cp's OEIS Frontend

A231987 Decimal expansion of the side length (in radians) of the spherical square whose solid angle is exactly one steradian.

%I A231987 #14 Jun 06 2023 04:20:39
%S A231987 1,0,4,1,1,9,1,8,0,3,6,0,6,8,7,3,3,4,0,2,3,4,6,0,7,5,3,3,5,9,2,5,6,8,
%T A231987 7,8,8,9,0,0,6,9,6,6,7,6,0,0,6,0,8,7,1,3,4,9,1,5,2,3,0,2,8,1,3,1,2,9,
%U A231987 9,7,1,9,7,0,4,8,2,2,3,8,5,8,9,2,8,9,5,5,5,8,8,7,1,8,8,6,4,4,3,0,7,2,7,5,9
%N A231987 Decimal expansion of the side length (in radians) of the spherical square whose solid angle is exactly one steradian.
%C A231987 This is an inverse problem (but not an inverse value) to the one leading to A231986: what is the side s of a spherical square (in radians, rad) if it covers a given solid angle (in steradians, sr)? The solution (inverse of the formula in A231896) is s = 2*arcsin(sqrt(sin(Omega/4))). In this particular case, Omega = 1.
%H A231987 Stanislav Sykora, <a href="/A231987/b231987.txt">Table of n, a(n) for n = 1..2000</a>
%H A231987 Wikipedia, <a href="http://en.wikipedia.org/wiki/Solid_angle#Pyramid">Solid angle</a>, Section 3.3 (Pyramid).
%H A231987 Wikipedia, <a href="http://en.wikipedia.org/wiki/Steradian">Steradian</a>.
%F A231987 Equals 2*arcsin(sqrt(sin(1/4))).
%e A231987 1.041191803606873340234607533592568788900696676006087134915230281312997...
%t A231987 RealDigits[2*ArcSin[Sqrt[Sin[1/4]]], 10, 120][[1]] (* _Amiram Eldar_, Jun 06 2023 *)
%o A231987 (PARI)
%o A231987 default(realprecision, 120);
%o A231987 2*asin(sqrt(sin(1/4))) \\ or
%o A231987 solve(x = 1, 2, 4*asin((sin(x/2))^2) - 1) \\ least positive solution - _Rick L. Shepherd_, Jan 28 2014
%Y A231987 Cf. A072097 (rad/deg), A019685 (deg/rad), A231981 (sr/deg^2), A231982 (deg^2/sr), A231986 (inverse problem), A231896.
%K A231987 nonn,cons,easy
%O A231987 1,3
%A A231987 _Stanislav Sykora_, Nov 17 2013
%E A231987 Formula and comment corrected by _Rick L. Shepherd_, Jan 28 2014