![]() ![]() Analogously to their plane counterparts, spherical polygons with more than 3 sides can always be treated as the composition of spherical triangles. Polygons with higher numbers of sides (4-sided spherical quadrilaterals, 5-sided spherical pentagons, etc.) are defined in similar manner. Three arcs serve to define a spherical triangle, the principal subject of this article. ![]() Two-sided spherical polygons- lunes, also called digons or bi-angles-are bounded by two great-circle arcs: a familiar example is the curved outward-facing surface of a segment of an orange. Such polygons may have any number of sides greater than 1. Its sides are arcs of great circles-the spherical geometry equivalent of line segments in plane geometry. Spherical polygons Ī spherical polygon is a polygon on the surface of the sphere. Preliminaries Eight spherical triangles defined by the intersection of three great circles. Since then, significant developments have been the application of vector methods, quaternion methods, and the use of numerical methods. The subject came to fruition in Early Modern times with important developments by John Napier, Delambre and others, and attained an essentially complete form by the end of the nineteenth century with the publication of Todhunter's textbook Spherical trigonometry for the use of colleges and Schools. The origins of spherical trigonometry in Greek mathematics and the major developments in Islamic mathematics are discussed fully in History of trigonometry and Mathematics in medieval Islam. Spherical trigonometry is of great importance for calculations in astronomy, geodesy, and navigation. ![]() On the sphere, geodesics are great circles. Spherical trigonometry is the branch of spherical geometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. The octant of a sphere is a spherical triangle with three right angles. Geometry of figures on the surface of a sphere ![]()
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