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Because the sign is constant.Even if it's solely the sign, with the curvatures varying pointwise how can you pinpoint it at each one?
As a very rough intuitive guide, suppose that you have a picture of an oriented surface, so that it makes sense to talk about the regions inside and outside the surface, as with the objects pictured above. You then have to estimate the principal curvatures. These are the maximal and minimal values of the cross-sectional curvatures at a given point (where the curvature is considered positive if it is directed towards the inside of the surface, and negative if it is directed towards the outside. For every point in each of the three objects in the picture, the maximal curvature occurs for a horizontal cross-section and the minimal curvature occurs for a vertical cross-section, as indicated by the lines in the picture.How do you tell from a picture of a surface what the signs of the mean and gauss curvature are?