2 problems

Let $\mathbf{K}$ and $\mathbf{C}$ be convex bodies in $\mathbb{E}^d$, with $d\geq 2$, and let $m$ be a positive integer. For each body, let $r_{\mathbf{C}}(\cdot,m)$ denote its $m$…

Let $C\subset\mathbb{R}^d$ be a convex body in Euclidean space, and cut it by $n-1$ hyperplanes, producing $n$ resulting pieces. Alexander's reformulation. One of the resulting pie…