Continued Fraction Expansion of Golden Mean/Rate of Convergence

Theorem
Consider the continued fraction expansion to the golden mean:
 * $\phi = \left[{1, 1, 1, 1, \ldots}\right] = 1 + \cfrac 1 {1 + \cfrac 1 {1 + \cfrac 1 {\ddots}}}$

This continued fraction expansion has the slowest rate of convergence of all continued fractions.