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Let $S$ be a set of $n$ points in the plane in general position. Each 3 points of S span a triangle. Total number of triangles spanned by S: $$\binom{n}{3}=\frac{n(n-1)(n-2)}{6}=\frac{1}{6} n^3-O(n^2 )...

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 ...

Following A claim on the concurrency of area bisectors of planar convex regions, let me record a couple of simple queries. An area bisector (perimeter bisector) of a planar convex region is a chord ...