# Use probability to approach Pi

Once I found this interview question: calculate Pi. Where, all of us have learned calculating Pi in our primary math class by using regular polygon to approach a circle.

Today I am gonna show you a probability way.

## Method

Check the following graph. I hope it is self-explainatory. ## Code

https://gist.github.com/xianminx/b59eef29b8137827f1f0#file-pi-java

class Pi{
public static void main(String[] args){
if(args.length < 1)
System.exit(0);

long iter = Long.parseLong(args);
double pi = calculate(iter);
System.out.println(String.format("after %d iterations, pi is %f", iter, pi ));
}

public static double calculate(long simNum){
long i =0L;
long count =0L;
while(i++<simNum){
double x = Math.random();
double y = Math.random();
double result = x*x+y*y;
if(result < 1.0D){
count++;
}
}
return 4.0D* count/simNum;
}

}



## Experiment

lucas@lucas-ubuntu:~/dev/workspace/pi$java Pi 1000 after 1000 iterations, pi is 3.032000 lucas@lucas-ubuntu:~/dev/workspace/pi$ java Pi 10000
after 10000 iterations, pi is 3.137200
lucas@lucas-ubuntu:~/dev/workspace/pi$java Pi 100000 after 100000 iterations, pi is 3.140240 lucas@lucas-ubuntu:~/dev/workspace/pi$ java Pi 1000000
after 1000000 iterations, pi is 3.144108
lucas@lucas-ubuntu:~/dev/workspace/pi$java Pi 10000000 after 10000000 iterations, pi is 3.141199 lucas@lucas-ubuntu:~/dev/workspace/pi$ java Pi 100000000
after 100000000 iterations, pi is 3.141486
lucas@lucas-ubuntu:~/dev/workspace/pi\$


## Conclusion

When iteration is set to 100,000,000, it takes about half a minute on my i7 Core Mac Pro with precision only to 3 digits.

• This algorithm is unacceptable.
• The precision cannot be guranteed as it is using a probabilistic way.