It is proposed to caluculate pi by using the Monte Carlo method. A circle of radius 1 is inside a square of side 2. We count how many of m random points in the square happen to lie in the circle. Assume that the error is 1/square root m. How many points must be taken to obtain pi with three accurate figures? Write a program to find the answer. Solution /* Program to compute Pi using Monte Carlo methods */ #include <stdlib.h> #include <stdio.h> #include <math.h> #include <string.h> #define SEED 35791246 main(int argc, char* argv) { int niter=0; double x,y; int i,count=0; /* # of points in the 1st quadrant of unit circle */ double z; double pi; printf(\"Enter the number of iterations used to estimate pi: \"); scanf(\"%d\",&niter); /* initialize random numbers */ srand(SEED); count=0; for ( i=0; i<niter; i++) { x = (double)rand()/RAND_MAX; y = (double)rand()/RAND_MAX; z = x*x+y*y; if (z<=1) count++; } pi=(double)count/niter*4; printf(\"# of trials= %d , estimate of pi is %g \ \",niter,pi); } .

1. It is proposed to caluculate pi by using the Monte Carlo method. A circle of radius 1 is inside a
square of side 2. We count how many of m random points in the square happen to lie in the
circle. Assume that the error is 1/square root m. How many points must be taken to obtain pi
with three accurate figures? Write a program to find the answer.
Solution
/* Program to compute Pi using Monte Carlo methods */
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <string.h>
#define SEED 35791246
main(int argc, char* argv)
{
int niter=0;
double x,y;
int i,count=0; /* # of points in the 1st quadrant of unit circle */
double z;
double pi;
printf("Enter the number of iterations used to estimate pi: ");
scanf("%d",&niter);
/* initialize random numbers */
srand(SEED);
count=0;
for ( i=0; i<niter; i++) {
x = (double)rand()/RAND_MAX;
y = (double)rand()/RAND_MAX;
z = x*x+y*y;
if (z<=1) count++;
}
pi=(double)count/niter*4;

2. printf("# of trials= %d , estimate of pi is %g ",niter,pi);
}