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