#include <iostream>
#include <iomanip>

using namespace std;

// first version, just print the first N things from the fibonacci sequence
// use doubles because the numbers git big very quickly

void fibseq1(int N) // number of numbers to be printed
{ double curr = 1;
  double prev = 1;
  while (N > 0)
  { const double next = prev + curr;
    cout << prev << "\n";
    prev = curr;
    curr = next;
    N -= 1; }
  cout << "All done\n"; }

// second version, look at the ratios between successive numbers

void fibseq2(int N)
{ double curr = 1;
  double prev = 1;
  while (N > 0)
  { const double next = prev + curr;
    const double ratio = curr / prev;
    cout << prev << "  " << ratio << "\n";
    prev = curr;
    curr = next;
    N -= 1; }
  cout << "All done\n"; }

// third experiment: the number 5 magically appears

void fibseq(int N)
{ double curr = 1;
  double prev = 1;
  while (N > 0)
  { const double next = prev+curr;
    const double ratio = curr/prev;
    const double x = ratio * 2 - 1;
    const double xsq = x * x;
    cout << prev << " " << curr << " " << setprecision(17)  << xsq << "\n";
    prev = curr;
    curr = next;
    N -= 1; }
  cout << "All done\n"; }

int main()
{ fibseq(1000); }