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how can you compute the sum of the angles on a non-euclidian surface, on the surface of a S2 sphere for example ?

I know that (for an elliptic geometry) if the triangle is small enough, the sum would be 180 degrees, and grow with the size of the triangle, so there might be an integral over the triangle involved, and the metric tensor would be of some use at one point...

So if you could give the outline and directions, it will be a good start to know which notions to check and learn, even if I do not understand the answer immediately.

Thank you for your help,


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And also here. – Xiang Jul 16 '11 at 7:03
@ks0830: Welcome to the site. I've converted your answer to a comment (it sounded like this is what you intended). Also, if you register your account, you will gain the ability to delete your own answers. – Zev Chonoles Jul 16 '11 at 7:23

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