login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A243710 Decimal expansion of the solid angle of an equilateral spherical triangle with a side length of 1 radian. 2

%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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 29 10:44 EDT 2024. Contains 371268 sequences. (Running on oeis4.)