pi

#define _USE_MATH_DEFINES
#include <cmath>
#include <iostream>
#include <time.h>

using namespace std;

//quadratic simplifier

long double quadP(long double& a, long double& b, long double& c){

    cout << "Numerator:    " << -b - sqrt(b*b - 4*a*c) << endl;
    cout << "Denominator:  " << 2*a << endl;



    return (-b - sqrt(b*b - 4*a*c))/(2*a);

}

//compute pi
int main(){
long runt = time(NULL);
long double A, B, C,  sides;

//iterations
long long i = pow(10, 3);

//S(n) n=3
long double S = 2;

for (int n = 2; n < i; n++){
    //"animation"
        system("cls");
        cout << n << endl;
        cout << i << endl;

    //sides
    sides = pow(2, n);

    //Parameters
    A = 2 + 2 * cos(M_PI * (sides - 2) / sides);
    B = -4*S;
    C = S*S;

    cout<< "A: " << A << endl;
    cout<< "B: " << B << endl;
    cout<< "C: " << C << endl;

    cout<<"Descriminant: " << sqrt(B*B - 4*A*C)<<endl;

    A = quadP(A, B, C);

    cout<<"Quad Out:     " << A << endl;

    S = S - 2*A;

    cout<< "Sides:            " << sides*2<< endl;
    cout<< "Side Length =     " << S <<endl;
    cout<< "N-gon perimeter = " << S*sides*2;

    cin.ignore();

    }

cout << "\n" << S << "\n" << "Runtime: " << time(NULL) - runt << "sec";

cin.ignore();

return 0;
}