﻿ Winding Number & Linking Number: Articles, Studies and Background Information
Articles, Studies and Background Information

Resources

### Definitions

A winding number represents the total number of times that a curve travels around a point. The winding number is positive if the curve travales around the point counterclockwise and negative if the curve travels clockwise.

 Winding No. +2 Winding No. -2

A linking number represents the number of times that two curves wind one around the other. The linking number may be positive or negative depending on the winding orientation of the two curves regarding each other.

### Background Information

• Linking number - Wikipedia [View Resource]
• Winding number - Wikipedia [View Resource]

### K-12 Resources and Science Fair Projects

• On the Expected Winding Number of a Random Walk on the Unit Lattic [View Resource]
• What is algebraic topology? [View Resource]

### Advanced Articles, Studies and Research

• DNA linking number change induced by sequence-specific DNA-binding proteins [View Resource]
• Pontryagin invariants and integral formulas for Milnor's triple linking number [View Resource]
• Dividing a supercoiled DNA molecule into two independent topological domains [View Resource]
• Polyakov's Model [View Resource]
• Faddeev-Hopf knots and the two-component Ginzburg-Landau model [View Resource]
• Computing the Writhing Number of a Polygonal Knot [View Resource]
• Rational linking and contact geometry [View Resource]
• Transversal Torus Knots [View Resource]
• Winding Numbers and Topology [View Resource]
• A Winding Number and Point-in-Polygon Algorithm [View Resource]
• Vector Fields. Winding Number and Index. Poincare Theorem. [View Resource]
• Fixed Winding Number and the Quasiperiodic Route to Chaos in a Convective Fluid [View Resource]
• Decomposition of the linking number of a closed ribbon: A problem from molecular biology [View Resource]
• The Enhanced Linking Number [View Resource]

### Theses and Dissertations

• On the Vassiliev invariants for knots and for pure braids [View Resource]
• On the uniform thickness property and Contact geometric knot theory [View Resource]
• Computational methods in protein structure comparison and analysis of protein interaction networks [View Resource]
• Intersection and linking numbers of digital curves and application to the characterization of topology preservation in computer imagery [View Resource]
• Contributions to Geometric Knot Theory of Curves and Surfaces [View Resource]