The diameter of a nonempty subset of a metric space is . For a Euclidean circle it is the longest chord length; the same definition applies to arbitrary metric subsets.
In a normed vector space, the diameter of the convex hull of finitely many points equals their greatest pairwise distance. For and , with nonnegative coefficients each summing to one,The triangle inequality gives . The reverse inequality holds because all the vertices belong to the convex hull. Thus a continuum of distances inside a convex polygon can be controlled by finitely many vertex pairs.
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Diameter is a protocol designed for authentication, authorization, and accounting (AAA) in computer networks. It is an evolution of the older RADIUS (Remote Authentication Dial-In User Service) protocol. Diameter offers several enhancements and improvements over RADIUS, making it more suitable for managing AAA needs in modern networks, especially in environments like telecommunications and mobile networks.
