In the left panel are five points that can be moved about.[br]How can you make a measure of how crowded they are?[br][br]The right plane shows some geometric constructs formed[br]by these points. The convex hull, the polygon ABCDE, and [br]all the pairwise distances between the points.[br][br]How does the polygon formed by the five points differ from [br]convex hull? How many five-vertex polygons are there?[br][br]What are some reasonable measures of 'crowdedness'?[br]Under what circumstances is each to be preferred?