Knots and Braids

By Sasha Abanov, PhD

This course will combine an introduction to the mathematical theory of knots and braids with the art of knot tying. We will learn how to draw knots and how to distinguish knots that can not be untied by coloring their diagrams. We will talk about braids and find out how to turn braids into knots. Each SemiLab will have a knot tying part where we will learn how to tie some of the most useful sailing knots such as figure-of-eight, bowline, constrictor and thief knot.

Detailed description

Session 1. A) What is a knot? What is the difference between real and mathematical knots? Equivalent knots. How to draw knot diagrams. B) What are sailing knots? Learning how to tie square knot, thief knot, figure-of-eight knot and sheet bend knot.

Session 2. A) How to untie knots using knot diagrams. Knot invariants. B) Learning how to tie bowline and constrictor.

Session 3. A) Coloring knots into three colors. Number of 3-colorings as a knot invariant. Reidemeister moves. B) Learning how to tie rolling hitch and round turn and two half hitches.

Session 4. A) Braids. How to turn braids into knots. Multiplying braids. B) Other useful knots.