2 problems

Let $R$ be a finite subset of Euclidean space. It is called Ramsey if, for every number of colors $r\in\mathbb{N}$, there is a dimension $n=n(R,r)$ such that every $r$-coloring of…

Let $\mathcal{F}$ be a finite spherical configuration, meaning a configuration of points that can be inscribed in some sphere, and let $S\subseteq\mathbb{R}^n$ have positive upper…