Spherical Geometry

Spherical geometry is the study of figures on the surface of a sphere, such as the spherical triangle and spherical polygon, as opposed to the type of geometry studied in plane geometry or solid geometry. In spherical geometry, the analogues of straight lines are great circles, so any two of them meet in two points. There are also no parallel lines. The angle between two such circles in spherical geometry is the angle between the planes containing them, and a spherical triangle is defined by its three angles. There is no concept of similar triangles in spherical geometry. Spherical geometry is a basic example of non-Euclidean Riemannian geometry with constant positive curvature (Veritasium 2023, Big Think 2026).