On the surface of a sphere, we can find the radius of cuvature of the sphere by:(adsbygoogle = window.adsbygoogle || []).push({});

angle excess / area = 1/ r_s^2

http://en.wikipedia.org/w/index.php?title=Angle_excess&oldid=543583039

If we use triangles, for instance, the angle excess is the sum of the angles of the triangle minus 180 degrees.

Can we use this basic idea to define the sectional curvature of a plane in terms that are relatively layman-friendly, and leverage this up to a fuller explanation of the Riemann curvature tensor?

T seems to me it's that "angle excess" is the same basic idea as talking about the parallel transport of a vector around a closed path, but expressed in simpler language.

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# Angle Excess

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