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

%I A381264 #21 Feb 26 2025 02:13:08
%S A381264 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,
%T A381264 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,
%U A381264 6,6,9,1,6,7,6,0,5,9,6,6,5,4,7,9,3,8,0,3,9,6,7,0
%N A381264 Decimal expansion of the edge length of the dodecahedron inside a circumscribed unit sphere.
%H A381264 Paolo Xausa, <a href="/A381264/b381264.txt">Table of n, a(n) for n = 0..10000</a>
%H A381264 Wikipedia, <a href="https://en.wikipedia.org/wiki/Regular_dodecahedron">Regular Dodecahedron</a>.
%F A381264 Equals 2/(sqrt(3)*A001622) = 1/A179296.
%F A381264 Equals 2*sin(A156547/2).
%F A381264 Minimal polynomial: 9*x^4 - 36*x^2 + 16. - _Amiram Eldar_, Feb 26 2025
%e A381264 0.7136441795461798638839396860921757479633721504937...
%p A381264 g := (1+sqrt(5))/2 ; Digits := 100 ; evalf(2/sqrt(3)/g) ;
%t A381264 First[RealDigits[2/(Sqrt[3]*GoldenRatio), 10, 100]] (* _Paolo Xausa_, Feb 19 2025 *)
%Y A381264 Cf. A156547, A001622, A179296.
%K A381264 nonn,cons
%O A381264 0,1
%A A381264 _R. J. Mathar_, Feb 18 2025