Nevertheless, it can be approximated arbitrarily closely by such rational numbers. These two approximations are the respective elementary options of each Pell's equation, to which extra solutions are algebraically associated. Newton's method for locating the foundation of an arbitrary operate. For a typical guess, the approximation converges quadratically (roughly doubles the number of appropriate digits at every step). 1 − φ . − φ ¯ n 5 . 1