on the perimeter of a unit square?
[2] What is the mean distance between two random points on the interior of a unit square?
(In reply to
re: Part 2 in two different ways. by Charlie)
In case this helps, here's a breakdown of the distances involved and how many times they occur in the summation for the case n=4:
increment number of
differences occurrences length
0 0 16 0
0 1 48 .25
0 2 32 .5
0 3 16 .75
1 1 36 .3535533905932738
1 2 48 .5590169943749475
1 3 24 .7905694150420949
2 2 16 .7071067811865476
2 3 16 .9013878188659973
3 3 4 1.060660171779821

Posted by Charlie
on 20130602 11:05:45 