"Repetition and Self-Similarity in Modern Poetics" offers some notes toward a rethinking of patterns which occur in thought about mathematics and poetics. Repetitions come in an overwhelming number of forms. Because mathematics has no real semantics until we bring it to specific applications, there are no obvious parallels until we enter the realm of syntactics or the structures of linguistic and mathematical forms. Here repetitions are obvious but analogies very difficult to hold together. The paper invites working mathematicians and physicists to think of standard analytical tools brought to both simple and complex poetic forms. Specifically rhyme, consonance and assonance, and rhythm through the use of patterns of accents are examined. Rhyme and rhythm are fundamental tools in our understanding of the way a poem works. Any effort to work with parallels between math and language will do well to consider rhythm and rhyme in poetic forms as evidence of iterative and self-similar features.