근사 공식
\frac{\pi}{\sqrt{12}} = \sum^\infty_{k=0} \frac{(-3)^{-k}}{2k+1}
을 이용하여 근사값 계산하는 프로그램을 Java 언어로 작성해 보았다.
<![CDATA[/*
* Filename: ApproximatePiOverSqrt12.java
*
* Compile: javac -d . ApproximatePiOverSqrt12.java
* Execute: java ApproximatePiOverSqrt12
*/
public class ApproximatePiOverSqrt12 {
/*
Using the series:
\frac{\pi}{\sqrt{12}} = \sum^\infty_{k=0} \frac{(-3)^{-k}}{2k+1}
BND : 급수에서 합할 항의 개수
*/
public static double approximate(int BND) {
int i;
double sum = 0;
double x;
x = 1;
sum = 1;
for (i = 1; i <= BND; i++) {
x = - (x / 3);
sum = sum + x/(2*i + 1);
}
return sum;
}
public static void main(String[] args) {
int BOUND = 100;
double value1, value2, err;
System.out.println( "Approximate the value of PI/sqrt(12)" );
System.out.println( "-------------------------------------------" );
value1 = Math.PI / Math.sqrt(12.0);
System.out.println( " Evaluated directly: " + value1 );
value2 = approximate(BOUND);
System.out.println( "Estimated by series: " + value2 );
err = value2 - value1;
System.out.println( " Error: " + err );
}
}
]]>
실행 결과:
Approximate the value of PI/sqrt(12)
-------------------------------------------
Evaluated directly: 0.9068996821171089
Estimated by series: 0.9068996821171091
Error: 2.220446049250313E-16
