/*
 *  Archimedes' calculation for the perimeter of the polygons inscribed in
 *   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 below.
 */

#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 r = 1.0;
  double s = sqrt(3.0);
  double k = 1.0;

  printf("%5s  %8s  %15s\n", "n", "pi_n'", "error (under)");
  printf("--------------------------------\n");

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

  _getch();
}