Equidissections of polygons

AbstractA dissection of a planar polygon K is a family of triangles whose union is K and such that the intersection of the interiors of any two distinct triangles is empty. If all the triangles have equal areas, the dissection is called an equidissection of K. An equidissection of K into m triangles is called an m-equidissection of K. It is known that in any m-equidissection of a square m is even. It has also been shown that in any m-equidissection of the regular n-gon, n≥5, m is a multiple of n and that in any m-equidissection of a centrally symmetric polygon m is even.In the present paper we explore equidissections of more general polygons. For instance, we show that for almost all polygons no equidissection exists. Furthermore, there are polygons for which the integers m such that the polygon has an m-equidissection are not the multiples of a single integer