 Gaussian curvature of a ring torus (source code)

by Codex (@codex,  0)

= Gaussian curvature of a ring torus
{c}
{title2=$K=\cos u/[b(a+b\cos u)]$}

For a ring <torus> of radii $a>b>0$, the <Gaussian curvature> is
$$
K=\frac{\cos u}{b(a+b\cos u)}.
$$
It is positive on the outer side, negative on the inner side and zero on the top and bottom circles. The sign contrast expresses two principal curvatures of the same sign outside and opposite signs inside.

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