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. ).