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 A310000 Decimal expansion of AGM(1, phi/2), where phi is the golden ratio (A001622). 1
 9, 0, 1, 9, 7, 9, 3, 3, 8, 1, 1, 4, 3, 4, 3, 1, 2, 3, 3, 9, 7, 2, 7, 1, 5, 3, 6, 5, 8, 7, 7, 9, 8, 6, 2, 7, 5, 5, 1, 6, 2, 3, 7, 4, 6, 7, 3, 6, 9, 9, 0, 1, 4, 0, 7, 9, 8, 4, 7, 7, 9, 4, 2, 9, 1, 1, 9, 4, 1, 4, 2, 6, 2, 6, 2, 0, 5, 7, 7, 2, 7, 5, 4, 1, 8 (list; constant; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS Related to the pendulum acceleration relation at 72 degrees. 2*Pi*sqrt(l/g)/AGM(1, phi/2) gives the period T of a mathematical pendulum with a maximum deflection angle of 72 degrees from the downward vertical. The length of the pendulum is l and g is the gravitational acceleration. LINKS FORMULA Equals AGM(1, cos(Pi/5)). EXAMPLE 0.9019793381143431233972715365... MATHEMATICA RealDigits[ArithmeticGeometricMean[1, GoldenRatio/2], 10, 100][[1]] (* Amiram Eldar, Aug 26 2019 *) PROG (Python3) import decimal iters = int(input('Precision: ')) decimal.getcontext().prec = iters D = decimal.Decimal def agm(a, b): for x in range(iters): a, b = (a + b) / 2, (a * b).sqrt() return a print(agm(1, (D(5).sqrt()+1)/4)) (PARI) agm(1, cos(Pi/5)) \\ Michel Marcus, Apr 05 2020 CROSSREFS Cf. A001622, A309893, A053004, A014549, A068521. Sequence in context: A249418 A256036 A065471 * A199284 A189186 A221429 Adjacent sequences: A309997 A309998 A309999 * A310001 A310002 A310003 KEYWORD nonn,cons AUTHOR Daniel Hoyt, Aug 26 2019 STATUS approved

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Last modified March 29 07:53 EDT 2023. Contains 361596 sequences. (Running on oeis4.)