double circle_pi(int rectangles)
{
/* creates and initializes the doubles the function will be using. */
  double width, awidth, radius = 2, height, x, area, tarea = 0;
  int i;
/* will run this algorithm until i is less than rectangles. */
  for (i = 0; i < rectangles; i++)
  {
    width = radius / rectangles; /* sets the width */
    awidth = width / 2; /* gets the mid point of the first width */
    x = awidth + (i * width); /* gets the midpoint of the rectangle in use */
    height = sqrt((radius * radius) - (x * x)); /* calculates the height */
    area = width * height; /* calculates the area of a single rectangle */
    tarea = area + tarea; /* adds the rectangle area to a total */
  }
  return tarea; /* returns the value of approximated pi */
}