On sets of points that determine only acute angles
type: Item
instance of: scholarly article
title: On sets of points that determine only acute angles
zbMATH Open document ID: 1181.52013
author: Eyal Ackerman
author: Oren Ben-Zwi
published in: European Journal of Combinatorics
publication date: 2009-06-17T00:00:00Z
review text: The authors prove that for every integer \(d\) there is a set of points in the \(d\)-dimensional Euclidean space \({\mathbb E}^d\) of size \(\Omega ((\frac{2}{\sqrt{3}})^d\sqrt{d})\) such that every angle determined by three points in the set is acute, that is, smaller than \(\pi/2\). This result improves on the best known lower bound by a factor of \(\Theta (\sqrt{d})\). The short and elegant proof is probabilistic in nature and it uses a theorem of \textit{C. Bertram-Kretzberg} and \textit{H. Lefmann} [SIAM J. Comput. 29, No. 1, 201--230 (1999; Zbl 0937.68056)] about \(3\)-uniform hypergraphs.
Mathematics Subject Classification ID: 52A37
Mathematics Subject Classification ID: 52C35
Mathematics Subject Classification ID: 05D40
zbMATH DE Number: 5565536
zbMATH Keywords: acute angles
zbMATH Keywords: finite point sets
zbMATH Keywords: hypergraphs
zbMATH Keywords: probabilistic methods
reviewed by: Ferenc Fodor
MaRDI profile type: Publication
full work available at URL: j.ejc.2008.07.020
OpenAlex ID: W2085975631
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DOI: 10.1016/J.EJC.2008.07.020
description: scientific article; zbMATH DE number 5565536