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

1,2

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

Links

Stanislav Sykora, Table of n, a(n) for n = 1..2000

Wikipedia, Platonic solid

Index entries for algebraic numbers, degree 2

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

Example

1.30901699437494742410229341718281905886015458990288143106772431135263...

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 *)

Prog

(PARI) (3+sqrt(5))/4

Crossrefs

Cf. A001622,

Midsphere radii in Platonic solids:

A020765 (tetrahedron),

A020761 (octahedron),

A010503 (cube),

A019863 (icosahedron).

Sequence in context: A167004 A287632 A259346 * A019827 A329284 A269557

Adjacent sequences: A239795 A239796 A239797 * A239799 A239800 A239801

Keyword

nonn,cons,easy

Author

Stanislav Sykora, Mar 27 2014

Status

approved