A243445 - OEIS

%I #19 Nov 12 2018 03:02:46

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

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

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

%N Decimal expansion of the polar angle of the cone circumscribed to a regular dodecahedron from one of its vertices.

%C The angle is in radians.

%H Stanislav Sykora, <a href="/A243445/b243445.txt">Table of n, a(n) for n = 1..2000</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Dodecahedron">Dodecahedron</a> (use the point coordinates to derive the formula).

%F arccos(1/(phi*sqrt(3))), where phi = A001622.

%F arctan(phi^2), where phi = A001622. - _Jon Maiga_, Nov 11 2018

%e 1.20593249868141343750392336173309109440033174266369606513299755...

%t RealDigits[ArcCos[1/(GoldenRatio Sqrt[3])],10,120][[1]] (* _Harvey P. Dale_, May 17 2016 *)

%o (PARI) acos(2/(1+sqrt(5))/sqrt(3))

%Y Cf. A001622 (phi), A003881 (octahedron), A195695 (tetrahedron), A195696 (cube), A195723 (isosahedron).

%K nonn,cons

%O 1,2

%A _Stanislav Sykora_, Jun 06 2014