import java.util.Random;
import java.util.Scanner;

public class Lab10 {
    public static void main(String[] args) {
        System.out.println(estimatePi(100000));
    }

    /**
     * Estimates the value of pi using a classical algorithm.  The algorithm
     * is a summation of n terms that is multiplied by the square root of 12.
     * The summation is from i=0 to n of (-1)^i * 1/((ith odd number) * 3^i)
     * <p>
     * For example, the summation using 3 terms is:
     * <p>
     * 1 - 1/(3*3) + 1/(5*3^2)
     *
     * @param n the number of terms to use in the summation
     */
    public static double estimatePi(int n) {
        double sum = 0;
        int pow3 = 1;
        for (int i = 0; i < n; i++, pow3 *= 3) {
            double t = 1 / ((2*i + 1) * pow3);
            if (i % 2 == 0) {
                sum += t;
            } else {
                sum -= t;
            }
        }
        return sum * Math.sqrt(12);
    }
}