# diameter

Pronunciation: US say "dy-AM-i-ter" /daɪˈæmɪdɚ/; UK say "dy-AM-i-tuh" /daɪˈæmɪtə(ɹ)/

## Noun

1. The length of a straight line that runs through the center of a circle from one side to the other.
   - Simple: The distance across a circle or round object, measured straight through its middle.
   - _The new water main has an inside diameter of twelve inches._
   - _The surgeon compared the diameters of the left and right arteries on the scan._
2. A straight line that passes through the center of a circle and joins two points on its circumference.
   - Simple: A straight line that goes from one side of a circle to the other through the middle.
   - _Draw a diameter and label its endpoints A and B._
   - _Any angle drawn from the two ends of a diameter to a point on the circle is a right angle._
3. The greatest distance between any two points in a metric space.
   - Simple: In math, the longest distance between any two points of a space.
   - _A subset whose diameter is finite is said to be bounded._
   - _Under the taxicab metric, the diameter of the unit square is two._
4. The largest eccentricity of any vertex in a graph, which equals the greatest shortest-path distance between two of its vertices.
   - Simple: In a graph, the largest number of steps between two points, always going the shortest way.
   - _A complete graph has a diameter of one, since every vertex is joined to every other._
   - _Researchers found that the friendship network had a surprisingly small diameter._

## Origin

From Old French diametre, from Latin diametrus, from Ancient Greek διάμετρος (diámetros), as in diametros grammē ("line measuring across"), from διά (diá, "across") + μέτρον (métron, "measure"). By surface analysis it is dia- + -meter.

Source: DictionaryAI, https://dictionaryai.com/define/diameter (written from Wiktionary data, CC BY-SA 4.0: https://creativecommons.org/licenses/by-sa/4.0/).