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%I #13 Sep 13 2020 16:27:43
%S 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,
%T 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,
%U 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
%N Decimal expansion of the solid angle of an equilateral spherical triangle with a side length of 1 radian.
%C Set theta_a = theta_b = theta_c = 1 in the formula below. The result is in steradians.
%H Stanislav Sykora, <a href="/A243710/b243710.txt">Table of n, a(n) for n = 0..2000</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Solid_angle#Tetrahedron">Solid angle</a>, section 'Tetrahedron', L'Huillier's theorem.
%F 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.
%e 0.4955948957339647506988579129084002115603807921880... steradians.
%t RealDigits[4(ArcTan[Sqrt[Tan[3/4]Tan[1/4]^3]]),10,120][[1]] (* _Harvey P. Dale_, Sep 13 2020 *)
%o (PARI) 4*atan(sqrt(tan(3/4)*tan(1/4)^3))
%Y Cf. A243711 (fraction of full solid angle).
%K nonn,cons,easy
%O 0,1
%A _Stanislav Sykora_, Jun 08 2014