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Smallest maximal snakes of translates of convex domains

✍ Scribed by Károly Böröczky; Valeriu Soltan

Publisher
Springer
Year
1995
Tongue
English
Weight
738 KB
Volume
54
Category
Article
ISSN
0046-5755

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📜 SIMILAR VOLUMES

Illumination by translates of convex set
Illumination by translates of convex sets
✍ Marilyn Breen 📂 Article 📅 1992 🏛 Springer 🌐 English ⚖ 379 KB

Let S be a compact set in the plane. If every three points of S are illuminated dearly by some translate of the compact convex set T, then there is a translate of T which illumines every point of S. Various analogues hold for translates of fiats in R d as well. Mathematics subject classifications (

Geometric permutations of disjoint trans
Geometric permutations of disjoint translates of convex sets
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The object of this paper is to study how many essentially different common transversals a family of convex sets on the plane can have. In particular we consider the case where the family consists of pairwise disjoint translates of a single convex set.

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✍ Tibor Bisztriczky; Karoly Börözky; Heiko Harborth; Lothar Piepmeyer 📂 Article 📅 1991 🏛 Springer 🌐 English ⚖ 202 KB

For p ¢ q, let pq = conv{p, q}, Ipql be the length ofpq and ff~ be the ray from p through q. For points p, q and r, let / (p, q, r) be the absolute measure of the angle determined by q"~ and ~ in conv(~'pu~). Thus 0 <~ /(p,q,r) <<. lz. Henceforth, let S, = {D1,..., D,} be a collection of n >i 1 clo