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Non-Euclidean Spherical Geometry
On a sphere's surface, Euclidean geometry does not apply:
- The shortest path between two surface points is a geodesic along a great circle arc.
- The interior angles of a spherical triangle always sum to more than 180° (spherical excess: = \alpha + \beta + \gamma - 180^\circ$).
- Parallel lines do not exist: any two great circles inevitably intersect at two opposite antipodal points.