cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A205769 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.

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%I A205769 #30 Aug 20 2025 10:49:56
%S A205769 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 A205769 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 A205769 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 A205769 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 A205769 A quadratic number with denominator 2 and minimal polynomial 4x^2 - 14x + 1. - _Charles R Greathouse IV_, Apr 21 2016
%D A205769 Alfred S. Posamentier and Ingmar Lehmann, Phi, The Glorious Golden Ratio, Prometheus Books, 2011.
%H A205769 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>
%H A205769 <a href="/index/Al#algebraic_02">Index entries for algebraic numbers, degree 2</a>
%F A205769 Equals phi^2/(1 + 1/phi^2 - 1/phi).
%F A205769 Equals (phi^4)/2 = 1+3*phi/2. - _Clark Kimberling_, Oct 24 2012
%e A205769 3.427050983124842272306880251548457176580463769708644293203172934...
%t A205769 x = GoldenRatio; RealDigits[x^4/(1 - x + x^2), 10, 111][[1]]
%o A205769 (PARI) (1+sqrt(5))^4/32 \\ _Charles R Greathouse IV_, Dec 12 2013
%Y A205769 Cf. A001622.
%K A205769 nonn,cons
%O A205769 1,1
%A A205769 _Robert G. Wilson v_, Jan 31 2012