1st Edition

Crafting by Concepts
Fiber Arts and Mathematics

ISBN 9781568814353
Published March 24, 2011 by A K Peters/CRC Press
264 Pages

USD $200.00

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Book Description

From the editors of the popular Making Mathematics with Needlework, this book presents projects that highlight the relationship between types of needlework and mathematics. Chapters start with accessible overviews presenting the interplay between mathematical concepts and craft expressions. Following sections explain the mathematics in more detail, and provide suggestions for classroom activities. Each chapter ends with specific crafting instructions. Types of needlework included are knitting, crochet, needlepoint, cross-stitch, quilting, temari balls, beading, tatting, and string art. Instructions are written as ordinary patterns, so the formatting and language will be familiar to crafters.

Table of Contents

Introduction: Welcome Back
Chapter Structure
Research Update
A Note for Educators
How to Use This Book

Knit Knit Revolution
Teaching Ideas
Crafting Revolutionary Hats

Generalized Helix Striping
Teaching Ideas
Crafting a Helix Striped Spiral Nightcap and Bed Socks

A Knitted Cross-Cap
The Math and Motivation behind the Pattern
Crafting the Knitted Cross-Cap

Fashioning Fine Fractals from Fiber
Teaching Ideas
Crafting the Sierpiriski Triangle

Diaper Patterns in Needlepoint
Teaching Ideas
Crafting the Symmetry Cube

Group Actions in Cross-Stitch
Teaching Ideas
Crafting the Two-Color Symmetry Sampler

Perfectly Simple: Squaring the Rectangle
The Math and Motivation behind the Pattern
Crafting Perfectly Simple

Spherical Symmetries of Ternari
Teaching Ideas
Crafting Three Temari Balls

Quilting Semiregular Tessellations
Teaching Ideas
Crafting Semiregular Quilts

About the Contributors


Fiber Arts Bibliography


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sarah-marie belcastro and Carolyn Yackel earned their Ph.D.s in mathematics from the University of Michigan. Carolyn Yackel is an Associate Professor in the mathematics department at Mercer University in Macon, Georgia, specializing in connections between mathematics and art. sarah-marie belcastro is a Research Associate at Smith College in Northampton, Massachusetts.

Featured Author Profiles

Author - Diane  Herrmann

Diane Herrmann

Senior Lecturer, University of Chicago, Department of Mathematics
Chicago, IL, USA

Learn more about Diane Herrmann »


The beauty of the visual patterns of mathematics is highlighted in this engaging book. The mathematics is carefully laid out, but following every detail of the mathematics is not necessary to create the patterns of the crafts projects presented. … Excellent photographs throughout amply illustrate the use of mathematics … I highly recommend this book to teachers looking for beautiful projects for their students or to anyone who loves or is curious about circles, spirals, helixes, cross-caps, fractals, diaper patterns, symmetry groups, squaring the rectangle, and tiling spheres or the plane.
—Marcia Weller Weinhold, Mathematics Teacher, November 2012

There is something in this book for everyone from crafters to mathematicians to educators and students. … This book has a lot to offer for mathematicians and non-mathematicians, presented in a beautifully illustrated and well-organized volume.
L’Enseignement Mathematique (2) 57, 2011

If Crafting by Concepts does nothing else, it should help non-math-geek knitters to understand there’s nothing to fear in the typical math of a knitting pattern. It also illustrates that a little mystery can be a lot of fun.
For knitters who are into mathematical knitting, this book offers a lot of interesting things to think about. … Crafty math teachers will enjoy the teaching suggestions that will allow them to use these projects and concepts in the classroom, hopefully bringing up the next generation of crafty mathematicians. And these projects take geek craft to a whole new level, which is pretty cool.
—Sarah E. White, About.com Knitting

I stumbled over this book and simply had to buy it … The authors’ interest is in linking mathematics and craft …
—Cally Booker, chairman of the Journal for Weavers, Spinners and Dyers, on her blog, August 2011

The editors have collected nine projects from various authors and have presented them attractively in this beautiful book. … The book is wide-ranging, covering many mathematical topics and many craft ideas. … This book would be a great present for a mathematician interested in craft or a craft enthusiast open to thinking about mathematics.
—Vicky Neale, Plus magazine, August 2011

Fiberarts and mathematics in a marvelous union to not just create but to understand applications in Temari, Quilting, Knitting and ever cross stitch.
Lacis Tools & Materials