The maximum number of empty congruent triangles determined by a point set
Adrian Dumitrescu, János Pach, Tóth Géza · Infoscience (Ecole Polytechnique Fédérale de Lausanne) · 2005
Letbe a set of points in the plane and consider a family of (nondegenerate) pair- wise congruent triangles whose vertices belong to .While the number of such triangles can grow superlinearly in -as it happens in lattice sections of the integer grid -it has been conjectured by Brass that the number of pairwise congruent empty triangles is only at most linear.We disprove this conjecture by constructing point sets with empty congruent triangles.