Generalized Diameter
المؤلف:
Croft, H. T.; Falconer, K. J.; and Guy, R. K
المصدر:
Unsolved Problems in Geometry. New York: Springer-Verlag
الجزء والصفحة:
...
21-7-2021
2412
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 
of a Euclidean space 
is therefore given by
![diamE=sup<span style=]() {|x-y|:x,y in E}, " src="https://mathworld.wolfram.com/images/equations/GeneralizedDiameter/NumberedEquation1.gif" style="height:18px; width:196px" /> |
where 
denotes the supremum (Croft et al. 1991).
For a solid object or set of points in Euclidean 
-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.
REFERENCES:
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." https://www.ics.uci.edu/~eppstein/junkyard/diam.html.
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