Sets of points determining only acute angles and some related colouring problems
Summary: We present both probabilistic and constructive lower bounds on the maximum size of a set of points \({\mathcal S} \subseteq \mathbb R^d\) such that every angle determined by three points in \({\mathcal S}\) is acute, considering especially the case \({\mathcal S} \subseteq \{0,1\}^d\). These results improve upon a probabilistic lower bound of \textit{P. Erdős} and \textit{Z. Füredi} [Ann. Discrete Math. 17, 275--283 (1983; Zbl 0534.52007)]. We also present lower bounds for some generalisations of the acute angles problem, considering especially some problems concerning colourings of sets of integers.
scientific article; zbMATH DE number 5006925