Let a spherical triangle have sides of length 
, 
, and 
, and semiperimeter 
. Then the spherical
excess 
is given by
![tan(1/4E)=sqrt(tan(1/2s)tan[1/2(s-a)]tan[1/2(s-b)]tan[1/2(s-c)]).](/images/equations/LHuiliersTheorem/NumberedEquation1.svg) |
L'Huilier's Theorem
See also
Girard's Spherical Excess Formula, Spherical Excess, Spherical TriangleExplore with Wolfram|Alpha
References
Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 148, 1987.Zwillinger, D. (Ed.). CRC Standard Mathematical Tables and Formulae. Boca Raton, FL: CRC Press, p. 469, 1995.Cite this as:
Weisstein, Eric W. "L'Huilier's Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/LHuiliersTheorem.html