  This paper determines the minimal degree sequence for two compact rational
knots, namely the trefoil and figure-eight knots. We find explicit projections
with the minimal degree sequence of each knot. This is done by modifying a
non-compact rational minimal-degree parameterization of the trefoil and
figure-eight knots to make it compact. This research was conducted at Ramapo
College of New Jersey during the summer of 2011 with Dr. Donovan McFeron.
