Generalized Diameter

The generalized diameter is the greatest distance between any two points on the boundary of a closed figure. The diameter of a subset E of a Euclidean space R^n is therefore given by

 diamE=sup{|x-y|:x,y in E},

where sup denotes the supremum (Croft et al. 1991).

For a solid object or set of points in Euclidean n-space, the generalized diameter is equal to the generalized diameter of its convex hull. This means, for example, that the generalized diameter of a polygon or polyhedron can be found simply by finding the greatest distance between any two pairs of vertices (without needing to consider other boundary points).

The generalized diameter is related to the geometric span of a set of points.

See also

Blaschke's Theorem, Borsuk's Conjecture, Convex Hull, Diameter, Geometric Span, Graph Diameter, Jung's Theorem, Minimal Enclosing Circle, Polygon Diameter

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Croft, H. T.; Falconer, K. J.; and Guy, R. K. Unsolved Problems in Geometry. New York: Springer-Verlag, p. 2, 1991.Eppstein, D. "Width, Diameter, and Geometric Inequalities."

Referenced on Wolfram|Alpha

Generalized Diameter

Cite this as:

Weisstein, Eric W. "Generalized Diameter." From MathWorld--A Wolfram Web Resource.

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