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A236558 Vertex solid angle (steradians) in a regular dodecahedron. 4

%I #14 May 22 2023 02:45:40

%S 2,9,6,1,7,3,9,1,5,3,7,9,7,3,1,4,9,6,7,8,7,4,0,9,0,3,8,6,0,2,3,3,9,4,

%T 6,4,8,1,8,4,1,9,5,8,6,2,5,4,5,9,1,3,7,0,1,9,2,0,2,7,1,5,6,2,3,1,4,5,

%U 0,1,7,9,5,6,4,0,3,2,9,6,1,5,2,1,5,8,1,8,2,6,4,6,2,5,7,2,2,2,1,1,6,6,0,6,6

%N Vertex solid angle (steradians) in a regular dodecahedron.

%H Stanislav Sykora, <a href="/A236558/b236558.txt">Table of n, a(n) for n = 1..2000</a>

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

%F Equals Pi - arctan(2/11).

%e 2.9617391537973149678740903860233946481841958625459137019202715623145...

%t RealDigits[Pi - ArcTan[2/11], 10, 120][[1]] (* _Amiram Eldar_, May 22 2023 *)

%o (PARI) Pi-atan(2/11)

%Y Cf. Analogs: A236555 (tetrahedron), A236556 (octahedron), A019669 (cube), A236557 (icosahedron).

%K nonn,cons,easy

%O 1,1

%A _Stanislav Sykora_, Jan 28 2014

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