(adsbygoogle = window.adsbygoogle || []).push({}); [SOLVED] Prove: Sum of angles > 180 in curved space

1. The problem statement, all variables and given/known data

If I have a positively curved space (i.e. a sphere) and I draw a triangle on it, the sum of the angles of the triangle exceed [tex]\pi[/tex], more precisely,

v1 + v2 + v3 = pi + A/R^2

where v1, v2 and v3 are the angles of the triangle, A is the area of the triangle and R is the radius of the sphere.

This is what I have to prove.

3. The attempt at a solution

Ok, first I setup the "environment". I will look at a triangle with equal long sides with one corner at the north-pole. What would be the next step from here?

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# Prove: Sum of angles > 180 in curved space

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