  We show that in any triangulation of a solid torus, there is a pre-core curve
that lies in the 2-skeleton and that intersects the interior of each face in at
most 10 straight arcs. By definition, a pre-core curve is a simple closed curve
that becomes a core curve when a collar is attached to the boundary of the
solid torus. This theorem imposes restrictions on the possible Riemannian
metrics on a solid torus. It also has applications in knot theory.
