spherical excess

Spherical excess is a measure used in spherical geometry to understand the size of a spherical triangle, which is a triangle drawn on a sphere's surface. Unlike flat triangles, the angles of a spherical triangle add up to more than 180 degrees. The spherical excess is the amount by which the sum of these angles exceeds 180 degrees. It is directly related to the area of the triangle on the sphere: larger excess means a larger area. This concept is important in fields like astronomy and navigation, where precise measurements on curved surfaces are essential.