3 problems

Let $\mathcal{Q}$ be a simple $n$-gon, meaning that it has no self-intersections, and consider the regions of points $M$ for which the circumcenter map produces area contraction. R…

Let $\mathcal{P}$ be a regular $n$-gon, with $n\geq 3$, and let $\mathcal{P}'=\mathcal{C}_M^n(\mathcal{P})$. Write $\alpha$ for the angle of rotation in the similarity taking…

Let $\mathcal{P}$ be a regular $n$-gon, with $n\geq 3$, and let $M$ vary in the plane. After $n$ applications of the circumcenter map, classify the connected regions according to w…