  It is known that there are infinitely many exceptional sequences of quiver
representations for Euclidean quivers. In this paper we study those of type
$\tilde{\mathbb{A}}_n$ and classify them into finitely many parametrized
families. We first give a bijection between exceptional collections and a
combinatorial object known as strand diagrams. We will then realize these
strand diagrams as chord diagrams and then arc diagrams on an annulus. Using
arc diagrams, we will define parametrized families of exceptional collections
and use arc diagrams to show that there are finitely many such families. We
moreover show that these families of exceptional collections are in bijection
with equivalence classes of small arc diagrams. Finally, we provide an
algebraic explanation of parametrized families using the transjective component
of the bounded derived category.
