//**************************************
//     
// Name: Precise Calculation of Pi
// Description:This code calculates an e
//     stimated value of Pi using the Leibnitz 
//     series (which is basically a power serie
//     s expansion of a trigonometric function 
//     which allows to estimate Pi very well)
// By: Eli
//
// Inputs:n/a
//
// Returns:Prints the estimated value of
//     Pi
//
// Assumes:n/a
//
// Side Effects:n/a
//
//This code is copyrighted and has// limited warranties.Please see http://
//     www.Planet-Source-Code.com/xq/ASP/txtCod
//     eId.360/lngWId.3/qx/vb/scripts/ShowCode.
//     htm//for details.//**************************************
//     

#include <iostream.h>
#include <math.h>
#define NUM_OF_ELEMENTS 20000
int main()
    {
    double pi = 0;
    // Calculating pi/4
    for (long int n = 1; n <= NUM_OF_ELEMENTS; n++)
        {
        pi += (double) pow(-1, n+1)/(2*n-1);
    }

    // Calculating pi
    pi *= 4;
    cout << "Estimated PI value (" << NUM_OF_ELEMENTS << " elements of Leibnitz series): "<< pi;
    return 0;
}