Is there a formula for calculating the surface area of a region on a sphere which is bounded by 3 geodesics? Or, given three points on a sphere is there a way to calculate the surface area of the region bounded by the 3 geodesics going through those points?
2026-03-26 03:11:03.1774494663
Surface Area bounded by Geodesics
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The geodesics are great circles in spherical geometry. (If we measure arc length in the embedding Euclidean 3D space.)
So, we are talking about spherical triangles. The area of a spherical triangle is
$$(\alpha+\beta+\gamma-\pi)*R^2$$ where the angles are the angles between the corresponding tangent lines (by the definition the spherical angle.) As shown below.