Write a Matlab function that uses the Monte Carlo approach to approximating "pi" using the relative areas of a square and an inscribed circle. I have code but I am not sure how to change it to monte carlo
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r = 1; % the circle radius
nodp = 1:5; % Number of Decimal Places (NODP) for Pi
i=1; % Counter for number of decimal places
estimates = zeros(1,5); % Estimation for each NODP
steps = zeros(1,5); % Number of steps for each Pi estimation
while i<= length(nodp)
n=0; % No. of points in unit circle
N = 0; % No. of Steps counter/ Points in unit square
flag =0; % Flag for exit condition
while flag == 0
%Generating random points inside unit square
x = rand();
y = rand();
if ((x^2+y^2)<=r^2)
n = n+1; % Successful event for estimating Pi
end
N = N + 1;
estimate = (4*n)/(N);
% Setting appropriate floating point length to store estimate
estimaten = vpa(estimate);
% Counting number of decimal places
d=0;
while (floor(estimaten*10^d)~=estimaten*10^d)
d=d+1;
end
if d == nodp(i) % Required decimal precision achieved
flag = 1; % exit condition set TRUE
estimates(i) = vpa(estimaten); % storing estimate
steps(i) = N; % storing steps
i = i+1; % Next NODP
end
end
end
estimates = estimates.';
nodp = nodp.';
steps = steps.';
format long g
estimates;
T = table(nodp, estimates, steps);
T
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