
Journal for Geometry and Graphics 18 (2014), No. 1, 001006 Copyright Heldermann Verlag 2014 The Differentiable Manifold of Spherical Deltoids: Their Classification Catarina P. Avelino Universidade de TrásosMontes e Alto Douro, Quinta de Prados, 5000801 Vila Real, Portugal cavelino@utad.pt Altino F. Santos Universidade de TrásosMontes e Alto Douro, Quinta de Prados, 5000801 Vila Real, Portugal afolgado@utad.pt We introduce the concepts of spherical deltoid of type II and spherical deltoid of type II, describing geometrical methods to construct both types. It is shown that any spherical deltoid is congruent to a spherical deltoid of type I and to a spherical deltoid of type II. We classify spherical deltoids taking into account the relative positions of the spherical moons containing their sides. This allows us to conclude that the class of all spherical deltoids is a differentiable manifold of dimension three. Keywords: Spherical geometry, applications of spherical trigonometry. MSC: 51E12; 51K05 [ Fulltextpdf (139 KB)] for subscribers only. 