Centroids, Centers, Medians: What is the Difference? |
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Authors: | Marco Baronti Emanuele Casini Pier Luigi Papini |
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Institution: | (1) Instituto di Ingegneria –, Università di Genova, Piazzale Kennedy, Pad. D, 16129 Genova, Italy;(2) Instituto di Scienze Matematiche, Fisiche e Chimiche, Università, Via Lucini 3, 22100 Como, Italy;(3) Dipartimento di Matematica, Piazza Porta S. Donato 5, 40127 Bologna, Italy |
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Abstract: | Consider a finite subset F of a real normed space. In this paper we try to evaluate the largest possible distance between pairs of points which are, for F, the centroid, a center, or a median. The results seem to show that only when X is a two-dimensional, strictly convex space, or when X is a Hilbert space, what the geometrical intuition indicates is more or less true. We give some examples showing some of the 'pathological' situations which can arise. Also, we indicate some open problems. |
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Keywords: | Center centroid median Weber problem location |
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