2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/31834We show that the traditional criterion for a simplex to belong to the Delaunay triangulation of a point set is equivalent to a criterion which is a priori weaker. The argument is quite general; as well as the classical Euclidean case, it applies to hyperbolic and hemispherical geometries and to Edelsbrunner's weighted Delaunay triangulation. In spherical geometry, we establish a similar theorem under a genericity condition. The weak definition finds natural application in the problem of approximating a point-cloud data set with a simplical complex.8 pages, 4 figuresComputational GeometryI.3.5text