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I looked up http://mathworld.wolfram.com/MetricTensor.html but it does not seem to provide me exact formula of generalized pythogorean theorem using metric tensor and tensor.

So, can anyone tell me what it is?

Thnx.

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en.wikipedia.org/wiki/… –  anon Jun 27 '12 at 5:27
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Just to check: do you want this in the case of triangles on a manifold or just triangles in a fixed tangent space? For the former there's no such thing as a Pythagorean theorem, at least nothing that holds in great generality. For the latter you may want to re-tag your question as "linear algebra" instead of "differential-geometry". –  Willie Wong Jun 27 '12 at 8:15

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