TITLE:
Using Parametric Mathematical Modeling to Develop a Geometric and Topological Intuition for Molecular Knots
AUTHORS:
Tahmineh Azizi, Jacob Pichelmeyer
KEYWORDS:
Synthetic Molecular Knots, Parametric Equations, Topology and Knot Theory, Trefoil Knot
JOURNAL NAME:
Applied Mathematics,
Vol.11 No.6,
June
10,
2020
ABSTRACT: Knot theory is a branch of topology in pure mathematics, however, it has been increasingly used in different sciences such as chemistry. Mathematically, a knot is a subset of three-dimensional space which is homeomorphic to a circle and it is only defined in a closed loop. In chemistry, knots have been applied to synthetic molecular design. Mathematics and chemistry together can work to determine, characterize and create knots which help to understand different molecular designs and then forecast their physical features. In this study, we provide an introduction to the knot theory and its topological concepts, and then we extend it to the context of chemistry. We present parametric representations for several synthetic knots. The main goal of this paper is to develop a geometric and topological intuition for molecular knots using parametric equations. Since parameterizations are non-unique; there is more than one set of parametric equations to specify the same molecular knots. This parametric representation can be used easily to express geometrically molecular knots and would be helpful to find out more complicated molecular models.