Re: Triangle on a sphere

Dear Jon and Mike,

It is true that angles in a triangles on a sphere add up to more than 180°. As an example, consider the triangle formed by the following points on a globe: (0° latitude 0° longitude), (0° latitude 90° longitude), (90° latitude 0° longitude). (This is the triangle formed by cutting a sphere with three perpendicular planes, or the surface covering 1/8 of the sphere.) Each angle in this triangle is a right angle, so that the sum of the angles is 270°.

Perhaps the reason why the angles in your triangle-on-a-sphere look the same as a triangle-on-a-plane is that your triangle is too small. When the size of the triangle is small compared to the size of the sphere, the region in which the triangle is drawn is relatively flat. That is, it looks just like a triangle drawn on a plane. However, when the triangle is about the same size of the sphere like the example above, then the curvature of the sphere plays a big role and the angles are noticeably different.

Your MAD Scientist,
Raymond Cheong