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Consider a polygonal sheet $P$ of area $A$ with $N$ vertices (it material is not stretchable or tearable). Let $n$ be a positive integer >=2. Question: Let $P$ lie on a flat plane. We need to fold ...

See Wikipedia for Monsky's theorem which states: it is not possible to dissect a square into an odd number of triangles all of equal area. Questions: Are there quadrilaterals that allow partition into ...

This is based on Chapter 6 of 'Convex figures' by Yaglom and Boltyanskii. This post also continues On two centers of convex regions. A point $P$ in the interior of a planar convex region $C$ divides ...

I have a 2D polygon of arbitrary geometry. I need to find any point that is inside of that polygon. Taking the center won't work, because the polygon might not be convex. Is there a way to quickly ...

Question: Given an $N$-vertex polygon (not necessarily convex). It is to be cut into the least number of acute isosceles triangles. Based on this MathSE discussion, one can think of a method to get $\...