1st Edition

# Crafting Conundrums Puzzles and Patterns for the Bead Crochet Artist

By Ellie Baker, Susan Goldstine Copyright 2014
272 Pages 325 Color Illustrations
by A K Peters/CRC Press

272 Pages
by A K Peters/CRC Press

Also available as eBook on:

Designed for crafters, puzzle lovers, and pattern designers alike, Crafting Conundrums: Puzzles and Patterns for the Bead Crochet Artist provides methods, challenges, and patterns that offer a springboard for creative exploration. All are illustrated with beautiful color diagrams and photographs. Experienced bead crochet crafters looking for a project may choose to skip ahead to the pattern pages and begin crocheting from an abundance of unique, mathematically inspired designs. Those wishing to design their own patterns will find many useful tools, template patterns, and a new methodology for understanding how to do so even without using math. Puzzle lovers without previous knowledge of bead crochet will also find ample inspiration for learning the craft.

The first part of the book describes the basic requirements and constraints of a bead crochet pattern and explains what makes designing in this medium so tricky. The authors present their new design framework and offer insight on how best to approach design choices and issues unique to bead crochet.

The second part presents a series of bead crochet design challenges informed by colorful bits of mathematics, including topology, graph theory, knot theory, tessellations, and wallpaper groups. Each chapter in this section begins with a design puzzle accompanied by an introduction to the mathematical idea that inspired it. The authors then discuss what made the challenge difficult, present some of their solutions, and describe the thinking and ideas behind their approach.

The final part contains nearly 100 original bead crochet patterns, including solutions to all the design challenges. This part also provides a tutorial on the fundamentals of bead crochet technique.

Behind the deceptively simple and uniform arrangement of beads is a subtle geometry that produces compelling design challenges and fascinating mathematical structures. In color throughout, Crafting Conundrums gives both math enthusiasts and crafters an innovative approach to creating bead crochet patterns while addressing a variety of mathematically inspired design questions. Supplementary materials, including demo videos, are available on the book’s CRC Press web page.

A Design Framework
Exploring the Bead Plane
Torus Basics
Flat Layouts
The Infinite Bead Plane
Hockey-Stick Translations
Repeat Translations
Lattices and Tilings
Designing in the Bead Plane
Extracting a Repeat From a Bead Plane Diagram
Twists
Cropping Visualization and the Limits of Physical Twists
New Design Challenges

Design Challenges
Seven-Color Tori

Geometric Cross Sections
One More Challenge: Möbius Bands
Faceted Bracelets: Another Design Springboard

Torus Knots
Construction Using Physical Twists
Construction Using Natural Twists
Combining Patchworks and Twists

Knotted and Linked Bracelets
Celtic Knots: Another Design Springboard

Escher Designs
Deforming Polygonal Tilings
Assembling Shaped Tiles
Generating Tiles from Lattices
Growing Symmetric Tilings
Escher Transformations: Another Design Springboard

Wallpaper Groups
Identifying Wallpaper Groups
Wallpaper Groups in the Bead Plane
Designing Wallpaper Bracelets

Instructions and Patterns
How to Bead Crochet
Pattern Selection
Stringing
Starting
Crocheting
Closing
Joining New Thread
Tips for Transformation Designs

Resources

Pattern Pages

### Biography

Ellie Baker, Susan Goldstine

"Coming from a mathematical perspective, Baker and Goldstine’s explorations of the challenges and their solutions is engaging and compelling for those interested in understanding the mechanics of geometric patterning. For those who would rather skip the analysis and make something beautiful, the nearly 100 bracelet patterns offer a wide range of styles to create. If you’re new to bead crochet, the thorough step-by-step guide will get you going. If you are at all interested in bead crochet, this book is a must."
Bead and Button, February 2016

"If bead crochet ropes interest you, then you will really want a copy of this book. It contains an amazing wealth of information and includes dozens of novel designs, all with easy-to-follow charts. … There is plenty of interesting theory for the mathematically inclined, but there are also sections on how to bead crochet for beginners … the authors explain how they created the designs in their beading charts. These explanations are really what separate this beading book from dozens of the other beading books I have seen. … if you are interested in designing your own projects, this book will be of particular interest because it offers a great deal of insight into the design process."
Journal of Mathematics and the Arts, Vol. 9, 2015

"Some books on the interactions between mathematics and other disciplines: … Crafting Conundrums by Ellie Baker and Susan Goldstine …"
The Best Writing on Mathematics 2015, Edited by Mircea Pitici. Princeton University Press, 2016, xix-xx.

