Sums of Distances - Peter Giblin

23rd February 2002

If building straight roads from four new towns to a central point, where is the best place to have this point so that the roads are as short as possible? What about when there are five towns, or three towns? These problems can be investigated geometrically, and it turns out that the latter (three towns) is harder than the others! Some pointers are given in the notes below, along with links to a number of interactive java applets which allow you to explore the problem for yourself.