write a code in matlab to calculate the value of Pi by estim

write a code in matlab to calculate the value of Pi by estimating the area of a 2x2 square and the inscribing circle of radius 1. (e.g. randomly throwing pebbles into a 2x2 square, and calcuate the pebble counts inside and outside the circle)

Solution

If the side of square 2*2 and Radius is r value=1,So Area of circle if pi*r*2 and area of square =(2r)^2

Ratio of area of circle and square is pi/4

If we pick n points at random inside the square then N*pi/4 of those points should fall inside the circle.

So we have to check inside the circle x^2+y^2<r^2 ,where x and y are the coordinates of points and r is radius.

So pi is then approximately

Pi=4*M(How many points picked so far)/N(How many of those points fell inside the circle )

fprintf(“Approximate Value Of PI”);

% initialize value for loop

Count_inside=0;

Count=0;

d=0;

While count<10000

d=sqrt(rand^2+rand^2)

if(d<1)

count_inside+=1;

count+=1;

end

x=4.0*count_inside/count;

fprintf(“Approximate Value is %.15g”,x);