Let a spherical triangle 
have angles 
, 
, and 
. Then the spherical excess
is given by
 |
Girard's Spherical Excess Formula
See also
Angular Defect, L'Huilier's Theorem, Spherical Excess, Spherical TriangleExplore with Wolfram|Alpha
References
Coxeter, H. S. M. Introduction to Geometry, 2nd ed. New York: Wiley, pp. 94-95, 1969.Girard, A. Invention nouvelle en algebra. Amsterdam, Netherlands, 1629.Zwillinger, D. (Ed.). CRC Standard Mathematical Tables and Formulae. Boca Raton, FL: CRC Press, p. 469, 1995.Referenced on Wolfram|Alpha
Girard's Spherical Excess FormulaCite this as:
Weisstein, Eric W. "Girard's Spherical Excess Formula." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GirardsSphericalExcessFormula.html