Girard's Theorem:

  On a sphere of radius \(\sf R \), the area of a triangle \(\sf T \) is given by

  \(\sf \qquad \text{area}(T) = R^2 ( r + g + b - \pi ) \)

where \(\sf r \), \(\sf g \), and \(\sf b \) denote the angular measure in radians of the three angles on the white triangle \(\sf T \) shown below.


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Updated 2013 May 30