  We give two proofs of a folkore result relating numerical semigroups of
embedding dimension two and binary cyclotomic polynomials and explore some
consequences. In particular, we give a more conceptual reproof of a result of
Hong et al. (2012) on gaps between the exponents of non-zero monomials in a
binary cyclotomic polynomial.
  The intent of the author with this expositional paper is to better unify the
various results within the cyclotomic polynomial and numerical semigroup
communities.
