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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 (list; constant; graph; refs; listen; history; text; internal format)
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.

PROG

(PARI) 4*atan(sqrt(tan(3/4)*tan(1/4)^3))

CROSSREFS

Cf. A243711 (fraction of full solid angle).

Sequence in context: A011003 A200011 A200241 * A242610 A197418 A137807

Adjacent sequences:  A243707 A243708 A243709 * A243711 A243712 A243713

KEYWORD

nonn,cons,easy

AUTHOR

Stanislav Sykora, Jun 08 2014

STATUS

approved

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Last modified May 23 04:09 EDT 2017. Contains 286909 sequences.