Journal ArticleDOI
How Many Triangles
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This article is published in The Mathematical Gazette.The article was published on 1970-10-01. It has received 6 citations till now.read more
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Coloring and Guarding Arrangements
Prosenjit Bose,Jean Cardinal,Sébastien Collette,Ferran Hurtado,Matias Korman,Stefan Langerman,Perouz Taslakian +6 more
TL;DR: Borders on the number c are given on the minimum size of a subset S of the intersections of the lines in A such that every cell is bounded by at least one of the vertices in S.
Journal ArticleDOI
Coloring and Guarding Arrangements
Prosenjit Bose,Jean Cardinal,Sébastien Collette,Ferran Hurtado,Matias Korman,Stefan Langerman,Perouz Taslakian +6 more
TL;DR: In this article, it was shown that the chromatic number of colors required to color the lines of an arrangement of lines in the plane so that no cell of the arrangement is monochromatic is more than O(n√).
Journal ArticleDOI
Cell-paths in mono- and bichromatic line arrangements in the plane
Oswin Aichholzer,Jean Cardinal,Thomas Hackl,Ferran Hurtado,Matias Korman,Alexander Pilz,Rodrigo I. Silveira,Ryuhei Uehara,Pavel Valtr,Birgit Vogtenhuber,Emo Welzl +10 more
TL;DR: In this paper, it was shown that the dual graph of any arrangement of n lines in general position always contains a path of length at least n 2/4 where red and blue lines are crossed alternatingly.
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The Eternal Triangle—A History of a Counting Problem
TL;DR: The Eternal Triangle as discussed by the authors is a history of counting problems and counting problems, and it is a counting problem with an infinite number of counting points in the infinite triangle, which is called the counting problem.
Journal ArticleDOI
How many tetrahedra
TL;DR: In this article, the authors consider a tetrahedra whose sides have all length n and whose interior is partitioned into n unit squares, as shown in Figure 1.86.