6 problems

Consider $n$ points in the plane that are not all collinear, and count the distinct angles they determine. Erdős–Purdy's regular-polygon conjecture. The regular polygon is the opti…

Let $P$subseteq$\mathbb R^2$ be a non-collinear set of $N$ points. An angle is formed by a triple of points of $P$, and the two examples described above are a regular polygon toget…

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…

Optimality conjecture for the regular and projected polygons. The regular $n$-gon and its projection onto the line are optimal configurations for $A(n)$, each determining the minim…