Part 1
Determine the mean distance between two random points on the perimeter of a unit (convex) regular hexagon.
Part 2
Determine the mean distance between two random points on the interior of a unit (convex) regular hexagon.
(In reply to
comment by Steven Lord)
The standard to these sort of point-picking problems is to assume a uniform distribution.
For the perimeter that is pretty easy since you can just pick a side and then pick a random number on (0,1).
For the area that's a bit trickier. For a simulation you can do what Charlie did and pick points in a square and then test to see if they land in the hexagon.
A more complex approach that does not test to accept or reject points would be to split the hexagon into three parallelograms, choose a parallelogram and choose a random point in the parallelogram.
Choosing a point in the parallelogram can be done by taking a pair of sides as vectors, randomly choose a length of each vector (0 to the full length of the side), then adding the two vectors to find your random point.
re: comment
