/*
   Name: Pi Calculator Beta, via integration of y=1/((a^2)*(x^2)).
   Author: Shamashis Sengupta.
   Description: This program approximates pi.
   Date: Monday, June 16, 2003.
   Copyright: This program is distributed under the GNU General Public License.

Details: If y=1/((a^2)*(x^2)), then integral (y)dx=arctan(x/a)+c,
where 'a' is a constant and 'c' is the integration constant.

When the y vs. x curve is drawn, the area under the curve from x=0 to x=a is
[arctan(a/a)-arctan(0/a)]=pi/4. In this program, the area under the above
mentioned curve from x=0 to x=a is calculated by dividing the area into a
number of thin strips. The width of each strip along the x-axis is unity.
The value of 'a' should be input by the user. The sum of the area of all the
strips is multiplied by 4 to calculate the approximate value of pi.

*/

#include<stdio.h>

int main()
{
    double keeptrack=1.0,a,pi,x,dx,y,sum=0.0,split;
	printf("Enter the upper limit 'a'.\n");
	scanf("%lf",&a);
	dx=1.0;
	split=a/100.0;
	for(x=dx;x<=a-dx;x=x+dx)
	{
		y=1/((a*a)+(x*x));
		sum=sum+(y*dx);
		if(x>=keeptrack*split)
		{
			printf("\n%.0lf of 100 completed.",keeptrack);
			keeptrack++;
		}
	}
	sum=sum+((((1.0/(a*a))+(1/(2*a*a)))/2.0)*dx);
	pi=4.0*sum*a;
	printf("\nPi=%.15lf",pi);
	return(0);
}