import java.io.PrintStream;
import java.util.Scanner;
import type.lib.Fraction;

public class ApproxPi
{
   public static void main(String[] args)
   {
      PrintStream output = System.out;
      Scanner input = new Scanner(System.in);
      
      final int MAX_TERMS = 20;
      output.print("How many terms do you want to sum? ");
      int numTerms;
      for (numTerms = input.nextInt();
           numTerms < 0 || numTerms > MAX_TERMS;
           numTerms = input.nextInt())
      {
         output.print("Number of terms must be from 0-20... try again: ");
      }
      
      Fraction sum = new Fraction();
      for (int i = 1; i <= numTerms; i++)
      {
         int denom = i * 2 - 1;
         if (i % 2 == 0)
         {
            denom = -denom;
         }
         Fraction f = new Fraction(1, denom);
         sum.add(f);
      }
      sum.multiply(new Fraction(4, 1));
      double pi = (double) sum.getNumerator() / sum.getDenominator();
      
      output.println("The approximate value of pi is");
      output.print(sum);
      output.print(" = ");
      output.println(pi);
      output.println("The value of Math.PI is ");
      output.println(Math.PI);
   }
}