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%I #39 Oct 30 2023 20:56:32
%S 5,1,7,6,3,8,0,9,0,2,0,5,0,4,1,5,2,4,6,9,7,7,9,7,6,7,5,2,4,8,0,9,6,6,
%T 5,6,6,9,8,1,3,7,8,0,2,6,3,9,8,6,1,0,2,7,6,2,8,0,0,6,4,1,4,6,3,0,1,1,
%U 3,9,4,9,4,9,7,6,0,3,9,9,3,8,4,4,7,3,5,9,4,9,3,8,8,4,9,9,3,3
%N Decimal expansion of sqrt(2 - sqrt(3)), edge length of a regular dodecagon with circumradius 1.
%C sqrt(2 - sqrt(3)) is the shape of the lesser sqrt(6)-contraction rectangle, as defined at A188739. - _Clark Kimberling_, Apr 16 2011
%C This is a constructible number, since 12-gon is a constructible polygon. See A003401 for more details. - _Stanislav Sykora_, May 02 2016
%C It is also smaller positive coordinate of (symmetrical) intersection points of x^2 + y^2 = 4 circle and y = 1/x hyperbola. The bigger coordinate is A188887. - _Leszek Lezniak_, Sep 18 2018
%H G. C. Greubel, <a href="/A101263/b101263.txt">Table of n, a(n) for n = 0..5000</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Dodecagon.html">Dodecagon</a>.
%H <a href="/index/Al#algebraic_04">Index entries for algebraic numbers, degree 4</a>
%F Equals sqrt(A019913). - _R. J. Mathar_, Apr 20 2009
%F Equals 2*sin(Pi/12) = 2*cos(Pi*5/12). - _Stanislav Sykora_, May 02 2016
%F Equals i^(5/6) + i^(-5/6). - _Gary W. Adamson_, Jul 07 2022
%e 0.517638090205041524697797675248096656698137802639861027628006414630113....
%t r = 6^(1/2); t = (r - (-4 + r^2)^(1/2))/2; FullSimplify[t]
%t N[t, 130]
%t RealDigits[N[t, 130]][[1]] (*A101263*)
%t RealDigits[Sqrt[2-Sqrt[3]],10,120][[1]] (* _Harvey P. Dale_, Apr 24 2018 *)
%o (PARI) 2*sin(Pi/12) \\ _Stanislav Sykora_, May 02 2016
%Y Cf. A003401, A188887.
%K cons,nonn
%O 0,1
%A Jun Mizuki (suzuki32(AT)sanken.osaka-u.ac.jp), Jan 25 2005
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