All Questions

Observations: any thin isosceles triangle has exactly 1 partition into 2 congruent pieces - only 1 line, bisector of its apex, does it. By attaching a right triangle with base 1 and altitude 2 to an ...

A contact between two planar convex regions obviously happens either along a line segment or at a single point. Question: Given a planar convex region $C$ and a number $n$, we need to lay out $n$ ...

The set of convex polygons which tile the plane is, as of $2017$, known: it consists of all triangles, all quadrilaterals, $15$ families of pentagons, and three families of hexagons. Euler's formula ...

Triggered by the MO question, "How many convex shapes can be made with the pieces of the Stomachion?," I would like to pose this question: Q. Given $n$ polygons in a set $S$, say each with integer ...

Simply put, my question is this: what is the smallest dimension, if any, where we can know for sure that a convex body exists whose translative packing constant is strictly larger than its lattice ...