Spherical geometry is the three-dimensional study of geometry on the surface of a sphere. It is the spherical equivalent of two-dimensional planar geometry, the study of geometry on the surface of a plane. A real-life approximation of a sphere is the planet Earth—not its interior, but just its surface. (Earth is more accurately called an "oblate spheroid" because it is slightly flattened at the ends of its axis of rotation, the North and South Poles.) The surface of a sphere together with its interior points is usually referred to as the spherical region; however, spherical geometry generally refers only to the surface of a sphere.

As seen in the figure on the next page, a sphere is a set of points in three-dimensional space equidistant from a point O called the center of the sphere. The line segment from point O (at the center of...