|
%I #22 Oct 02 2022 22:57:47
%S 1,6,3,4,0,4,5,4,6,5,2,0,4,3,6,4,4,2,4,8,6,8,1,4,0,7,0,9,7,6,0,7,4,5,
%T 0,9,4,1,1,7,3,8,6,8,8,2,7,9,3,5,1,6,3,5,9,1,6,5,7,1,8,3,3,1,8,8,5,3,
%U 0,7,5,7,2,3,8,6,3,8,5,3,7,2,9,7,0,6,7,5,9,6,5,0,0,9,6,7,7,0,8,4,0,3,0,2,4,9,1,5,0,8,9,4,0,6,7,3,0,6,9,7,5,6,1,1,3,6,4,4,6,0
%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>
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e 0.1634045465204364424868140709760745094117386882...
%t r = 2*Pi; t = (r - (-4 + r^2)^(1/2))/2; FullSimplify[t]
%t N[t, 130]
%t RealDigits[N[t, 130]][[1]] (* A189088 *)
%t ContinuedFraction[t, 120]
%t RealDigits[Pi-Sqrt[Pi^2-1],10,150][[1]] (* _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.
%K nonn,easy,cons
%O 0,2
%A _Clark Kimberling_, Apr 16 2011
|
