Question

Determining t Experimentally Recall that π is the ratio of a circle's circumference to its diameter and that we can calculate the area of a circle with the formula A-r Below is a circle enscribed within the unit square What is the ratio of the areas of the enscribed circle to that of the unit square? If we pick a random point within the unit square what is the probability that the point will also lie within the circle? If we repeat this experiment an arbitrarily large number of times the ratio of the number of points which lie within the circle to the number of points within the unit square (all of them) will approach π4 Using the language structures we have discussed write a program that will do the above experiment an arbitary (determined at run-time) number of times and report back the approximate value of u.

CODE IN JAVA PLEASE MAKE SURE IT 'LL COMPILE AND RUN

Answer 1

Hey,

Below is the code to your question

import java.util.Scanner;

import java.util.Random;

public class PI

{

public static int checkPoint(double x,double y)

{

if(x*x+y*y<=1)

return 1;

return 0;

}

public static void main(String[] args)

{

int counts=0;

Random rand = new Random();

Scanner sc = new Scanner(System.in);

System.out.println("Enter number of times: ");

int n=sc.nextInt();

for(int i=0;i<n;i++)

{

double x = 2.0*rand.nextDouble()-1.0;

double y = 2.0*rand.nextDouble()-1.0;

if(checkPoint(x,y)==1)

{

counts++;

}

}

double Pi=4.0*(double)counts/(double)n;

System.out.printf("The vlue of PI is estimated as %.4f\n",Pi);

}

}

1000 Copy RunRun+URL (Generates URL as well) Time(sec): 0.12 Memory (MB) : 56.2617 Output: Copy Enter number of times: The vlue of PI is estimated as 3.1240

Kindly revert for any queries

Thanks.