The closest pair problem is the famous problem of finding out the closest pair of points given an arbitrary set of points on a plane. This problem has a divide and conquer algorithm and often is used in algorithms classes to illustrate the divide and conquer paradigm.
I also intend to do the same, but I would like to begin with some comments on why this algorithm is useful. Are there any interesting examples I can use here? A google search reveals nothing.
This is for an introductory algorithms course, and the audience is not expected to be an expert on this topic and has a mediocre level of mathematical maturity.