근사 공식
\frac{\pi}{\sqrt{12}} = \sum^\infty_{k=0} \frac{(-3)^{-k}}{2k+1}
을 이용하여 근사값 계산하는 프로그램을 Pascal 언어로 작성해 보았다.
<![CDATA[(*****************************************************)
(* Filename: approximatePiOverSqrt12.pas *)
(* *)
(* Compile: fpc approximatePiOverSqrt12.pas *)
(* Execute: approximatePiOverSqrt12,pas *)
(*****************************************************)
program ApproximatePiOverSqrt12;
var
BOUND : integer = 100;
value1, value2, err : real;
function approximate(BND : integer) : real;
(* BND : 급수에서 합할 항의 개수 *)
(*
Using the series:
\frac{\pi}{\sqrt{12}} = \sum^\infty_{k=0} \frac{(-3)^{-k}}{2k+1}
*)
var
i : integer;
sum : real = 0;
x : real;
begin
x := 1;
sum := 1;
for i := 1 to BND do
begin
x := - (x / 3);
sum := sum + x/(2*i + 1);
end;
approximate := sum;
end;
begin
writeln( 'Approximate the value of PI/sqrt(12)' );
writeln( '-------------------------------------------' );
value1 := PI / SQRT(12.0);
writeln( ' Evaluated directly:', value1 );
value2 := approximate(BOUND);
writeln( 'Estimated by series:', value2 );
err := value2 - value1;
writeln( ' Error:', err );
end.
]]>
실행 결과:
Approximate the value of PI/sqrt(12)
-------------------------------------------
Evaluated directly: 9.06899682117109E-001
Estimated by series: 9.06899682117109E-001
Error: 2.22044604925031E-016