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A236556 Decimal expansion of the steradian solid angle subtended by one square facet of the cuboctahedron. 6

%I #23 May 22 2023 02:45:35

%S 1,3,5,9,3,4,7,6,3,7,8,1,6,4,8,7,7,4,8,3,8,5,5,7,0,0,5,3,5,6,7,0,5,6,

%T 2,6,5,5,5,2,9,7,8,7,6,1,3,2,9,8,3,2,2,8,5,7,2,7,6,9,5,8,4,9,9,5,9,6,

%U 6,3,5,5,4,6,5,9,3,9,3,6,4,5,8,4,3,0,6,3,1,7,0,0,0,0,7,9,0,4,5,1,4,0,8,5,1

%N Decimal expansion of the steradian solid angle subtended by one square facet of the cuboctahedron.

%C Also the vertex solid angle of a regular octahedron.

%H Stanislav Sykora, <a href="/A236556/b236556.txt">Table of n, a(n) for n = 1..2000</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Cuboctahedron.html">Cuboctahedron</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SphericalPolygon.html">Spherical Polygon</a>.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Platonic_solid">Platonic solid</a>.

%F Equals 4*arcsin(1/3) = 4*A188615.

%F Equals 2*Pi - 4*arcsin(2*sqrt(2)/3). - _Bradley Klee_, Oct 04 2018

%F 8*A236555 + 6*this = 4*Pi. - _Bradley Klee_, Oct 04 2018

%e 1.35934763781648774838557005356705626555297876132983228572769584995966...

%p evalf(4*arcsin(1/3),100) ; # _R. J. Mathar_, Apr 26 2021

%t RealDigits[4*ArcSin[1/3], 10, 120][[1]] (* _Amiram Eldar_, May 22 2023 *)

%o (PARI) 4*asin(1/3)

%Y Cf. A188615, A236555. Icosidodecahedron: A319881, A319883. Vertex Angles: A019669, A236557, A236558.

%K nonn,cons,easy

%O 1,2

%A _Stanislav Sykora_, Jan 28 2014

%E Definition corrected by _Bradley Klee_, Oct 04 2018

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Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)