function area_sum = area_inside(radius, num_boxes)
%
% Calculate the area inside all boxes which fall inside the a circle
%   of the given radius.
%  
  box_length = (2.0*radius)/num_boxes;
  box_rad = box_length*0.5;
  box_area = box_length*box_length;

  area_sum = 0;
  for (xi = 1 : num_boxes)
    xc = -1 + box_rad + box_length*(xi - 1);
    
    for (yi = 1 : num_boxes)
      yc = -1 + box_rad + box_length*(yi - 1);
   
      % now, find the center of this box, and decide whether it lies
      %  inside a circle of radius 1 or not.  If it does, we add
      %  its area to the running total
      dist = sqrt((xc*xc) + (yc*yc));
      if (dist < radius)
        area_sum = area_sum + box_area;
      end

    end 
  end

% end of "area_inside" function

