Rectifiable curves in Sierpinski carpets Estibalitz Durand-CartagenaJeremy Tyson 28A8030L9911B57fractalrectifiable curveFarey fraction We characterize the slopes of nontrivial line segments contained in self-similar and non-self-similar Sierpi\'nski carpets. The set of slopes is related to Farey sequences and the dynamics of punctured square toral billiards. Our results provide a first step towards a description of the rectifiable curves contained in such carpets. Indiana University Mathematics Journal 2011 text pdf 10.1512/iumj.2011.60.4382 10.1512/iumj.2011.60.4382 en Indiana Univ. Math. J. 60 (2011) 285 - 310 state-of-the-art mathematics http://iumj.org/access/