CURE: Interdisciplinary Undergraduate Research: Knot the Usual Suspects: Finding the Diagrammatic Representations of Physical Knots

Knot the Usual Suspects: Finding the Diagrammatic Representations of Physical Knots

CURE: Interdisciplinary Undergraduate Research: Knot the Usual Suspects: Finding the Diagrammatic Representations of Physical Knots

Student Presenters

Silas Rickards, Teertho Bhattacharya, Grace Cheng, Joshua Valan, Zachary Webb

Faculty Mentor

Dr. Anne Donnelly

College

Center for Undergraduate Research

Abstract

In the last few hundred years, mathematicians have been attempting to describe the topological and algebraic properties of mathematical knots. Regarding the study of knots, there exists a disconnect between examining a knot’s mathematical and physical definitions. This is due to the inherent difference in the topology of an open-ended physical knot and a closed mathematical knot. By closing the ends of a physical knot, this paper presents a method to break this discontinuity by establishing a clear relation between physical and mathematical knots. By joining the ends and applying Reidemeister moves, we calculate the equivalent mathematical prime or composite knots for several commonly used physical knots. In the future, it will be possible to study the physical properties of these knots and their potential to expand the field of mathematical knot theory.

Poster

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