All Questions

Let $S$ be a set of $n$ points in the plane in general position (no 3 on a line), $n$ even. A halving line is a line through $2$ points of $S$ that partitions $S$ into 2 equal parts ($(n-2)/2$ points ...

These questions are inspired by Yaglom and Boltyanskii's 'Convex figures'. Winternitz Theorem: If a 2D convex figure is divided into 2 parts by a line $l$ that passes through its center of gravity, ...

This question is related to my previous posting Angle subtended by the shortest segment that bisects the area of a convex polygon Let $C$ be a convex region in the plane and let $s$ be the shortest ...

I have a set of points $S=\{(x_1,y_1),(x_2,y_2),\ldots,(x_n,y_n)\}$. Then how to find the boundary points (which is a subset of $S$) of $S$? There are methods like convex hull, concave hull and $\...