monte_carlo.m

%the value of ? can be approximated using a Monte Carlo method

%Draw a square of area 1 on the ground, then inscribe a circle within it.
%Now, scatter some small objects (for example, grains of rice or sand) throughout the square.
%If the objects are scattered uniformly, then the proportion of objects within the circle vs objects within the square should be approximately ?/4,
%which is the ratio of the circle's area to the square's area. 
%Thus, if we count the number of objects in the circle, multiply by four, 
%and divide by the number of objects in the square, we get an approximation to pi.

n = input('n :');

A = rand(1,n);
        
B = rand(1,n);

C = A.^2 + B.^2  ; 

 e=find(C<1);
 
 p = numel(e);

 PI = 4.*(p./n)

  
plot(A,B,'.');

hold on
axis([-1 1 -1 1])
theta = 0:.1:2.*pi;

X = cos(theta);
Y = sin(theta);
plot(X,Y,'y')

pi=pi

disp('the relative deviation ')

dev = (sqrt((PI - pi).^2)/pi).*100