William W. Reith
Honors in Mathematics: Creating Knots with Arcs
A great deal of research has focused on the least number of line segments required to create knots, called the stick number. My research extends this notion to finding the fewest number of hyperbolas and ellipses required to create knots, called the arc number. My research describes a method of creating arc diagrams from stick diagrams and places an upper bound on the number of arcs needed to create a knot, given its stick number. An upper bound for the arc number of the connect sum of two knots is given, as well as a proof that the arc number of a knot equals three if and only if the knot is the trefoil.