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%I #25 Aug 21 2023 11:18:42
%S 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,
%T 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,
%U 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
%N Decimal expansion of 3*(sqrt(25 + 10*sqrt(5))), the surface area of a regular dodecahedron with edges of unit length.
%C Surface area of a regular dodecahedron: A = 3*(sqrt(25 + 10*sqrt(5)))* a^2, where 'a' is the edge.
%H G. C. Greubel, <a href="/A131595/b131595.txt">Table of n, a(n) for n = 2..10001</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Dodecahedron.html">Dodecahedron</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Platonic_solid">Platonic solid</a>
%H <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>
%F From _Stanislav Sykora_, Nov 30 2013: (Start)
%F Equals 15/tan(Pi/5).
%F Equals 15*phi/xi, where phi is the golden ratio (A001622) and xi its associate (A182007). (End)
%e 20.64572880706760307310814372866331519288849004012237995...
%p evalf(3*(sqrt(25+10*sqrt(5))),130); # _Muniru A Asiru_, Nov 02 2018
%t RealDigits[3 Sqrt[25+10Sqrt[5]],10,120][[1]] (* _Harvey P. Dale_, Jun 21 2011 *)
%o (PARI) default(realprecision, 100); 3*(sqrt(25 + 10*sqrt(5))) \\ _G. C. Greubel_, Nov 02 2018
%o (Magma) SetDefaultRealField(RealField(100)); 3*(Sqrt(25 + 10*Sqrt(5))); // _G. C. Greubel_, Nov 02 2018
%Y Cf. A102769, A001622 (phi), A182007 (associate of phi), A010527 (icosahedron/10), A010469 (octahedron), A002194 (tetrahedron). - _Stanislav Sykora_, Nov 30 2013
%K nonn,cons,easy
%O 2,1
%A _Omar E. Pol_, Aug 30 2007
%E More terms from _Harvey P. Dale_, Jun 21 2011
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