Large-scale data sets of Internet measurements are commonly used by researchers and operators for investigating Internet performance or for tackling network issues. Looking at sequences of traceroutes in such data sets it is common to observe paths that change over time. We are interested in verifying if there are periodic phenomena affecting such path changes and, if yes, in determining if they depend on artifacts of the used data set or on topology changes of the network. For this purpose we devise a novel algorithm for detecting periodicities in sequences of traceroutes. Then, we exploit the algorithm for analyzing the traceroutes produced by RIPE Atlas, a popular public measurement platform. We study and report the features of the found periodicities and some of their causes. We found that: (i) a surprisingly large percentage of the traceroutes exhibit a periodic behaviour, (ii) a large amount of periodicities depend on the RIPE Atlas platform itself, and (iii) a smaller amount is related to MPLS and load balancing.