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 …

Dec 3, 2025 · A spherical triangle is a figure formed on the surface of a sphere by three great circular arcs intersecting pairwise in three vertices. The spherical triangle is the spherical …

To derive the basic formulas pertaining to a spherical triangle, we use plane trigonometry on planes related to the spherical triangle. For example, planes tangent to the sphere at one of …

Jul 23, 2025 · What are Spherical Triangles? A spherical triangle is a geometric figure formed on the surface of a sphere by three great circle arcs. These arcs are the intersections of the …

In order to undertake calculations on the celestial sphere, whether for the purposes of astronomy, navigation or designing sundials, some understanding of spherical triangles is essential.

Spherical triangles are defined by their three vertices, which lie on the surface of a sphere, and their three sides, which are arcs of great circles. The angle sum of a spherical triangle can …

Although spherical geometry is not as old or as well known as Euclidean geometry, it is quite old and quite beautiful. The original motivation probably came from astronomy and navigation, …

Spherical Triangle Any section made by a cutting plane that passes through a sphere is circle. A great circle is formed when the cutting plane passes through the center of the sphere. …

On the plane, the sum of the interior angles of any triangle is exactly 180°. On a sphere, however, the corresponding sum is always greater than 180° but also less than 540°.

Great circles play the role of straight lines in spherical geometry. Given two distinct points on S2, there is a great circle passing through them obtained by the intersection of S2 with the plane …