This is Chapter 8 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:

Most quilts lie flat, but not the ones in this chapter. We design quilts to illustrate a construction by mathematician William Thurston, which begins with interlocking rings in space. For the illustration to work, the rings need to be part of the quilts, so the places where the rings cross must be incorporated into the design. Consequently, the quilts cannot lie flat. The construction presents another design challenge that will interest quilters: Starting from the usual blanket-like configuration, we must be able to cinch each quilt into a ball in a way prescribed by the construction. Additionally, the colorings of the quilt blocks and details of the sashing have mathematical significance. By design, each configuration, as well as the transformation between them, respects the deep mathematics it represents. As such, the quilts can help us understand a groundbreaking construction from the field of low-dimensional topology.

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!