Clouds of planar convex bodies

Abstract

Let {K, K1, ?, Kn } be a family of convex bodies in the plane. We say that the bodies K1,..., Kn form a deep cloud around K if the bodies K, K1,..., Kn are mutually non-overlapping and every ray emanating from K intersects the interior of at least one of K1,..., Kn. In this paper we are concerned with the following question: What is the minimum number of congruent copies of a given convex body K forming a deep cloud around K?