Diameterrelated

Diameterrelated is a term used to describe properties, measurements, or relationships that involve a diameter, in particular the diameter of circles and the diameter of graphs or networks. It is applied across geometry and graph theory to discuss how diameter interacts with other attributes such as radius, chords, and distances.

In circle geometry, the diameter is a straight line that passes through the center and connects two points on the circumference. Its length is twice the circle’s radius. The diameter is the circle’s longest chord. Thales’ theorem states that the angle subtended by a diameter at any point on the circle is a right angle. Related formulas express diameter in terms of other quantities: with diameter d, radius r = d/2, area A = πr² = πd²/4, and circumference C = 2πr = πd.

Chord geometry also uses diameterrelated concepts. For a circle of radius r, a chord at distance h from the center has length L = 2√(r² − h²). This ties chord lengths to the circle’s diameter and central distances, illustrating how diameter-related measures constrain other features of the circle.

In graph theory, the diameter of a graph is the greatest distance between any pair of vertices, measured as the length of the shortest path between them. Related notions include the radius (the minimum eccentricity of a vertex) and the center (vertices achieving the radius). A key relation is that the diameter is at most twice the radius, i.e., diameter ≤ 2 × radius, and radius ≤ diameter. Diameterrelated concepts help quantify efficiency and reach in networks.