Introduction

How could one best go about finding the longest cells in a group of millions of biological cells? Or, objectively comparing the precision of two people at a firing range? Or, classifying sections of the brain from scan images? Answering any of these questions involves identifying characteristics of large sets of points on a flat surface. One very important characteristic is the greatest distance between any two points.

This distance is called the diameter of the points. For any two points x and y we will use d (x, y) to denote the distance between x and y. By distance we mean Euclidean distance, the staight-line distance between two points on a two-dimensional plane. We could also consider higher dimensions and other distance metrics (see, e.g. [8]).