Repeated angles in \(E_ 4\)
The maximum number \(f_ 4(n,\alpha)\) of occurences of the angle \(\alpha\) determined by a set of n points in the euclidean 4-space is searched. The author proves that \(f_ 4(n,\alpha)=o(n^ 3)\) if \(\alpha\neq \pi /2\), \(f_ 4(n,\pi /2)\geq [n/3]^ 3.\) [Cf. \textit{J. H. Conway}, \textit{H. T. Croft}, \textit{P. Erdős} and \textit{M. J. T. Guy}, J. Lond. Math. Soc., II. Ser. 19, 137-143 (1979; Zbl 0414.05006).]
points in four-dimensional Euclidean space
scientific article; zbMATH DE number 4024177