In the book **Neverending fractions** from Borwein, van der Poorten, Shallit and Zudilin, there is the so called **distance formula** (Theorem 2.45, p. 43) stated:
$$\alpha_1\alpha_2\cdot...\cdot\alpha_n=\frac{(-1)^n}{p_{n-1}-q_{n-1}\alpha}$$

for $n\geq 0$ with $p_{-1}=1$ and $q_{-1}=0$, where $$\alpha=[a_0;a_1,...,a_{j-1},\alpha_j]$$ ($\alpha_j$ being the tail of the continued fraction development of $\alpha$) and, as usual, $$\frac{p_n}{q_n}=[a_0;a_1,...,a_{n}]$$

In the book, the authors explain the name with

It turns out that one may usefully think of $\left|\log(\left|p_{n-1}-q_{n-1}\alpha\right|)\right|$ as measuring the weighted distance that the continued fraction has traversed in moving from $\alpha$ to $\alpha_n$

My questions are:

- Does this distance formula only hold for
*quadratic*irrationals? - Where can I find additional literature / information on this formula? (I couldn't find any other references for it so far)