A237603 Decimal expansion of the inscribed sphere radius in a regular dodecahedron with unit edge.

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

Offset

1,4

Comments

Equals phi^2/(2*xi), where phi is the golden ratio (A001622, 2*cos(Pi/5)) and xi is its associate (A182007, 2*sin(Pi/5)).

Links

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

Wikipedia, Platonic solid

Formula

Equals A001622^2/A182007 = (cos(Pi/5))^2/sin(Pi/5) = A019863^2/A019845 = cos(Pi/5)*cotan(Pi/5) = A019863*A019952 = 1/sin(Pi/5) - sin(Pi/5) = A019845^(-1) - A019845 = sqrt(250+110*sqrt(5))/20.

Example

1.1135163644116067351943750394869493758831503698864877726012080...

Mathematica

RealDigits[ Cos[Pi/5]^2 / Sin[Pi/5], 10, 111][[1]] (* Or *)
RealDigits[ Sqrt[5/8 + 11/(8 Sqrt[5])], 10, 111][[1]] (* Robert G. Wilson v, Feb 28 2014 *)

Prog

(PARI) sqrt(250+110*sqrt(5))/20

Crossrefs

Cf. A001622, A182007, A019863, A019863, A019952.

Cf. Platonic solids inradii: A020781 (tetrahedron), A020763 (octahedron), A179294 (icosahedron).

Sequence in context: A344076 A333336 A061649 * A073365 A316152 A302204

Adjacent sequences: A237600 A237601 A237602 * A237604 A237605 A237606

Keyword

nonn,cons

Author

Stanislav Sykora, Feb 25 2014

Status

approved