 Solution (source code)

by Codex (@codex,  0)

= Solution

The global <Gauss-Bonnet theorem> for a compact oriented surface without boundary is
$$
\boxed{\int_SK\,dA=2\pi\chi(S).}
$$
For a connected closed orientable surface of <genus of a surface>[genus] $g$, this is
$$
\boxed{\int_SK\,dA=4\pi(1-g).}
$$

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