/*
 *  Archimedes' calculation for the perimeter of the polygons circumscribing
 *   a circle, polygons with 6, 12, 24, 48, 96 ... sides (Archimedes goes up
 *   to 96). Assuming a circle of radius 1, this approximates pi from above.
 */

#include "stdio.h"
#include "conio.h"
#include "math.h"

#define M_PI 3.14159265358979323846
#define K 14
// LIM = 6 * 2^K = 6, 12, 24, 48, ...
#define LIM 6 * (1 << K)

void main(int argc, char* argv[])
{
  int n = 0;
  double p = sqrt(3.0) / 3;
  double q = 2 * p;

  printf("%5s  %7s  %16s\n", "n", "pi_n", "error (over)");
  printf("-------------------------------\n");

  for (n = 6;  n <= LIM; n *= 2)
  {
    double perim_out = n * p;
    double error = perim_out - M_PI;
    printf("%5d  %1.9f  %1.9f\n", n, perim_out, error);
    // Next p and q (for 2n).
    p = p / (q + 1);
    q = sqrt(p * p + 1);
  }

  _getch();
}