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A350219
Decimal expansion of 16*(Pi-1) / (5*Pi^2 - 4*(Pi-1)): an approximation for sin(1) from Bhāskara I's sine approximation formula.
0
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, 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, 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
OFFSET
0,1
COMMENTS
The Indian mathematician Bhāskara I (c. 600 - c. 680) proposed this remarkable approximation formula for sin(x), in his work Mahabhaskariya, chapter 7:
sin(x) ~ 16*x*(Pi-x) / (5*Pi^2 - 4*x*(Pi-x)), x in radian, 0 <= x <= Pi.
Formula and sine coincide for x = 0, Pi/6, Pi/2, 5Pi/6, and Pi.
Sin(1) = 0.8414... (A049469) while approximation = 0.8402...
FORMULA
Equals 16*(Pi-1) / (5*Pi^2 - 4*(Pi-1)).
EXAMPLE
0.8402181198803792154616083256772446982979410956914...
MAPLE
evalf(16*(Pi-1) / (5*Pi^2 - 4*(Pi-1)), 100);
MATHEMATICA
RealDigits[16*(Pi - 1)/(5*Pi^2 - 4*(Pi - 1)), 10, 100][[1]] (* Amiram Eldar, Mar 27 2022 *)
PROG
(PARI) 16*(Pi-1)/(5*Pi^2-4*Pi-4) \\ Charles R Greathouse IV, Oct 02 2022
CROSSREFS
Cf. A049469.
Sequence in context: A100253 A175040 A238292 * A200108 A088397 A021123
KEYWORD
nonn,cons
AUTHOR
Bernard Schott, Mar 27 2022
STATUS
approved