"The mathematics presented in Crafting Conundrums is broad and deep, enriched by its application to bead crochet. The pattern design techniques presented are powerful, effective, and clearly explained. Crafting Conundrums is an excellent resource for anyone interested in bead crochet or applications of mathematics in the arts."
AWM Newsletter, September–October 2015

"This beautifully illustrated book is a delight for both the bead crocheter and the student of mathematics. It can be enjoyed by the crafter without exploring the mathematics or the mathematician without trying the craft. But it will entice the crafter to do mathematics, and the mathematician to crochet tangible displays of her work.
Mathematics at its essence is the study of patterns and bead crochet is a beautiful medium for making tangible objects to display patterns. Here we have an extensive study of the possibilities for bead crochet by two knowledgeable mathematicians. Starting with a simple hexagonal grid, a wealth of possibilities emerge. The surprising complexity of this medium is explored in depth.
Readers can choose from clearly illustrated patterns or design their own while learning about the underlying mathematics. With ideas from topology, tilings, graph theory, knot theory, and group theory, an entire liberal arts mathematics course can be designed around this text. Whether you are looking to introduce mathematics topics into your arts curriculum, generate enthusiasm in your mathematics courses, or simply create stunning bead crochet, you will find great ideas for exploration."
—Eve Torrence, Professor of Mathematics, Randolph-Macon College

"This book is a collection of wonderful tools for mastering geeky and beautiful projects that in a tactile and creative way explore notions like universal covering space, four color theorem, wallpaper groups, and seven color tori that unfairly seem to be reserved for mathematicians only. Crafters, puzzle lovers, and pattern designers will be delighted to find clear instructions on how to do the projects. I hope that non-crafting mathematicians will also peek in the book to see how mathematical concepts can be expressed in amazingly visual ways. It is indeed written with experience and love of both math and craft."
—Daina Taimina, Adjunct Associate Professor of Mathematics, Cornell University, and Author of Crocheting Adventures with Hyperbolic Planes

"This delightful book will give readers a visual understanding of mathematically inspired designs in bead crochet ropes. It is a well-written book that straddles the fence between mathematics and craft. The theory, patterns, projects, and instructions are presented in a clear and concise manner. If the technical aspects don’t interest you, then skip ahead to the pattern pages for a full library of designs. This book will keep the experienced bead crocheter busy for a long while."
—Judith Bertoglio-Giffin, Bead Line Studios, www.beadline.com

"This is a must-have book for anybody interested in bead crochet bracelets and cords. It provides a perfect balance between the design and construction of bead crochet, and the underlying mathematics that dictates what is and is not possible within this art form."
—Gwen Fisher, beAd Infinitum, www.beadinfinitum.com

"Crafting Conundrums is a wonderful book that shows the unity of art, craft, and mathematics. It is a feast for the eyes as well as the mind. The authors integrate accessible discussions of the mathematics of pattern and shape with design challenges and step-by-step instructions, so that readers can be as practical or as idea-oriented as the spirit moves them. Crafting Conundrums will join other special books, like Taimina’s Crocheting Adventures with Hyperbolic Planes and belcastro and Yackel’s Making Mathematics with Needlework, on my bookshelf. I need only to look at them to be reminded that art and math were ‘separated at birth.’ Baker and Goldstine have reunited them. I wish math could have been like this when I was in school!"
—Sarah Kuhn, Professor of Psychology, University of Massachusetts Lowell

"Baker and Goldstine offer a beautiful and precise mathematical introduction to the deep ideas of bead crochet, leading the reader to feel like a participant in the development. Myriad accompanying patterns afford readers an excellent venue for experiencing the mathematics themselves and for becoming severely addicted to bead crochet. The mathematical theory is followed by a generous invitation to further play with the mathematics through beading, theoretical exploration, or a combination of both. This book is a wonderful resource for people wanting to deepen their understanding of mathematics through crafting, people who love mathematics and crafting, and people who enjoy design. College libraries, parents of the mathematically gifted, and technically oriented people take note: You want this book!"
—Carolyn Yackel, Associate Professor of Mathematics, Mercer University, and Coeditor of Making Mathematics with Needlework and Crafting by Concepts