A381264 Decimal expansion of the edge length of the dodecahedron inside a circumscribed unit sphere.

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

Offset

0,1

Links

Paolo Xausa, Table of n, a(n) for n = 0..10000

Wikipedia, Regular Dodecahedron.

Index entries for algebraic numbers, degree 4.

Formula

Equals 2/(sqrt(3)*A001622) = 1/A179296.

Equals 2*sin(A156547/2).

Minimal polynomial: 9*x^4 - 36*x^2 + 16. - Amiram Eldar, Feb 26 2025

Example

0.7136441795461798638839396860921757479633721504937...

Maple

g := (1+sqrt(5))/2 ; Digits := 100 ; evalf(2/sqrt(3)/g) ;

Mathematica

First[RealDigits[2/(Sqrt[3]*GoldenRatio), 10, 100]] (* Paolo Xausa, Feb 19 2025 *)

Prog

(PARI) 4/(1+sqrt(5))/sqrt(3) \\ Charles R Greathouse IV, Apr 24 2026
(PARI) polrootsreal(9*x^4 - 36*x^2 + 16)[3] \\ Charles R Greathouse IV, Apr 24 2026

Crossrefs

Cf. A156547, A001622, A179296.

Sequence in context: A362923 A201585 A089562 * A383267 A104621 A331900

Adjacent sequences: A381261 A381262 A381263 * A381265 A381266 A381267

Keyword

nonn,cons

Author

R. J. Mathar, Feb 18 2025

Status

approved