#### Figuring Fibers

##### edited by Carolyn Yackel with assistance from sarah-marie belcastro

Welcome! Here is some information about Figuring Fibers. The book (published by the American Mathematical Society) is available from the AMS, AmazonUS (and Amazon Japan, Brazil, UK, and France), Target, Barnes and Noble, Book Depository (UK), Blackwell's (UK), Angus&Robertson (Australia), QBD (Australia), Kinokuniya (Japan), CDON.COM (Finland), Saxo (Denmark), Waterstone's (UK), and San Min Book Co., Ltd. (Taiwan) as well.
And here is the WorldCat/OCLC entry.

How does Figuring Fibers compare to Making Mathematics with Needlework and Crafting by Concepts? Figuring Fibers begins with a reader's guide in the form of abstracts of the chapters meant for crafters as well as abstracts meant for mathematicians. As in the earlier volumes, each chapter includes accessible overviews, deep mathematics, and project instructions.

A review by Tien Chiu

###### Mathematical topics, authors, and projects:

Chapter title links are to individual chapter purchase pages at the publisher.

Chapter 1 by Jake Wildstrom is about center-worked crafts. The mathematical meat of the chapter has to do with buffers. Using the language of recreational mathematics, Wildstrom looks at polyominoes, which are familiar to lay people as Tetris pieces and similar objects. He gives careful instructions involving unusual and inventive stitches for crocheting the polyominoes made of four and five base squares (tetrominoes and pentominoes). Amazing contemporary pieces of art can be assembled from the resulting polyominoes!
Ravelry pattern page

Chapter 2 by Kyle Calderhead discusses how to build a Gosper Curve fractal (aka flowsnake) in a manner similar to the way that the Hilbert curve is built up in iterative steps. Using the technique of intermeshed crochet, which is explained in the chapter, Calderhead gives directions for crocheting three practice trivets and a stunning Gosper Curve afghan.
Ravelry pattern page

Chapter 3 by Carolyn Yackel counts the number of variant patterns that can be found by reconceiving of a typical counterpane block in terms of the mathematical art construct of flexible Truchet tiles. The chapter pattern directs readers to knit a lace stole in which the lace pattern varies subtly over the squares so that opposite ends of the stole differ starkly.
Ravelry pattern page

Chapter 4 by Mary Shepherd applies graph theory to the historically interesting Snake's Trail Quilt Blocks that a mathematician might call rounded Truchet tiles. The chapter solves the problem of laying out a Snake in a Hollow Maze Quilt as well as a Racetrack quilt. Clear directions for making both wonderful quilts are provided.

Chapter 5 by Berit Givens extends the Chinese Remainder Theorem and shows how both the original theorem and its extension apply to designing knitwear with knit patterns having different stitch repeat lengths. This chapter is rich in worked examples. Importantly, the chapter also discusses the math involved in rescaling stitch counts for different gauge knitting!! The chapter pattern is a fetching cowl.
Ravelry pattern page

Chapter 6 by sarah-marie belcastro discusses knitting certain torus knots and links, including the mathematics and technique. Algorithms for making pointy and round versions of the torus knots and links are included. While these make beautiful works of art, belcastro also shows them being used as cowls and bracelets. If you are wondering about the amazing cover image on the book, it is a hand-dyed (8,6) torus link.
Ravelry pattern page

Chapter 7 by S. Louise Gould discusses making polyhedra, which are the three-dimensional versions of polygons. Her chapter relates the regular and semi-regular plane tessellations to the regular and semi-regular polyhedra, moving then to polyhedral surfaces. She shows the reader how to make mind-boggling finite slices of infinite triply periodic surfaces from cloth using a plotter-cutter and an embroidery machine.

Chapter 8 by Barbara Nimershiem exposes and illustrates work by the famous mathematician Bill Thurston. The thrust of the chapter is to show that the complement of the Borromean rings decomposes into two hyperbolic octahedra that are identified on their boundaries. Nimershiem's chapter project is an ingenious pair of so-called quilts with sashing, colored pencils, and drawstrings that transform from flat pieces to octahedra and back. Readers interested in fully understanding the chapter will absolutely want to make these color-coded quilts, as will professors teaching this material.
Article on the quilt