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%I #24 Aug 21 2023 12:18:42
%S 3,4,2,7,0,5,0,9,8,3,1,2,4,8,4,2,2,7,2,3,0,6,8,8,0,2,5,1,5,4,8,4,5,7,
%T 1,7,6,5,8,0,4,6,3,7,6,9,7,0,8,6,4,4,2,9,3,2,0,3,1,7,2,9,3,4,0,5,7,8,
%U 9,0,6,9,4,2,2,8,3,5,3,6,7,4,5,6,0,8,1,0,8,0,6,2,8,4,0,8,6,7,0,6,2,2,7,1,3
%N Given an equilateral triangle T, partition each side (with the same orientation) into segments exhibiting the Golden Ratio. Let t be the resulting internal equilateral triangle t. Sequence gives decimal expansion of ratio of areas T/t.
%C A quadratic number with denominator 2 and minimal polynomial 4x^2 - 14x + 1. - _Charles R Greathouse IV_, Apr 21 2016
%D Alfred S. Posamentier & Ingmar Lehmann, Phi, The Glorious Golden Ratio, Prometheus Books, 2011.
%H <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>
%H <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>
%F = phi^2/(1 + 1/phi^2 - 1/phi).
%F Also, = (phi^4)/2 = 1+3*phi/2 [Clark Kimberling, Oct 24 2012]
%e 3.427050983124842272306880251548457176580463769708644293203172934...
%t x = GoldenRatio; RealDigits[x^4/(1 - x + x^2), 10, 111][[1]]
%o (PARI) (1+sqrt(5))^4/32 \\ _Charles R Greathouse IV_, Dec 12 2013
%Y Cf. A001622.
%K nonn,cons
%O 1,1
%A _Robert G. Wilson v_, Jan 31 2012