/*
 * Calculate pi as the limit of a perimeter of a regular polygon
 * inscribed in a unit circle as the number of polygon's sides grows
 * doubling at each iteration.
 */

#include <stdio.h>
#include <math.h>

#define N 28

int main (void)
{
    int i;
    long n;
    double s, piapprox;

    i = 0;
    n = 4;            // initial number of sides in a polygon
    s = 1./sqrt(2.);  // sin(pi/4)
    piapprox = n*s;
    printf("%3d   %10ld   %.14f    % .14f    % .14f\n",
           i, n, s, piapprox, M_PI-piapprox);

    for(i = 1; i < N; i++)
    {
        n *= 2;       // double the number of sides
        /*
         * calculate sin of half-angle given the sin on an angle
         */
        s = sqrt((1. - sqrt(1. - s*s))/2.);   // sin(pi/n)
        piapprox = n*s;
        printf("%3d   %10ld   %.14f    % .14f    % .14f\n",
               i, n, s, piapprox, M_PI-piapprox);
    }

    return 0;
}