cp's OEIS Frontend

A248411 Decimal expansion of the best lower bound for the Steiner ratio rho_3, the least upper bound on the ratio of the length of the Steiner minimal tree to the length of the minimal tree in dimension 3.

%I A248411 #5 Oct 06 2014 15:58:48
%S A248411 6,1,5,8,2,7,7,4,8,1,2,3,4,0,6,6,0,6,7,1,7,1,1,4,3,9,7,3,0,1,4,4,1,3,
%T A248411 9,3,4,4,1,0,9,6,5,3,5,1,3,3,2,1,3,2,9,4,3,0,9,3,9,3,5,0,2,2,4,8,6,7,
%U A248411 6,9,8,4,1,1,7,4,9,8,0,8,0,3,0,7,8,2,3,6,4,5,8,9,0,6,0,1,3,9,9,3,8,2
%N A248411 Decimal expansion of the best lower bound for the Steiner ratio rho_3, the least upper bound on the ratio of the length of the Steiner minimal tree to the length of the minimal tree in dimension 3.
%D A248411 Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, Section 8.6 Steiner Tree Constants, p. 504.
%F A248411 b = (2 + x - sqrt(x^2 + x + 1))/sqrt(3), where x is the positive root of 128*x^6 + 456*x^5 + 783*x^4 + 764*x^3 + 408*x^2 + 108*x - 28.
%e A248411 x = 0.1486637196311613967236467715222572732594626883945180141...
%e A248411 b = 0.6158277481234066067171143973014413934410965351332132943...
%t A248411 x0 = Root[128*x^6 + 456*x^5 + 783*x^4 + 764*x^3 + 408*x^2 + 108*x - 28, 2]; b = (2 + x0 - Sqrt[x0^2 + x0 + 1])/Sqrt[3]; RealDigits[b, 10, 102] // First
%Y A248411 Cf. A220351 (upper bound of rho_3).
%K A248411 nonn,cons
%O A248411 0,1
%A A248411 _Jean-François Alcover_, Oct 06 2014