3 problems

A point configuration $\mathcal P$ is self-similar if there is a point $A\in\mathcal P$ such that every angle formed by three points of $\mathcal P$ can also be formed with $A$ as…

Let $A$ be a pinned point in a configuration of $n$ points in general position in $\mathbb R^2$ or $\mathbb R^3$, where general position means no three points are collinear and no…

For $d\in\{2,3\}$, let $A_{\mathrm{gen}}^{(d)}(n)$ denote the minimum number of distinct angles formed by a set of $n$ points in general position in $\mathbb R^d$, where general po…