5. The USF math department has forgotten the value of pi and they want you to ca

Question

5. The USF math department has forgotten the value of pi and they want you to calculate it for them. Assume you have a quarter circle inside a square with sides of 1x1 unit. Then the radius of the circle is 1. The area of a circle is Pir^2. If r = 1, the area is re and the area of a quarter circle is Pi/4. Use a for loop beginning at 1 and ending at a number input from the keyboard to add random points in the square (use the MATLAB function rand() to get the points). If a point lands inside the circle, it is a hit else it is a miss. The approximate area of the circle is the (hits)/(total points).

Explanation / Answer

clear all
close all
ndarts=input('please enter the number ' );
for i=1:ndarts
xcoord(i)=rand-0.5;
ycoord(i)=rand-0.5;
end
distancesq=xcoord.^2+ycoord.^2;
nhits=0;
for i=1:ndarts
if distancesq(i)<=0.25
nhits=nhits+1;
end
end
estimate=4*nhits/ndarts

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