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%I #9 Oct 02 2022 22:58:14
%S 6,1,1,9,7,8,0,7,6,0,6,5,9,1,5,0,0,3,4,4,3,8,4,7,2,6,9,5,5,8,2,9,3,1,
%T 2,5,8,9,8,2,6,0,0,1,1,0,4,7,0,8,6,0,0,0,6,0,3,3,3,1,7,3,5,1,4,2,7,1,
%U 0,2,0,5,5,3,3,3,7,7,9,4,5,9,9,5,9,0,0,2,0,5,4,1,8,3,2,6,6,4,2,7,5,6,1,2,7,1,2,5,7,9,3,7,1,5,7,8,8,2,5,9,6,6,2,6,5,5,2,7,7,3
%N Decimal expansion of Pi + sqrt(-1 + Pi^2).
%C Decimal expansion of the shape (= length/width = Pi + sqrt(-1 + Pi^2)) of the greater 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 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%e 6.119780760659150034438472695582931258982600110...
%t r = 2*Pi; t = (r + (-4 + r^2)^(1/2))/2; FullSimplify[t]
%t N[t, 130]
%t RealDigits[N[t, 130]][[1]] (*A189089*)
%t ContinuedFraction[t, 120] (*A189090*)
%o (PARI) Pi + sqrt(Pi^2-1) \\ _Charles R Greathouse IV_, Oct 02 2022
%Y Cf. A188738, A189090, A189088.
%K nonn,cons
%O 1,1
%A _Clark Kimberling_, Apr 16 2011
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