Answer to Question #319383 in Geometry for Nzuzi

Question

There are other geometries. One such is spherical geometry.

What can you say about the sum of the interior angles of a triangle in spherical geometry?

Answer 1

The sum of the angles of a triangle on a sphere is 180°(1 + 4f), where f is the fraction of the sphere's surface that is enclosed by the triangle. For any positive value of f, this exceeds 180° and less than 540°.