% Two Chips and the Unit Circle [#10.33]
% The big circle has radius 1.
% If we generate x1 in [-1,1) and y1 in [-1, 1),
% we will determine if (x1,y1) is in the big circle.
% Similarly, we generate (x2,y2) and check.
% If both centers are in the big circle, then how do we determine if the
% two chips overlap?
% 
% Initialize the overlap counter.
overlap = 0;
% You can change this value for the radius!
% Note that MATLAB is case sensitive.  Use upper case for "R".
R = 0.5;
% It turns out that we need the diameter squared!
DiamSq = (2*R)^2;
for i=1:1000
    % Initialize x1 & y1 to stupid values.
    x1 = 10;
    y1 = 10;
    % Generate the random variates and test.
    while (x1^2 + y1^2 > 1)
        x1 = 2.*rand - 1.;
        y1 = 2.*rand - 1.;
    end;
    % Do the same for x2 & y2.
    x2 = 10;
    y2 = 10;
    while (x2^2 + y2^2 > 1)
        x2 = 2.*rand - 1.;
        y2 = 2.*rand - 1.;
    end;
    % Now both centers are in the big circle.
    % Write an appropriate test (if) and increment
    % the overlap counter.
    % HERE!
    % Use the constant DiamSq.  This will speed up the program.
end;
% Divide by the total number of attempts.
fprintf('The fraction overlapping is %6.4f.\n',overlap/1000.);