This is Chapter 6 of Figuring Fibers, edited by Carolyn Yackel and sarah-marie belcastro.

This self-contained chapter contains directions for a complete project in a downloadable PDF file. You may also purchase the entire volume or see a list of all chapters available for individual purchase.

Background for crafters:

We commonly think of knots as tangles in yarn that can't be removed without manipulating the free ends. This is conceptually the same as the idea of mathematical knots—the main difference is that a mathematical knot has no free ends, which is achieved by fusing together the free ends of an ordinary knot. Many mathematical knots are pretty and some are symmetrical. This chapter is about the mathematics of a class of knots that are conveniently able to wind around the neck many times, and about the mathematics that arises when making cowls that have the form of these knots.

About Figuring Fibers:

Pick up this book and dive into one of eight chapters relating mathematics to fiber arts! Amazing exposition transports any interested person on a mathematical exploration that is rigorous enough to capture the hearts of mathematicians. The zenith of creativity is achieved as readers are led to knit, crochet, quilt, or sew a project specifically designed to illuminate the mathematics through its physical realization. The beautiful finished pieces provide a visual understanding of the mathematics that can be shared with those who view them. If you love mathematics or fiber arts, this book is for you!