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I am trying to argue that an ellipse is a good approximation for some discontinuity in a material. The ellipse and the interpolated curve I get from the photo look very much alike, but I need an actual number to show how much the two curves differ from each other. I thought of

[tex]\frac{Area_{actual} - Area_{ellipse}}{Area_{actual}}[/tex]

but it doesn't really give any information about how much the curves match (a square with the same area as the ellipse would give 0 deviation).

I'm kind of new to Riemannian geometry, but I thought that maybe I could use the Riemann curvature tensor, although I don't really know how to do it yet :P . I would appreciate any suggestions you are able to give!

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# Looking for a metric to express difference between two curves

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