A trigonometria esférica e o globo terrestre

Abstract

The spherical trigonometry came from the needs of Astronomy, in the search for mathematically describing the solar system. Brilliant minds like Euclides, Aristarco of Samos, Apolônio of Perga, Hiparco, Menelau of Alexandria, Ptolomeu, and others, have studied the spherical triangles. In this work, we study the fundamental results spherical trigonometry seeking an association with the globe. We begin with the study of the fundamental elements of a spherical surface, where we define the spherical triangles and prove their important properties, such as sum of the measures of the internal angles and the Girard formula to calculate its area. Then, we present the classification of spherical triangles and the main relationships between the sides and angles of these triangles, as the law of sines and law of cosines, and a brief study of spherical rectangle triangles. Finally, we consider the Earth as a sphere called earth globe, over which we address various geographical concepts such as parallels, meridians, latitudes, longitudes, in order of use of spherical trigonometry to calculate distances and angles on the Earth's surface, creating strong interdisciplinary character between Mathematics and Geography.