A243445 Decimal expansion of the polar angle of the cone circumscribed to a regular dodecahedron from one of its vertices.

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

Offset: 1

Author

Stanislav Sykora, Jun 06 2014

Keywords

• nonn
• cons

Comments

The angle is in radians.

Examples

			1.20593249868141343750392336173309109440033174266369606513299755...
		

Links

• Stanislav Sykora, Table of n, a(n) for n = 1..2000
• Wikipedia, Dodecahedron (use the point coordinates to derive the formula).

Crossrefs

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

Programs

Mathematica

RealDigits[ArcCos[1/(GoldenRatio Sqrt[3])],10,120][[1]] (* Harvey P. Dale, May 17 2016 *)

PARI

acos(2/(1+sqrt(5))/sqrt(3))

Formula

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

arctan(phi^2), where phi = A001622. - Jon Maiga, Nov 11 2018