/* 
 * Program to approximate pi using numerical integration.
 */ 
#include <stdio.h>

double estimate_pi(long slices);

int main(void) {
	long slices;
	printf("enter number of slices:\n"); 
	if ((scanf("%ld", &slices) != 1) || (slices <= 0)) {
		printf("not a positive number\n");
		return 1;
	}
	double pi = estimate_pi(slices);
	/* .15f says print 15 digits after decimal point -- default is less */
	printf("for %ld slices, estimated pi = %.15f\n", slices, pi);
	return 0;
}	

double estimate_pi(long slices) {
	double sum_of_heights = 0.0;
	double width_of_slice = 1.0/slices;
	for (long i = 0; i < slices; ++i) {
		/* height = 4/(1+x*x) at the midpoint */
		double midpoint = (i + 0.5)*width_of_slice;
		sum_of_heights += 4/(1 + midpoint*midpoint);
	}
	double pi = sum_of_heights * width_of_slice;
	return pi;
}