

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((thetatheta_a)/2)*tan((thetatheta_b)/2)*tan((thetatheta_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 A292484 A197418
Adjacent sequences: A243707 A243708 A243709 * A243711 A243712 A243713


KEYWORD

nonn,cons,easy


AUTHOR

Stanislav Sykora, Jun 08 2014


STATUS

approved



