Harriot’s 1603 result on the sphere: the angular excess of a triangle is the Gaussian curvature times the area, which we may think of as the total amount of curvature residing within the triangle.
It is also valid for geodesic $n$-gons on a sphere:
$$ \frac{1}{R^2} \mathcal{A}(n\text{-gon})=[\text{angle sum}]-(n-2)\pi $$where $R$ is the radius fo the sphere.
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Author of the notes: Antonio J. Pan-Collantes
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