Spherical Geometry: Deriving The Formula For The Area Of A Spherical Triangle

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Summary:
► A spherical triangle is a surface area of a sphere bounded by 3 arcs of great circles.
► Any spherical triangle has it's antipodal duplicate
► Each of these spherical triangles are intersections of 3 different spherical lunes.
► Adding up the area of all 6 lunes results in the surface area of a sphere with 4 additional spherical triangles.

►Girard's Theorem: the area (T) of a spherical triangle, with interior angles a,b and c, is given by T = r^2 (a + b + c - pi). The

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