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%I #30 Oct 01 2022 00:43:39
%S 6,5,0,6,4,5,1,4,2,2,8,4,2,8,6,5,0,4,2,7,6,6,1,8,8,0,3,3,9,0,5,9,5,4,
%T 0,7,2,0,8,7,2,6,1,4,5,0,0,0,2,9,2,2,0,1,0,5,5,2,2,5,5,0,7,3,2,4,3,0,
%U 9,1,9,3,4,0,6,6,3,2,4,5,5,9,7,3,6,4,6,0,5,4,7,1,1,3,2,4,0,8,4
%N Decimal expansion of Pi/(2 + 2*sqrt(2)).
%C This is the first of the three angles (in radians) of a unique triangle that is right angled and where the angles are in a harmonic progression: Pi/(2+2*sqrt(2)) (this sequence), Pi/(2+sqrt(2)) (A193373), Pi/2 (A019669). The angles (in degrees) are approximately 37.279, 52.721, 90. The common difference between the denominators of the harmonic progression is sqrt(2).
%H G. C. Greubel, <a href="/A193355/b193355.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F Equals Pi/(2+2*sqrt(2)).
%F Equals Integral_{x=0..Pi/2} cos(x)^2/(1 + sin(x)^2) dx = Integral_{x=0..Pi/2} sin(x)^2/(1 + cos(x)^2) dx. - _Amiram Eldar_, Aug 16 2020
%e 0.6506451422...
%p evalf(Pi/(2+2*sqrt(2)),120); # _Muniru A Asiru_, Sep 30 2018
%t N[Pi/(2 + 2*Sqrt[2]), 100]
%t Realdigits[Pi/(2 + 2*Sqrt[2]), 10, 100][[1]] (* _G. C. Greubel_, Sep 29 2018 *)
%o (PARI) default(realprecision,100); Pi/(2+2*sqrt(2))
%o (Magma) SetDefaultRealField(RealField(100)); R:= RealField(); Pi(R)/(2 + 2*Sqrt(2)); // _G. C. Greubel_, Sep 29 2018
%K easy,nonn,cons
%O 0,1
%A _Frank M Jackson_, Jul 24 2011
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