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A243710
Decimal expansion of the solid angle of an equilateral spherical triangle with a side length of 1 radian.
2
4, 9, 5, 5, 9, 4, 8, 9, 5, 7, 3, 3, 9, 6, 4, 7, 5, 0, 6, 9, 8, 8, 5, 7, 9, 1, 2, 9, 0, 8, 4, 0, 0, 2, 1, 1, 5, 6, 0, 3, 8, 0, 7, 9, 2, 1, 8, 8, 0, 4, 5, 1, 6, 8, 3, 7, 4, 7, 2, 7, 3, 0, 9, 0, 5, 8, 5, 8, 8, 6, 9, 2, 1, 6, 7, 4, 0, 4, 2, 8, 4, 7, 2, 0, 7, 5, 9, 0, 0, 4, 9, 7, 4, 3, 5, 0, 7, 2, 3, 3, 2, 5, 0, 1, 0
OFFSET
0,1
COMMENTS
Set theta_a = theta_b = theta_c = 1 in the formula below. The result is in steradians.
LINKS
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
Cf. A243711 (fraction of full solid angle).
Sequence in context: A344078 A200011 A200241 * A242610 A292484 A197418
KEYWORD
nonn,cons,easy
AUTHOR
Stanislav Sykora, Jun 08 2014
STATUS
approved