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

Author

Omar E. Pol, Aug 30 2007

Keywords

• nonn
• cons
• easy

Comments

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

Examples

			20.64572880706760307310814372866331519288849004012237995...
		

References

• Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, §12.4 Theorems and Formulas (Solid Geometry), p. 451.

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.

Crossrefs

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

Programs

Magma

SetDefaultRealField(RealField(100)); 3*(Sqrt(25 + 10*Sqrt(5))); // G. C. Greubel, Nov 02 2018

Maple

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

Mathematica

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

PARI

default(realprecision, 100); 3*(sqrt(25 + 10*sqrt(5))) \\ G. C. Greubel, Nov 02 2018

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)

Extensions

More terms from Harvey P. Dale, Jun 21 2011