Answer to Question #319088 in Geometry for Nhlonipho Manganyi

Question

All of the previous questions used what we know as Euclidean geometry.

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

Some value greater than 180 degrees. It depends on the triangle.

Think about a sphere, like the Earth. A very small triangle, say one with sides less than a meter, is very close to a similar triangle in Euclidean space. The sum of the angles is very close to 180 degrees.

But a very large triangle, with two of its vertices on the equator and the third at the north pole has the right angles at the vertices on the equator, and the other can be anything between zero and 360 degrees.

The only thing you can say is that the sum of the angles is greater than 180 degrees.