A Method to approximate Pi

This method is called Monte carlo simulation  it is a class of computer algorithm that aggregates data from a random sampling then uses laws of probability to find out some meaningful result  from the Data.

The basic idea is simple 

1-Draw a semicircle with radius r=1.00

2-And make a square of side 1 units coinciding with the circle .

3-Now randomly (uniformly ) throw some darts onto this arrangement .

4-Finally count the number of darts inside the circle(Nin) and total no of darts thrown (Ntot)

  now we know from the laws of probability that  P(Nin) = area of circular region divided by total  area of  the square , which comes to be Pi/4=Nin/Ntot

 hence Pi can be calculated by Pi = 4*(Nin/Ntot)

How do we implement this in a program ?

1 -Assume 2 axes x & y of 1000 units each .

2- Make a circle with origin as the center . and a square as shown earlier 

3- Define two variables x and y :

                  and call for a random value between 0 and 1000 for both of them separately (x,y)

4- Find the distance of this point from the origin if this distance is less than 1000 then the point is inside the circle.

5-Count the numbers of inside throws and divide by Total no of throws which was 1000 here multiply this by 4 for the value of PI π

#include<stdio.h> #include<stdlib.h> #include<math.h> int main(void) { int throws,cntin=0; scanf("%d",&throws); int temp=throws; while(throws--) { int a=rand()%1000; int b=rand()%1000; int c=(int)(sqrt(a*a+b*b)); if(c<1000) cntin++; } float ans=((4.000*cntin)/temp); printf("%0.02f \n",ans); }

or download code from here

But Its more interesting like this , if you like code golfing  

#include<namit.h>
#include <stdio.h>
main()
{
    long int d = 1;
    double p = 1;
    for(;;){printf("%.20f\n",(p+=((d-1)%4)?(1.0/(d+=2)):-1.0/(d+=2))*4);}