Geodesic
Two New Approaches to Obtaining Estimates in the Danzer–Grünbaum Problem
Matematičeskie zametki, Tome 87 (2010) no. 4, pp. 519-527 Cet article a éte moissonné depuis la source Math-Net.Ru

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We use probabilistic methods to estimate the cardinality of a set $S$ in a Euclidean space such that no three points of $S$ form a right or an obtuse angle. Let $a(n)$ be the cardinality of a maximal subset $S\subset\mathbb R^n$ with this property. We prove that $$ a(n)\ge\frac23\biggl\lfloor\sqrt2\biggl(\frac2{\sqrt3}\biggr)^n\biggr\rfloor. $$
Keywords: Euclidean space, angle, set of points, Erdős–Füredi method.
Mots-clés : Danzer–Grünbaum problem 
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     author = {L. V. Buchok},
     title = {Two {New} {Approaches} to {Obtaining} {Estimates} in the {Danzer{\textendash}Gr\"unbaum} {Problem}},
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L. V. Buchok. Two New Approaches to Obtaining Estimates in the Danzer–Grünbaum Problem. Matematičeskie zametki, Tome 87 (2010) no. 4, pp. 519-527. http://geodesic.mathdoc.fr/item/MZM_2010_87_4_a4/

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