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Abrarov","submitted_at":"2017-06-03T13:13:56Z","abstract_excerpt":"In this paper we present a two-term Machin-like formula for pi \\[\\frac{\\pi}{4} = 2^{k - 1}\\arctan\\left(\\frac{1}{u_1}\\right) + \\arctan\\left(\\frac{1}{u_2}\\right)\\] with small Lehmer's measure $e \\approx 0.245319$ and describe iteration procedure for simplified determination of the required rational number $u_2$ at $k = 27$ and $u_1 = 85445659$. With these results we obtained a formula that has no irrational numbers involved in computation and provides $16$ digits of pi at each increment by one of the summation terms. 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M. Quine, S. M. Abrarov","submitted_at":"2017-06-03T13:13:56Z","abstract_excerpt":"In this paper we present a two-term Machin-like formula for pi \\[\\frac{\\pi}{4} = 2^{k - 1}\\arctan\\left(\\frac{1}{u_1}\\right) + \\arctan\\left(\\frac{1}{u_2}\\right)\\] with small Lehmer's measure $e \\approx 0.245319$ and describe iteration procedure for simplified determination of the required rational number $u_2$ at $k = 27$ and $u_1 = 85445659$. With these results we obtained a formula that has no irrational numbers involved in computation and provides $16$ digits of pi at each increment by one of the summation terms. 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