//File:   pi
//Author: Jesse D
//Date:   Feb. 12, 2007
//
//Description: This program uses a loop to estimate pi to the hundreth place.
//             The first time pi reaches 3.14, the number of iterations
//             it took to reach this value is printed to the screen.
//             On each iteration through the loop, the pi estimate is multiplied 
//             by 100. This value is is then rounded down. If the value of this 
//             variable is 314 then we know that the estimate is between 3.14 and
//             and 3.15 not inlcuding 3.15.

#include <iostream>
#include <cmath>
using namespace std;

int main()
{ 
    double pi_Estimate = 0;   //Holds the value of Pi
    double n = 0;             //Increment for the loop.      
    double pi_Temp;           
    
    while (!(pi_Temp == 314)) //Jumps out when pi first becomes 3.14
    {
      //Increment the estimate by the next term .
      pi_Estimate += ((pow(-1, n)*4))/((2*n)+1);                                                
      pi_Temp = pi_Estimate*100; //Convert the decimal part as required.
      pi_Temp = floor(pi_Temp); //Round down.
      n+=1;

    
    }
    // Output the result.
    cout << endl;
    cout << "The value for Pi first reaches 3.14 on the " << n << "th iteration" <<< endl;
    return 0;
}