Another way of stating the gist of the question is: find the arrangement of n points such that one obtains the largest ratio between the area of the smallest triangle formed by three points to the area bounded by lines at the edge of the figure drawn by connecting all points in a plane. Points may not be collinear. Or if they are, this would not give the optimal solution since area = 0.
Something tells me that the optimal solution is always a distribution of points equidistant along the circumference of a circle, but I don't have the ability to prove it. Got any suggestions? Thanks guys.