Michael Kleber wrote: << On Tue, Mar 4, 2008 at 4:26 PM, Schroeppel, Richard <rschroe@sandia.gov> wrote:
. . . Consider a domino, two adjacent 1x1 squares. What's the average distance between a random point in the left square, and a random point in the right square? . . .
Just for the record, Mma (6.0) does fine: d[x1_,y1_,x2_,y2_] := Sqrt[ (x1-x2)^2+(y1-y2)^2 ] Integrate[ d[x1,y1,x2,y2], {x1,-1,0},{x2,0,1},{y1,0,1},{y2,0,1} ] (116 - 8 Sqrt[2] - 20 Sqrt[5] + 140 ArcCsch[2] - 40 ArcSinh[1] + 80 ArcSinh[2] + Log[32] + 10 Log[-1 + Sqrt[5]] - 15 Log[123 + 55 Sqrt[5]]) / 120
This answer is intriguingly random-looking. It seems to be daring us to come up with an explanation for why it should be as it is. How about a much simpler task: Can anyone suggest a reason for the denominator of 120 ? --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele