Continued Fraction Expansion of Golden Mean/Rate of Convergence

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

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