cp's OEIS Frontend

A239798 Decimal expansion of the midsphere radius in a regular dodecahedron with unit edges.

%I A239798 #30 Dec 02 2024 15:39:21
%S A239798 1,3,0,9,0,1,6,9,9,4,3,7,4,9,4,7,4,2,4,1,0,2,2,9,3,4,1,7,1,8,2,8,1,9,
%T A239798 0,5,8,8,6,0,1,5,4,5,8,9,9,0,2,8,8,1,4,3,1,0,6,7,7,2,4,3,1,1,3,5,2,6,
%U A239798 3,0,2,3,1,4,0,9,4,5,1,2,2,4,8,5,3,6,0,3,6,0
%N A239798 Decimal expansion of the midsphere radius in a regular dodecahedron with unit edges.
%C A239798 In a regular polyhedron, the midsphere is tangent to all edges.
%C A239798 Apart from leading digits the same as A019863 and A019827. - _R. J. Mathar_, Mar 30 2014
%H A239798 Stanislav Sykora, <a href="/A239798/b239798.txt">Table of n, a(n) for n = 1..2000</a>
%H A239798 Wikipedia, <a href="http://en.wikipedia.org/wiki/Platonic solid">Platonic solid</a>.
%H A239798 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>.
%F A239798 Equals phi^2/2, phi being the golden ratio (A001622).
%F A239798 Equals (3+sqrt(5))/4.
%F A239798 Equals lim_{n->oo} A000045(n)/A066983(n). - _Dimitri Papadopoulos_, Nov 23 2023
%F A239798 Equals Product_{k>=2} (1 + (-1)^k/A001654(k)). - _Amiram Eldar_, Dec 02 2024
%F A239798 Equals A094884^2 = A104457/2 = 10/A187799. - _Hugo Pfoertner_, Dec 02 2024
%e A239798 1.30901699437494742410229341718281905886015458990288143106772431135263...
%p A239798 Digits:=100: evalf((3+sqrt(5))/4); # _Wesley Ivan Hurt_, Mar 27 2014
%t A239798 RealDigits[GoldenRatio^2/2,10,105][[1]] (* _Vaclav Kotesovec_, Mar 27 2014 *)
%o A239798 (PARI) (3+sqrt(5))/4
%Y A239798 Cf. A000045, A001622, A001654, A019827, A019863, A066983, A094884, A104457, A187799.
%Y A239798 Midsphere radii in Platonic solids: A020765 (tetrahedron), A020761 (octahedron), A010503 (cube), A019863 (icosahedron).
%K A239798 nonn,cons,easy
%O A239798 1,2
%A A239798 _Stanislav Sykora_, Mar 27 2014