A243710 Decimal expansion of the solid angle of an equilateral spherical triangle with a side length of 1 radian.

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

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

Cf. A243711 (fraction of full solid angle).

Sequence in context: A344078 A200011 A200241 * A242610 A292484 A197418

Adjacent sequences: A243707 A243708 A243709 * A243711 A243712 A243713

Keyword

nonn,cons,easy

Author

Stanislav Sykora, Jun 08 2014

Status

approved