A341332 - OEIS

%I #25 Oct 02 2022 00:13:19

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

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

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

%N Decimal expansion of Pi/(2*phi).

%C This is the middle angle (in radians) of the unique right triangle whose angles are in geometric progression; common ratio is phi and the angles are (Pi/(2*phi^2), Pi/(2*phi), Pi/2) in radians, corresponding to approximately (34.377, 55.623, 90) in degrees.

%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>

%F Equals A019669/A001622 = A094881/2 = Pi/(1+sqrt(5)) = (Pi/4) * (sqrt(5)-1).

%e 0.970805519362733288673432814981347978817334946923024149753694108...

%p evalf(Pi/(1+sqrt(5)),150);

%t RealDigits[Pi/(2*GoldenRatio), 10, 100][[1]] (* _Amiram Eldar_, Feb 09 2021 *)

%o (PARI) Pi/(1+sqrt(5)) \\ _Michel Marcus_, Feb 09 2021

%Y Cf. A000796 (Pi), A001622 (phi), A019669 (Pi/2), A180014 (Pi/(2*phi^2)).

%K nonn,cons

%O 0,1

%A _Bernard Schott_, Feb 09 2021