5 problems

Let $C$ be a convex figure of perimeter one, and consider approximation by inscribed $k$-gons in the Hausdorff metric. Popov's conjecture. The regular $(k+1)$-gon is the worst case…

Let $\mathcal{P}$ be a family of convex polygons in $\mathbb{R}^{2}$ that is closed under taking subpolygons, where a subpolygon is the convex hull of a subset of the polygon's ver…

Let $C$ be a compact convex figure in the plane, let $\alpha(C,k)$ denote the best worst-case aperture-angle approximation of $C$ by an inscribed convex $k$-gon, and let…

Disk sharpness conjecture. The estimate

Inscribed-quadrangle conjecture. One has