A131595 Decimal expansion of 3*(sqrt(25 + 10*sqrt(5))), the surface area of a regular dodecahedron with edges of unit length.

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

Offset

2,1

Comments

Surface area of a regular dodecahedron: A = 3*(sqrt(25 + 10*sqrt(5)))* a^2, where 'a' is the edge.

Links

G. C. Greubel, Table of n, a(n) for n = 2..10001

Eric Weisstein's World of Mathematics, Dodecahedron

Wikipedia, Platonic solid

Index entries for algebraic numbers, degree 4

Formula

From Stanislav Sykora, Nov 30 2013: (Start)

Equals 15/tan(Pi/5).

Equals 15*phi/xi, where phi is the golden ratio (A001622) and xi its associate (A182007). (End)

Example

20.64572880706760307310814372866331519288849004012237995...

Maple

evalf(3*(sqrt(25+10*sqrt(5))), 130); # Muniru A Asiru, Nov 02 2018

Mathematica

RealDigits[3  Sqrt[25+10Sqrt[5]], 10, 120][[1]]  (* Harvey P. Dale, Jun 21 2011 *)

Prog

(PARI) default(realprecision, 100); 3*(sqrt(25 + 10*sqrt(5))) \\ G. C. Greubel, Nov 02 2018
(Magma) SetDefaultRealField(RealField(100)); 3*(Sqrt(25 + 10*Sqrt(5))); // G. C. Greubel, Nov 02 2018

Crossrefs

Cf. A102769, A001622 (phi), A182007 (associate of phi), A010527 (icosahedron/10), A010469 (octahedron), A002194 (tetrahedron). - Stanislav Sykora, Nov 30 2013

Sequence in context: A136656 A256850 A242561 * A290826 A124228 A115879

Adjacent sequences: A131592 A131593 A131594 * A131596 A131597 A131598

Keyword

nonn,cons,easy

Author

Omar E. Pol, Aug 30 2007

Extensions

More terms from Harvey P. Dale, Jun 21 2011

Status

approved