It is known, that $\phi := \frac{sqrt(5)-1}{2}$, is the number, that is hardest to approximate by rationals (cf e.g. the section **properties of the golden ratio $\phi$** here: http://en.wikipedia.org/wiki/Continued_fraction#A_property_of_the_golden_ratio_.CF.86).

In the section **Infinite continued fractions** on the same WIKI page, one finds the following "explanation" of how the terms of an infinite continued fraction relate to its "degree of irrationality":

The larger a term is in the continued fraction, the closer the corresponding convergent is to the irrational number being approximated. Numbers like π have occasional large terms in their continued fraction, which makes them easy to approximate with rational numbers. Other numbers like e have only small terms early in their continued fraction, which makes them more difficult to approximate rationally. The golden ratio ϕ has terms equal to 1 everywhere—the smallest values possible—which makes ϕ the most difficult number to approximate rationally. In this sense, therefore, it is the "most irrational" of all irrational numbers

That explanation is somewhat fuzzy: "small terms in the beginning" and "occasionally large terms" are not mutually exclusive; so that explanation can't be used for sorting continued fractions according to decreasing irrationality in the sense of rational approximability.

Question:is it possible to compare the degree of irrationality of infinite (periodic) continued fractions on basis of their terms?

Any suggestions or pointers to the literature would be great.