Spherical triangle

Geometry of figures on the surface of a sphereThe octant of a sphere is a spherical triangle with three right angles.Spherical trigonometry is the branch of spherical geometry and trigonometry that deals with the metrical relationships between the sides and angles of spherical triangles, traditionally expressed using trigonometric functions. On the sphere, geodesics are great circles. Spherical trigonometry is of great importance for calculations in astronomy, geodesy, and navigation. 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. The subject came to fruition in Early Modern times with important developments by John Napier, Delambre and others. Since then, significant developments have been the application of vector methods, quaternion methods, and the use of numerical methods. PreliminariesEight spherical triangles defined by the intersection of three great circles.Spherical polygonsA spherical polygon is a polygon on the surface of the sphere. Its sides are arcs of great circles—the spherical geometry equivalent of line segments in plan