Point sets with every triangle having a large angle (Q2354520)

For \(0<\alpha <\pi\), a point set \(H\) in \({R}^d\) is called a \(P_\alpha\)-set, if every triangle in \(H\) is degenerate or has an angle larger than \(\alpha\). A sequence of points \(X_1,X_2,...,X_n\) is called a \(P_\alpha\)-sequence, if for all \(1\leq i<j<k\leq n\), the angle of \(X_iX_jX_k\) exceeds \(\alpha\). The paper investigates the maximum size of \(P_\alpha\)-sets and \(P_\alpha\)-sequences in point sets and sequences in \({R}^d\).