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%I #19 Jan 22 2022 08:42:24
%S 1,3,3,2,4,7,8,8,6,4,9,8,5,0,3,0,5,1,0,2,0,8,0,0,9,7,9,1,9,5,5,5,8,5,
%T 4,4,1,3,3,4,9,8,0,2,7,7,4,5,1,8,9,5,6,8,5,6,6,2,9,4,7,6,8,5,6,0,7,9,
%U 5,7,9,7,8,7,5,8,1,1,8,5,6,3,4,1,5,8,1
%N Decimal expansion of the polar angle, in radians, of a cone which makes a golden-ratio cut of the full solid angle.
%C The polar angle (or apex angle) of a cone which cuts a fraction f of the full solid angle (i.e., subtends a solid angle of 4*Pi*f steradians) is given by arccos(1-2*f). For a golden cut of the sphere surface by a cone with apex in its center, set f = 1-1/phi, phi being the golden ratio A001622. This value is in radians, its equivalent in degrees is A238239.
%C The apex angle of the isosceles triangle of smallest perimeter which circumscribes a semicircle (DeTemple, 1992). - _Amiram Eldar_, Jan 22 2022
%H Stanislav Sykora, <a href="/A238238/b238238.txt">Table of n, a(n) for n = 1..2000</a>
%H Duane W. DeTemple, <a href="https://www.fq.math.ca/Scanned/30-3/detemple.pdf">The Triangle of Smallest Perimeter which Circumscribes a Semicircle</a>, The Fibonacci Quarterly, Vol. 30, No. 3 (1992), p. 274.
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Solid_angle">Solid angle</a>.
%F arccos(1-2*(1-1/phi)) = arccos(2/phi-1), with phi = A001622.
%e 1.3324788649850305102080097919555854413349802774518956856629476856...
%t RealDigits[ArcCos[2/GoldenRatio -1],10,120][[1]] (* _Harvey P. Dale_, Jul 05 2019 *)
%o (PARI) acos(4/(1+sqrt(5))-1)
%Y Cf. A001622, A019670, A137914, A238239.
%K nonn,cons,easy
%O 1,2
%A _Stanislav Sykora_, Feb 20 2014
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