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L'Huilier's Theorem


Let a spherical triangle have sides of length a, b, and c, and semiperimeter s. Then the spherical excess E 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)]).

See also

Girard's Spherical Excess Formula, Spherical Excess, Spherical Triangle

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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

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