### φ calculated with Fibonacci

The Golden Ratio φ "phi" can be calculated with a recursive definition. It is the limit of the quotient of the fibonacci sequence (f_{n})

_{n∈N}defined by

_{0}= f

_{1}= 0, f

_{n}= f

_{n-1}+ f

_{n-2}for n≥2

_{n→∞}(f

_{n}/f

_{n-1})

φ = |

Which has at least 9000 digits of exact precision (in fact it's full precision). The sequence calculating it is converging to

_{n}= (φ

^{n}- ψ

^{n}) / √5, with