a.) What can you say about the sum of the interior angles of triangles on spheres and hyperbolic planes? Are there maximum and or minimum values for the sum?
To do this problem I know I need to look at triangles with non-zero area and use forumlas....but I am not sure how to do this.
b.)What is the sum of the (interior) angles of a planar triangle?
Let triangle ABC be a triangle on the plane and imagine a sphere of raidus p passing through the point A, B, C. These three points also determine a small spherical triangle on the sphere. Now imagine the raidus p growing to infinity and the spehrical triangle converging to the planar triangle. This result for the plane is normally proved after invoking a parallel postulate. Here, we are making the assumption that the plane is a sphere of infinite radius.
Any help with this problem would be great....I have stated the background just dont know how to prove this.