# excess of a triangle

• Apr 28th 2013, 11:55 PM
henderson7878
excess of a triangle
Given that the angle sum of a triangle made of great circle arcs on a sphere (a spherical triangle) is greater than two right angles, define the excess of a triangle as the difference between its angle sum and 180°.Show that if a spherical triangle ABC is split into two triangles by an arc BD from vertex B to the opposite side, then the excess of triangle ABC is equal to the sum of the excesses of triangles ABD and BDC.
• Apr 29th 2013, 03:36 AM
topsquark
Re: excess of a triangle
Quote:

Originally Posted by henderson7878
Given that the angle sum of a triangle made of great circle arcs on a sphere (a spherical triangle) is greater than two right angles, define the excess of a triangle as the difference between its angle sum and 180°.Show that if a spherical triangle ABC is split into two triangles by an arc BD from vertex B to the opposite side, then the excess of triangle ABC is equal to the sum of the excesses of triangles ABD and BDC.

What have you been able to do with this?

-Dan