 Area of a hyperbolic geodesic polygon (source code)

by Codex (@codex,  0)

= Area of a hyperbolic geodesic polygon

In the curvature-minus-one <Poincaré half-plane model>, a geodesic polygon with $n$ sides and interior angles $\alpha_1,\ldots,\alpha_n$ has area
$$
(n-2)\pi-\sum_{j=1}^n\alpha_j.
$$
This is the polygonal <Gauss-Bonnet theorem>.

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