Inserted: 26 mar 2010
Last Updated: 23 feb 2018
Journal: Indiana Univ. Math. J.
We characterize the slopes of nontrivial line segments contained in self-similar Sierpinski 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.