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A094887 Decimal expansion of phi*sqrt(2), where phi = (1+sqrt(5))/2.

%I A094887 #21 Feb 16 2025 08:32:53
%S A094887 2,2,8,8,2,4,5,6,1,1,2,7,0,7,3,7,1,9,0,4,0,0,2,9,1,1,3,4,3,2,1,2,0,8,
%T A094887 3,0,6,1,4,4,6,1,3,5,0,7,3,5,1,0,8,2,4,5,0,0,1,7,0,9,2,2,9,5,3,9,1,6,
%U A094887 6,3,4,5,8,5,5,0,6,7,2,6,3,0,0,9,7,3,1,7,8,2,1,3,5,3,4,7,0,9,3
%N A094887 Decimal expansion of phi*sqrt(2), where phi = (1+sqrt(5))/2.
%C A094887 An algebraic number with minimal polynomial x^4 - 6x^2 + 4. - _Charles R Greathouse IV_, Mar 25 2014
%C A094887 The rhombus with diagonals phi*sqrt(2) and sqrt(2) is the unique golden rhombus -- by definition, the ratio of the diagonals of a golden rhombus is phi -- whose area is also phi (the golden ratio). - _Rick L. Shepherd_, Apr 10 2017
%H A094887 Ivan Panchenko, <a href="/A094887/b094887.txt">Table of n, a(n) for n = 1..1000</a>
%H A094887 MathWorld, <a href="https://mathworld.wolfram.com/GoldenRhombus.html">Golden Rhombus</a>
%H A094887 <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>
%e A094887 2.28824561127073719...
%t A094887 RealDigits[GoldenRatio Sqrt[2],10,120][[1]] (* _Harvey P. Dale_, Jan 24 2016 *)
%o A094887 (PARI) sqrt(3+sqrt(5)) \\ _Charles R Greathouse IV_, Mar 25 2014
%o A094887 (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Sqrt(2)*(1 + Sqrt(5))/2; // _G. C. Greubel_, Sep 27 2018
%Y A094887 Cf. A001622 (phi), A002193 (sqrt(2)).
%K A094887 cons,nonn
%O A094887 1,1
%A A094887 _N. J. A. Sloane_, Jun 15 2004