Beiträge zur Algebra und Geometrie Contributions to Algebra and Geometry Vol. 45, No. 1, pp. 275281 (2004) 

On seven points in the boundary of a plane convex body in large relative distancesZsolt LángiDepartment of Calculus, College of Dunaújváros, Dunaújváros, H2400, Hungary, email: zslangi@kac.poliod.huAbstract: 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 Full text of the article:
Electronic version published on: 5 Mar 2004. This page was last modified: 4 May 2006.
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