  In this paper we deal with the task of uniformly approximating an
$L$-biLipschitz curve by means of piecewise linear ones. This is rather simple
if one is satisfied to have approximating functions which are $L'$-biLipschitz,
for instance this was already done with $L'= 4L$ in [Daneri-Pratelli, Lemma
5.5]. The main result of this paper is to do the same with $L'=L+ \varepsilon$
(which is of course the best possible result); in the end, we generalize the
result to the case of closed curves.
