, Volume 60, Issue 2, pp 145-151

On the products of cross-ratios on diagonals of polygons

Abstract

The purpose of this paper is to establish a conjecture of B. Grünbaum, which states that in every n-polygon P in the plane, n ≥ 5, some diagonals intersect in a pattern that defines a new n-polygon δ(P), such that the product of the cross-rations on the diagonals of P is equal to the product of the corresponding cross-ratios on the diagonals of δ(P).