cp's OEIS Frontend

A231984 Decimal expansion of the solid angle (in deg^2) of a spherical square having sides of one degree.

%I A231984 #17 Aug 20 2017 14:44:38
%S A231984 9,9,9,9,7,4,6,1,6,4,3,9,2,7,8,6,5,4,3,2,1,9,8,5,0,9,4,7,8,4,9,6,8,2,
%T A231984 2,5,5,1,7,9,5,9,1,5,2,4,1,8,5,7,6,4,5,2,7,4,0,6,4,6,7,2,8,4,2,8,1,4,
%U A231984 8,7,7,7,6,0,7,1,7,3,3,6,5,8,1,8,1,5,1,7,6,0,5,8,9,6,7,7,1,4,7,6,7,1,4,5,7
%N A231984 Decimal expansion of the solid angle (in deg^2) of a spherical square having sides of one degree.
%C A231984 See the comments to A231983 which will make it clear why on a sphere the solid angle of a square with one degree arc-length side is not exactly one deg^2. The correct value, shown here, is A231983*A231981.
%D A231984 G. V. Brummelen, Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry, Princeton University Press, 2012, ISBN 978-0691148922.
%H A231984 Stanislav Sykora, <a href="/A231984/b231984.txt">Table of n, a(n) for n = 0..2000</a>
%H A231984 Wikipedia, <a href="http://en.wikipedia.org/wiki/Solid_angle#Pyramid">Solid angle</a>, Section 3.3 (Pyramid)
%H A231984 Wikipedia, <a href="http://en.wikipedia.org/wiki/Square_degree">Square degree</a>
%H A231984 Wikipedia, <a href="http://en.wikipedia.org/wiki/Steradian">Steradian</a>
%F A231984 4*arcsin(sin(R/2)sin(S/2))*(180/Pi)^2, where R = S = Pi/180.
%e A231984 0.9999746164392786543219850947849682255179591524185764527406467...
%t A231984 RealDigits[4*ArcSin[Sin[Pi/360]^2](180/Pi)^2,10,120][[1]] (* _Harvey P. Dale_, Aug 20 2017 *)
%o A231984 (PARI)
%o A231984 default(realprecision, 120);
%o A231984 4*asin(sin(Pi/360)^2)*(180/Pi)^2 \\ _Rick L. Shepherd_, Jan 28 2014
%Y A231984 Cf. A000796 (Pi), A072097 (rad/deg), A019685 (deg/rad), A231981 (sr/deg^2), A231982 (deg^2/sr), A231983 (this constant in sr), A231987 (for square with 1 rad side), A231985, A231986.
%K A231984 nonn,cons,easy
%O A231984 0,1
%A A231984 _Stanislav Sykora_, Nov 17 2013