Beitr\ EMIS ELibM Electronic Journals Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
Vol. 45, No. 1, pp. 275-281 (2004)

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On seven points in the boundary of a plane convex body in large relative distances

Zsolt Lángi

Department of Calculus, College of Dunaújváros, Dunaújváros, H-2400, Hungary, e-mail:

Abstract: By the relative distance of points $p$ and $q$ of a convex body $C$ we mean the ratio of the Euclidean length of the segment $pq$ to the half of the Euclidean length of a longest chord of C parallel to $pq$. We show that in the boundary of every plane convex body there exist seven points in pairwise relative distances at least $2 \over 3$ such that the relative distances of every two successive points are equal. Here the value $2 \over 3$ is the best possible one. We also give an estimate in case of three points.

Keywords: convex body, relative distance, packing

Classification (MSC2000): 52A40, 52A38, 52A10

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Electronic version published on: 5 Mar 2004. This page was last modified: 4 May 2006.

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