Dissections of polygons into triangles of equal areas (Q1429325)

A dissection of a plane polygon into triangles of equal area is called an equidissection if the intersection of any two triangles is either empty, a common vertex, or a common edge. The authors show a series of theorems on such polygons, like the following two. 1. If a convex polygon has rational vertex coordinates, then it has infinitely many different equidissections. 2. If a convex polygon is such that some subset of the first coordinates of its vertices is algebraically independent, then it has no equidissection. For a special class of quadrilaterals, the so-called spectrum is determined, that is the set of all numbers \(m\) such that there exists an equidissection into \(m\) triangles. A main tool for the proofs is Sperner's Lemma.