diameter

Here the diameter is a number, not a line: twice the radius, and the usual way round things are sized. Engineers specify the inside diameter of a pipe or the gage diameter of a toolholder shank, and medical scans report a transcerebellar diameter. The measurement extends to spheres and cylinders, taken straight through the middle, and it often carries a qualifier such as inside or gage.

Greek named it the line measuring across, from dia, across, and metron, measure, and English can still read it as dia- plus -meter. It is the longest chord a circle has, it cuts the circle into two equal halves, and every diameter of a circle crosses every other one at the center.

Mathematicians carry the circle's measurement over to any set where distance is defined, and they have to adjust it. In an open disk no two points reach the full width, because the rim is missing, so no greatest distance exists. The diameter is therefore taken as the smallest number that no distance between two points exceeds, which matches the plain maximum whenever there is one.

Graph theorists count edges instead of measuring lengths. A vertex's eccentricity is how far it sits from the vertex farthest from it, along the shortest route; the largest eccentricity in the graph is its diameter and the smallest is its radius, so the circle's pair of terms survives in a world with no circles. A small diameter means any two vertices are only a few steps apart.