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Mean Distance Two Points (Posted on 2013-06-01) Difficulty: 3 of 5
[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?

No Solution Yet Submitted by Danish Ahmed Khan    
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re(2): Part 2 in two different ways. | Comment 5 of 8 |
(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 2013-06-02 11:05:45
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