approximating Pi

[xxlt3xx]

I'm having trouble I cant get it to output the correct value for pi and its driving me crazy what am I doing wrong?

The program is giving me the the final value for pi for all iterations. I think it is my loop. here's what I have so far

just in case this is a sample of the output I'm getting
-----------------------------------------------------------------------
1.pi = 3.339682540 // it should be 4.000000000
2.pi = 3.339682540 // 2.666666666
3.pi = 3.339682540 // 3.466666667
4.pi = 3.339682540 // 2.895238095
5.pi = 3.339682540 // 3.339682540

Final pi = pi = 3.39682540
-----------------------------------------------------------------------

#include <iostream>

#include <iomanip>

#include <cmath>

using namespace std;


//function to read inputs from the user test for proper input

int validInput (string prompt)

  {
      int yourResponse = 0;

      cin >> yourResponse;

      cout << endl;

    while (yourResponse < 1)

      {

          cout << "Error, cannot be 0 or negative, please try again" << endl;

          cin >> yourResponse;

          cout << endl;

      }

          return yourResponse;

  }

int main()

  {

        double pi = 0;

        int numTerms = 0;

        int yourResponse = 0;

        int steps = 0;

        string userInput = "Please enter the number of terms to use: ";

        string userOutput = "Display Pi after how many steps ? ";

 

        cout << "This program will approximate the value of PI " << endl << endl;

        cout << userInput;
 
        numTerms = validInput (userInput);
 
        cout <<endl;
 
        cout << userOutput;

        steps = validInput (userOutput);
        
        cout << endl;
 

        // Calculating pi here is where I think I messed up

        for (double n = 1; n <= numTerms; n++)
          {

             pi += (double) pow(-1, n+1)/(2*n-1);
                         
          }
            pi *= 4;
         
        cout << fixed << showpoint << setprecision(9);
                
        cout << "RESULTS: " << endl;

        for(int i = 1; i <= numTerms; i ++) //to display steps
           
            if(i % steps == 0) 

             {

              cout << i <<": " << "Pi = " << pi << endl << endl; 
             
             }

        cout << endl;   
        
         
                 
        cout << "Final Pi = " << pi << endl;


        cout << endl << endl;

        system ("PAUSE");

        return 0;
 
  }

[hamsterman]

pi = 4/1 - 4/3 + 4/5 - ...
for example 100th member of this formula is 4/199 = 0.02. That means that even after 100 calculations you only have two real numbers of pi (3.1) and a lot of rubbish. You are getting the wrong result of pi becouse your num_terms is too small.

You printing won't work. cout << i <<": " << "Pi = " << pi << endl << endl; This line prints pi many times. Simply move it into the for loop that calculates pi.

Lastly, You shouldn't be using pow for such a simple task as this. It's very slow. You can do this without it. pi += (n%2 == 0 ? -4 : +4)/(2*n-1);

[xxlt3xx]

I fixed the printing issue with cout << i <<": " << "Pi = " << pi << endl << endl;

however

 for (double n = 1; n <= numTerms; n++)
          {
             pi += (n%2 == 0 ? -4 : +4)/(2*n-1);// wont compile and gives the error
                                               // invalid operands of types `double' and `int' to binary `operator%' 
          }

             pi *= 4;        
         

[hamsterman]

oh. I didn't notice that n was a double... You cannot do the % operation with non integer values. Just make n int and it should work.

[xxlt3xx]

I couldn't get the it to output the correct values so I reworked my equation and I finally got it to work. Thanks for all your help.