Mean curvature
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In mathematics, mean curvature of a surface is a notion from differential geometry.
Take a point P on a surface. There is a line passing through this point and perpendicular to the surface. This line is the normal at P. There are planes passing through this line. For any such plane, it and the surface's intersection is a curve. This curve has a curvature C at P.
For all such curvatures C of all the planes, there is a maximal and a minimal one (called principal curvatures). Their product is the Gaussian curvature at P of the surface. Their average is the mean curvature at P of the surface.
Symbolically, the mean curvature H is
- <math> H = {1 \over 2} (k_1 + k_2) <math>
where k1 and k2 are the principal curvatures.