Journal for Geometry and Graphics 18 (2014), No. 1, 001--006
Copyright Heldermann Verlag 2014
The Differentiable Manifold of Spherical Deltoids: Their Classification
Catarina P. Avelino
Universidade de Trás-os-Montes e Alto Douro, Quinta de Prados, 5000-801 Vila Real, Portugal
cavelino@utad.pt
Altino F. Santos
Universidade de Trás-os-Montes e Alto Douro, Quinta de Prados, 5000-801 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
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