Locating Diametral Points

Autor: Jin-ichi Itoh, Costin Vîlcu, Liping Yuan, Tudor Zamfirescu
Rok vydání: 2020
Předmět:
Zdroj: Results in Mathematics. 75
ISSN: 1420-9012
1422-6383
Popis: Let K be a convex body in $${\mathbb {R}} ^d$$, with $$d = 2,3$$. We determine sharp sufficient conditions for a set E composed of 1, 2, or 3 points of $$\mathrm{bd}K$$, to contain at least one endpoint of a diameter of K. We extend this also to convex surfaces, with their intrinsic metric. Our conditions are upper bounds on the sum of the complete angles at the points in E. We also show that such criteria do not exist for $$n\ge 4$$ points.
Databáze: OpenAIRE
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