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

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, 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, 3, 0, 2, 3, 1, 4, 0, 9, 4, 5, 1, 2, 2, 4, 8, 5, 3, 6, 0, 3, 6, 0

Offset: 1

Author

Stanislav Sykora, Mar 27 2014

Keywords

• nonn
• cons
• easy

Comments

In a regular polyhedron, the midsphere is tangent to all edges.

Apart from leading digits the same as A019863 and A019827. - R. J. Mathar, Mar 30 2014

Examples

			1.30901699437494742410229341718281905886015458990288143106772431135263...
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 1..2000
• Wikipedia, Platonic solid.
• Index entries for algebraic numbers, degree 2.

Crossrefs

Cf. A000045, A001622, A001654, A019827, A019863, A066983, A094884, A104457, A187799.

Midsphere radii in Platonic solids: A020765 (tetrahedron), A020761 (octahedron), A010503 (cube), A019863 (icosahedron).

Programs

Maple

Digits:=100: evalf((3+sqrt(5))/4); # Wesley Ivan Hurt, Mar 27 2014

Mathematica

RealDigits[GoldenRatio^2/2,10,105][[1]] (* Vaclav Kotesovec, Mar 27 2014 *)

PARI

(3+sqrt(5))/4

Formula

Equals phi^2/2, phi being the golden ratio (A001622).

Equals (3+sqrt(5))/4.

Equals lim_{n->oo} A000045(n)/A066983(n). - Dimitri Papadopoulos, Nov 23 2023

Equals Product_{k>=2} (1 + (-1)^k/A001654(k)). - Amiram Eldar, Dec 02 2024

Equals A094884^2 = A104457/2 = 10/A187799. - Hugo Pfoertner, Dec 02 2024