A134943 Decimal expansion of (golden ratio divided by 3 = phi/3 = (1 + sqrt(5))/6).

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

Offset: 0

Author

Omar E. Pol, Nov 15 2007

Keywords

• cons
• nonn

Comments

The vertex-to-face edge-length ratio between a dodecahedron and its enclosing dual icosahedron. See Wassell and Benito. - Michel Marcus, Sep 30 2019

Examples

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Links

• Stephen R. Wassell and Samantha Benito, Edge-Length Ratios Between Dual Platonic Solids: A Surprisingly New Result Involving the Golden Ratio, Fib. Q. 50(2), 2012, 144-154.

Crossrefs

Cf. A000045, A001622 (phi).

Programs

Mathematica

RealDigits[GoldenRatio/3,10,120][[1]] (* Harvey P. Dale, Jan 15 2012 *)

PARI

(1+sqrt(5))/6 \\ Michel Marcus, Sep 30 2019

Formula

Equals sqrt((3+sqrt(5))/18) or sqrt(6+2*sqrt(5))/6. See Wassell and Benito. - Michel Marcus, Sep 30 2019

Equals Product_{k>=2} (1 - 1/Fibonacci(2*k)). - Amiram Eldar, May 27 2021

Extensions

More terms from Harvey P. Dale, Jan 15 2012