I have the following problem: I have a square of area M. In the square, I can place P stations however I like. After that, I link every point in the square (and on its edge) to the closest station. My goal is to minimize the average distance of points to their closest stations.

My question is: is there a simple approximation to calculate the average minimal distance as a function of M and P?

I currently using the function sqrt(M/P).5, but I think there may be better ways to approximate this.