  Algebraic geometry has many connections with physics: string theory,
enumerative geometry, and mirror symmetry, among others. In particular, within
the topological study of algebraic varieties physicists focus on aspects
involving symmetry and non-commutativity. In this paper, we study a family of
classical algebraic curves, the hypocycloids, which have links to physics via
the bifurcation theory. The topology of some of these curves plays an important
role in string theory and also appears in Zariski's foundational. We compute
the fundamental groups of some of these curves and show that they are in fact
Artin groups.
