Envelopes of $\alpha$-sections

Nicolas Chevallier, Augustin Fruchard, Costin Vîlcu

Let $K$ be a planar convex body af area $|K|$, and take $0 \textless{} α\textless{} 1$.An $\alpha$-section of $K$ is a line cutting $K$ into two parts, one of whichhas area $\alpha |K|$. This…