Concept

Spherical Geometry

Spherical geometry explores shapes and measurements that lie on the curved surface of a sphere. This sets it apart from Euclidean geometry, which studies objects on a plane.
A sphere and a spherical triangle ABC

Compared to Euclidian geometry, properties of objects like spherical triangles and great circles also differ. For instance, in spherical triangles, the angles add up to more than because of the curved surface.

Measurements of a triangle on a sphere and a triangle on a plane

Additionally, measurements of side lengths and angles follow arcs of great circles instead of straight lines, resulting in different relationships between angles and sides.

A route connecting Chicago and New Mexico on a globe

Spherical geometry has various applications in fields such as astronomy and cartography. It is especially useful in navigation systems because it helps in determining the shortest routes between points on the Earth's surface and calculating the positions of stars.

Exercises