All Questions

Inspired by the question, "Shortest path connecting two opposite points on a cube": Q. What does the cut locus with respect to one corner of a hypercube in $\mathbb{R}^d$ look like? "The cut ...

Let $M$ be a smooth closed positively curved surface in Euclidean 3-space, $T$ be a geodesic triangulation of $M$, and $E$ be the edge graph of the convex hull of vertices of $T$. It is easy to see ...

Let $K\subseteq\mathbb R^d$ be a compact convex body with non-empty interior, and $E$ be a $(d-1)$-dimensional linear subspace of $\mathbb R^d$. Let $\theta\in\mathbb R^d$ be the unit vector such that ...