CONSTRUCTION OF POLYGONS BY TYING KNOTS WITH RIBBONS
By Laurie DeMaranville
Fall 1999
This thesis explores construction of regular polygons by tying torus knots with
ribbons. A model is developed that starts with a particular knot diagram of a torus knot,
converts that diagram to a straight-line knots diagram and then widens the straight-line
diagram into a ribbon.
Predictions can be made regarding the polygons that can be constructed. The
torus knots are broken into different classes—some yield polygons, others do not and
some appear to form polygons, but it is not proven. Conclusions are primarily based
upon the relationship between the number of longitudinal and meridional cycles of the
torus knot, the arrangements of the crossings of the knot diagram, and the direction of the
fold of the ribbon. A pentagon and all regular polygons with seven or more sides can be
formed by tying specific torus knots with ribbons.