cp's OEIS Frontend

A309893 Decimal expansion of AGM(1, sqrt(3)/2).

%I A309893 #38 Jul 27 2023 17:30:08
%S A309893 9,3,1,8,0,8,3,9,1,6,2,2,4,4,8,2,7,1,1,7,7,8,4,4,5,1,5,5,1,2,1,3,5,2,
%T A309893 9,7,5,7,8,7,6,6,4,2,8,4,1,3,4,2,6,8,6,1,1,1,0,2,2,0,6,1,3,4,8,9,1,6,
%U A309893 2,8,9,7,2,8
%N A309893 Decimal expansion of AGM(1, sqrt(3)/2).
%C A309893 Related to the pendulum acceleration relation at 60 degrees. In general, the period T of a mathematical pendulum with a maximum deflection angle theta is 2*Pi*sqrt(L/g)/AGM(1, cos(theta/2)), where L is the length of the pendulum, g is the gravitational acceleration, and 0 < theta <= 90 degrees. For theta = 60 degrees, the period is T = 2*Pi*sqrt(L/g)/AGM(1, sqrt(3)/2). - _Jianing Song_, Nov 21 2022
%H A309893 Wikipedia, <a href="https://en.wikipedia.org/wiki/Pendulum_(mechanics)#Arithmetic-geometric_mean_solution_for_elliptic_integral">Pendulum (mechanics)</a>
%F A309893 AGM(1, sin(Pi/3)).
%e A309893 0.931808391622448271177844...
%t A309893 RealDigits[ArithmeticGeometricMean[1, Sqrt[3]/2], 10, 100][[1]] (* _Amiram Eldar_, Aug 21 2019 *)
%o A309893 (Python)
%o A309893 import decimal
%o A309893 prec = int(input('Precision: '))
%o A309893 decimal.getcontext().prec = prec
%o A309893 D = decimal.Decimal
%o A309893 def agm(a, b):
%o A309893     for x in range(prec):
%o A309893         a, b = (a + b) / 2,(a * b).sqrt()
%o A309893     return a
%o A309893 print(agm(1, D(3).sqrt()/2))
%o A309893 (PARI) agm(1, sqrt(3)/2) \\ _Michel Marcus_, Aug 22 2019
%o A309893 (Sage)
%o A309893 RealField(300)(1.0).agm(sqrt(3)/2) # _Peter Luschny_, Aug 22 2019
%Y A309893 Cf. A310000 (AGM(1, cos(Pi/5))), A096427 (AGM(1, sqrt(2)/2)), A053004, A014549, A068521.
%K A309893 nonn,cons
%O A309893 0,1
%A A309893 _Daniel Hoyt_, Aug 21 2019