%N Decimal expansion of Pi - sqrt(Pi^2 - 1).
%C Decimal expansion of the shape (= length/width = Pi - sqrt(-1+Pi^2)) of the lesser 2*Pi-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.
%H G. C. Greubel, <a href="/A189088/b189088.txt">Table of n, a(n) for n = 0..5000</a>
%t r = 2*Pi; t = (r - (-4 + r^2)^(1/2))/2; FullSimplify[t]
%t N[t, 130]
%t RealDigits[N[t, 130]][] (* A189088 *)
%t ContinuedFraction[t, 120]
%t RealDigits[Pi-Sqrt[Pi^2-1],10,150][] (* _Harvey P. Dale_, Sep 25 2016 *)
%o (PARI) Pi*(1-sqrt(1-1/Pi^2)) \\ _Charles R Greathouse IV_, May 07, 2011
%Y Cf. A188738, A189089, A189090.
%A _Clark Kimberling_, Apr 16 2011