Question

Can someone help me to solve it by Matlab?

Use the Boffon's Needle experiment to approximate pi on the following scenario. A dart is thrown at a square with sidelength 2. A circle is inscribe within the square. First deduce what the probability of the dart landing inside or on the edge of the circle is. Now write a Matlab script which approximates by simulating many dart throws. Run your script when n-10000, 100000, 1000000, 10000000, and 100000000 times, and show me your output. Also turn in your script, of course

Answer 1

`Hey,

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clc
clear all
close all
n=[4:8];
n=10.^n;
for i=1:length(n)
fprintf('For n=%d\n',n(i));
throws = n(i); % percent makes the rest of the line a comment
x=rand(1,throws)*2; % a vector of 10000 pseudorandom numbers
% in the range [0,2)
theta=rand(1,throws); % semicolon supresses printing
theta=0.5*pi*theta; % theta now 10000 random numbers between 0 and pi/2
hits= x<=sin(theta); % hits is a vector of 0's where false
% and 1's where true
sum(hits); % no semicolon prints the number of hits out of the 10000 throws
piEst=throws/sum(hits)
end

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