Beiträge zur Algebra und Geometrie / Contributions to Algebra and Geometry, Vol. 41, No. 2, pp. 391-399 (2000)

Protecting Regular Polygons

Arnfried Kemnitz, Laszlo Szabo, Zoltan Ujvary-Menyhart

Diskrete Mathematik, Technische Universit{ä}t Braunschweig, Pockelsstr. 14, D-38106 Braunschweig, Germany; Computer and Automation Institute, Hungarian Academy of Sciences, Lagymanyosi ut 11, H-1111 Budapest, Hungary; Department of Geometry, Eötvös University, Rakoczi ut 5, H-1088 Budapest, Hungary

Abstract: The minimum number of mutually non-overlapping congruent copies of a convex body $K$ so that they can touch $K$ and prevent any other congruent copy of $K$ from touching $K$ without overlapping each other is called the protecting number of $K$. In this paper we prove that the protecting number of any regular polygon is three or four, and both values are indeed attained.

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