On Tue, Mar 4, 2008 at 4:26 PM, Schroeppel, Richard <rschroe@sandia.gov> wrote:
A similar problem appeared in the Technology Review Puzzle Corner, circa 1975:
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?
We did it by hand, and the answer was in closed form, but a mess. I found that Macsyma of that era could do most of the integral, with hand-holding, but ran into a problem at the final level.
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 --Michael Kleber -- It is very dark and after 2000. If you continue you are likely to be eaten by a bleen.