PI Calculation

01.  

     

Using this series calculate the value of π

#include <iostream>

#include<cmath>

using namespace std;

int main() {

int k ;

double val=0.0 , nval;

for(k=1;k<=1000000;k++)

{

val=val+ ( powf(-1,k+1)/(2*k-1) );

}

nval=4*val;

printf( "Approximate PI=%14.12lf\n ", nval );

printf( "Built in PI=%14.12lf\n ", M_PI );   

return 0;

}


02.  Here is the another way of calculating the value of  π.

#include<iostream>
#include<cmath>

using namespace std;

double val(int n){

       int i;

       double fal,kal;

       fal=6+powf(n+2,2);

       for( i=n; i>=1; i-=2 )  {

       kal = powf(i,2) / fal;

       fal = 6+kal;

       }

return kal;

}

int main(){

 double nval;

 nval = 3+val(177);               // here odd number value is needed

printf(" The approximate Pi is =%14.12lf \n", nval);

printf("Difference =%14.12lf \n", fabs(nval-M_PI) );

      

return 0;

}

3.0  Here is the another way of calculating the value of  π.

#include<iostream>

#include<cmath>

using namespace std;

double val ( int n ) {

       int i;

       double  fal , kal ;

       fal=2+ powf( n+2 , 2);

       for( i=n; i>=1; i-=2 ) {

       kal = powf(i,2)/fal;

       fal = 2+kal;  

   }

return kal;

}

int main() {

    double nval , pival;

    nval=1+val(1117);                // here odd number value is needed

    pival=4/nval;

printf("The approximate Pi is =%14.12lf \n",pival);

printf("Difference =%14.12lf \n",fabs(pival-M_PI));   

    

 return 0; 

  }

4.0  Here is the another way of calculating the value of  π.  It has the highest convergence among the other..

#include<iostream>

#include<cmath>

using namespace std;

double val( int n ) {          // it has the highest convergence

       int i;

       double fal , kal;

       fal = (2*n-1) + powf (n, 2);

       for( i=n-1; i>=1; i--)  

       {

       kal = powf(i,2) / fal;

       fal= (2*i-1) + kal;    

       }

return kal;

}

int main() {

    double nval,pival;

    nval=1+val(115);          // a integer number is needed

    pival = 4/nval;

printf("The approximate Pi is =%14.12lf \n",pival);

printf("Difference =%14.12lf \n",fabs(pival-M_PI));   

   

return 0; 

}