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...
LINKS
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
KEYWORD
nonn,cons
AUTHOR
Bernard Schott, Mar 27 2022
STATUS
approved