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%I #18 Oct 02 2022 00:17:48
%S 8,4,0,2,1,8,1,1,9,8,8,0,3,7,9,2,1,5,4,6,1,6,0,8,3,2,5,6,7,7,2,4,4,6,
%T 9,8,2,9,7,9,4,1,0,9,5,6,9,1,4,7,1,5,4,3,2,4,3,0,2,8,5,9,7,5,6,2,2,4,
%U 4,6,1,3,9,8,6,0,0,9,1,5,3,8,2,3,8,3,0,2,4,2,6,5,1,7
%N Decimal expansion of 16*(Pi-1) / (5*Pi^2 - 4*(Pi-1)): an approximation for sin(1) from Bhāskara I's sine approximation formula.
%C The Indian mathematician Bhāskara I (c. 600 - c. 680) proposed this remarkable approximation formula for sin(x), in his work Mahabhaskariya, chapter 7:
%C sin(x) ~ 16*x*(Pi-x) / (5*Pi^2 - 4*x*(Pi-x)), x in radian, 0 <= x <= Pi.
%C Formula and sine coincide for x = 0, Pi/6, Pi/2, 5Pi/6, and Pi.
%C Sin(1) = 0.8414... (A049469) while approximation = 0.8402...
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Bhāskara_I">Bhāskara I</a>.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Bhaskara_I's_sine_approximation_formula">Bhāskara I's sine approximation formula</a>.
%H <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F Equals 16*(Pi-1) / (5*Pi^2 - 4*(Pi-1)).
%e 0.8402181198803792154616083256772446982979410956914...
%p evalf(16*(Pi-1) / (5*Pi^2 - 4*(Pi-1)),100);
%t RealDigits[16*(Pi - 1)/(5*Pi^2 - 4*(Pi - 1)), 10, 100][[1]] (* _Amiram Eldar_, Mar 27 2022 *)
%o (PARI) 16*(Pi-1)/(5*Pi^2-4*Pi-4) \\ _Charles R Greathouse IV_, Oct 02 2022
%Y Cf. A049469.
%K nonn,cons
%O 0,1
%A _Bernard Schott_, Mar 27 2022
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