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Decimal expansion of (9-sqrt(65))/4.
1

%I #4 Mar 30 2012 18:57:23

%S 2,3,4,4,3,5,5,6,2,9,2,5,3,6,2,5,8,6,9,0,8,3,4,6,6,9,2,4,2,4,0,5,7,2,

%T 1,7,2,1,6,4,0,0,9,2,3,5,9,7,8,5,6,6,5,3,0,1,5,8,5,1,9,0,2,6,8,4,0,3,

%U 1,2,6,2,2,4,3,5,7,7,9,4,9,2,5,9,9,6,1,4,3,3,3,2,0,6,9,2,3,3,9,0,9,0,6,3,9,3,8,3,4,6,5,0,1,3,5,2,1,9,4,6,5,6,2,8,3,6,9,6,9,9

%N Decimal expansion of (9-sqrt(65))/4.

%C Decimal expansion of the shape (= length/width = ((9-sqrt(65))/4) of the lesser (9/2)-contraction rectangle.

%C See A188738 for an introduction to lesser and greater r-contraction rectangles, their shapes, and partitioning these rectangles into a sets of squares in a manner that matches the continued fractions of their shapes.

%e 0.23443556292536258690834669242405721721640...

%t r = 9/2; t = (r - (-4 + r^2)^(1/2))/2; FullSimplify[t]

%t N[t, 130]

%t RealDigits[N[t, 130]][[1]]

%t ContinuedFraction[t, 120]

%Y Cf. A188941, A188738.

%K nonn,cons

%O 1,1

%A _Clark Kimberling_, Apr 14 2011