Interactive Knot Theory with KnotPlot

Abstract

We give a brief introduction to the software KnotPlot. The goals of this chapter are twofold: 1) to help a new user get started with using KnotPlot and 2) to provide veteran users with additional background and functionality available in the software. This chapter is not linear. Each section is generally self contained. The list below provides a short description of what is in each section. We highlight three particular sections: Section 9 that lists and describes commonly used commands, Section 10 that shows the user how to change parameter values (like the background color), and Section 16 that lists commonly used commands in popular user activities. -Setting it up:Downloading and setting up KnotPlot 3 -Loading and saving: Basic input/output for knot/link models 4 -Changing the view or embedding: Rotating a model 5 -Relaxing knots and links examples: How to relax a knot/link so that it is visually appealing 6 -Making pictures:

Knots in Art

“…Some other examples of knot art, like Persian mosaics (and knots in mosaics in general), lace, textile, macrame, etc., remain out of the scope of this paper, together with knots in computer art. One of the most remarkable examples where mathematics (knot theory), computer science and art meet is computer software KnotPlot [40] by Rob Scharein-it will be a subject of our future paper focusing on the role of knots in art and science.…”

Nullification numbers of knots with up to 10 crossings

“…The nullification pathways shown for the knots 10 74 and 10 103 yield n 2 (L). These sequences were found by hand and with the aid the program KnotPlot [29]. The notation for the resulting links follows the conventions of the link table found on the knot atlas [2].…”

Diagrammatics in Art and Mathematics

“…Although each individual string in the diagram has a five-fold symmetry about its geometric center, the diagram as a whole has no rotational or translational symmetries. R. Scharein's computer program Knotplot enables visualization and manipulating mathematical knots in three and four dimensions [13]. It was used to create Tying and untying, a short movie [14] that addresses one of the principal questions in knot theory-unknotting and distinguishing knots.…”