OFFSET
0,1
COMMENTS
Set theta_a = theta_b = theta_c = 1 in the formula below. The result is in steradians.
LINKS
Stanislav Sykora, Table of n, a(n) for n = 0..2000
Wikipedia, Solid angle, section 'Tetrahedron', L'Huillier's theorem.
FORMULA
For a spherical triangle with sides theta_a, theta_b, theta_c, the solid angle is 4*atan(sqrt(tan(theta/2)*tan((theta-theta_a)/2)*tan((theta-theta_b)/2)*tan((theta-theta_c)/2))), where theta = (theta_a+theta_b+theta_c)/2.
EXAMPLE
0.4955948957339647506988579129084002115603807921880... steradians.
MATHEMATICA
RealDigits[4(ArcTan[Sqrt[Tan[3/4]Tan[1/4]^3]]), 10, 120][[1]] (* Harvey P. Dale, Sep 13 2020 *)
PROG
(PARI) 4*atan(sqrt(tan(3/4)*tan(1/4)^3))
CROSSREFS
KEYWORD
AUTHOR
Stanislav Sykora, Jun 08 2014
STATUS
approved