PI Approximation not approximating right

Question

i just started on C++ and i tried to convert my working PI approximation JS code to C++ But when compiling my C++ it doesn't approximate correctly...

I think it's because i'm not using double variables at the right way.

Here's my code:

#include <iostream>

using namespace std;

double four = 4, pi = 4, num = 1;
bool lever = false;

int calcpi() {
        while (true) {
            num = num +2;
            if (lever) {
                lever = false;
                pi = (four/num) - pi;
            } else if(lever == false){
                lever = true;
                pi = (four/num) + pi;
            }
            cout << pi <<"\n";
        }   
}
    
int main(){
    calcpi();
}

Answer 1

It looks like you're implementing the approximation

π = 4 – 4/3 + 4/5 – 4/7 + 4/9 – …

In that case, the line pi = (four/num) - pi; is backwards. It should be pi = pi - (four/num);, which represents the subtraction terms.

Also, subtraction from the initial value of 4 should be the first operation, so the lever flag should be initialized to true.

Here's the modified version that I got working after a little bit of troubleshooting.

void calcpi() {
    double pi = 4.0, num = 1.0;
    bool lever = true;

    for (int i = 0; i < 1000; i++) {
        num = num + 2.0;
        if (lever) {
            lever = false;
            pi = pi - (4.0 / num);
        }
        else {
            lever = true;
            pi = pi + (4.0 / num);
        }
        std::cout << pi << std::endl;
    }
}

This does give a slowly converging approximation of Pi.