Károly J. Böröczky

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G. Wegner [12] gave a geometric characterization of all so–called Groemer packing of n ≥ 2 unit discs in E2 that are densest packings of n unit discs with respect to the convex hull of the discs. In this paper we provide a number theoretic characterization of all n satisfying that such a “Wegner packing” of n unit discs exists, and show that the proportion(More)
Let C be a convex body in Euclidean d-space IE , i.e., a compact convex set with non-empty interior, and denote by P i n and P (n) the set of polytopes with at most n vertices inscribed to C and the set of polytopes with at most n facets circumscribed to C, respectively. Denote by δ(., .) the symmetric difference metric. Beginning with the work of L. Fejes(More)
How well a polytope of restricted complexity can approximate a smooth convex body in R? This natural question has attracted the attention of mathematicians of various background since the middle of the 20th century. In this extended abstract, polytopes are always inscribed, and restricted complexity mostly means restricting the number of vertices of the(More)