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The covering of a three-dimensional unbounded convex body by larger homothetic ones. (Russian) Zbl 0667.52012

The problem: The unbounded convex body M in the euclidean n-space has to be covered by bodies \(M_ 1,...,M_ m\) which are homothetic to M (some more requirements are fulfilled); determine \(\min m.\) The problem is solved in the paper for \(n=2,3\), and the relation to illumination of convex bodies is stated. [Cf. V. G. Boltyanskij and P. S. Soltan: Combinatorial geometry of various classes of convex sets. (Russian) (1978; Zbl 0528.52002)].
Reviewer: E.Jucovič

MSC:

52C17 Packing and covering in \(n\) dimensions (aspects of discrete geometry)
52A40 Inequalities and extremum problems involving convexity in convex geometry
52A10 Convex sets in \(2\) dimensions (including convex curves)
52A15 Convex sets in \(3\) dimensions (including convex surfaces)

Citations:

Zbl 0528.52002
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