Tighten Up: A Preliminary Study of Knots

Louisa G. Catalano

2011

Knots are a common occurrence in everyday life, so common, in fact, that they are often taken for granted. Knots are able to make one string out of two, without any adhesive, simply by entangling the strings' ends in a certain way. Some weaker knots may slip, but strong knots will outlast the string, forcing the string to break before the knot slips. This thesis outlines the initial steps in creating a solid basis for studying knots, both mathematical and physical. The basics of the mathematical field of knot theory are explored. Two preliminary simulations modeling the motion of knots slipping are discussed; the first simulation uses Newtonian mechanics to describe the motion of the strings, while the second uses Lagrangian mechanics. Exploratory experiments studying the behavior of a knot tied with two pieces of perciatelli pasta are also examined. This study lays the groundwork for further research into the properties and benefits of mathematical and physical knots.