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A243445 Decimal expansion of the polar angle of the cone circumscribed to a regular dodecahedron from one of its vertices. 4
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 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

The angle is in radians.

LINKS

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

Wikipedia, Dodecahedron (use the point coordinates to derive the formula).

FORMULA

arccos(1/(phi*sqrt(3))), where phi is the golden ratio A001622.

EXAMPLE

1.20593249868141343750392336173309109440033174266369606513299755...

MATHEMATICA

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

PROG

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

CROSSREFS

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

Sequence in context: A011435 A139309 A264299 * A227569 A011014 A002976

Adjacent sequences:  A243442 A243443 A243444 * A243446 A243447 A243448

KEYWORD

nonn,cons

AUTHOR

Stanislav Sykora, Jun 06 2014

STATUS

approved

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Last modified June 22 12:17 EDT 2017. Contains 288613 sequences.