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...at the January 2009 Joint Mathematics Meetings in Washington, DC. It was held Wednesday, January 7, 2009, 1:00 p.m.-5:50 p.m. and was organized by sarah-marie belcastro and Carolyn Yackel. (Information on the 2005 Special Session is here.) The Special Session and Exhibit were written up in the ICMS News.

The schedule was as follows. Speaker names link to their webpages, and speaker titles link to their abstracts (plain text). Photos, where available, are linked below as well; click on any image to enlarge it.

1:00--1:20 Carolyn Yackel (Mercer
University): *Temari Math and Geometry on the Sphere.*

photos

1:30--1:50 Ted Ashton (USG
Applied Math Researcher): *Don’t Blow a Gasket!*

photos

2:00--2:20 Diane
Herrmann (University of Chicago): *Diaper Pattern
in Needlepoint.*

2:30--2:50 Irena Swanson (Reed
College): *Semiregular tessellations*

photos

3:00--3:30 Mathematical Fiber Arts Exhibit (juried) photos (and detailed descriptions of exhibit items)

3:30--3:50 Mary
Shepherd (Southwest Missouri State): *Visualizing
Groups and Subgroups in Counted Cross Stitch.*

4:00--4:20 Daina Taimina (Cornell
University): *Exploring two-dimensional manifolds with
crochet hook.*

photos

4:30--4:50 Joshua Holden (Rose-Hulman
IT): *Braids, Cables, and Cells: An intersection of Mathematics,
Computer Science, and Fiber Arts.*

photos

5:00--5:20 sarah-marie belcastro (HCSSiM and Sarah
Lawrence College): *Braid words in generalized helix stripe
patterns*

5:30--5:50 Amy Szczepanski (University
of Tennessee, Knoxville): *Calculating Patterns for Knitted
Surfaces.*

photos

And, of course, we hosted the Knitting Circle on Tuesday, January 6, 2009,
8:15 p.m.-9:45 p.m.! Photos can be found here and here.

Amy F. Szczepanski

*Calculating Patterns for Knitted Surfaces.*

We present a method for calculating
the pattern for knitting some geometric shapes (such as spheres and tori)
that can be described as surfaces of revolution. Each of these shapes can
be knit as a series of circular rounds. Writing the pattern can be reduced
to a problem of determining how many stitches should be in each round and
how many rounds are needed. Some approximations will need to be done, as
rounds must have a whole number of stitches, and the overall pattern must
have a whole number of rounds. The number of stitches in each round can be
calculated by using a parameterization of the curve, rotation matrices, and
approximations of arclength. We present a description of the method and software
that has been written to calculate some patterns.

Carolyn Yackel

*Temari Math and Geometry on the Sphere.*

We will discuss the interplay between
mathematics and the craft of embroidered temari thread balls. Two different
ways of classifying temari ball designs will be considered; one presented by
Conway, Burgiel, and Goodman-Strauss in their recent book The Symmetries of
Things and the other as a pro jection of polyhedra onto the sphere. One portion
of the talk will demonstrate the use of temari as examples of spherical symmetries
or polyhedral pro jections. The other half will focus on which symmetries or
polyhedra can be realized in some mathematically exact sense given the restriction
to temari techniques.

Daina Taimina

*Exploring two-dimensional manifolds with crochet hook.*

Crocheted models of the hyperbolic plane are very inviting to play with. There
are many different ways to fold symmetric hyperbolic planes. Starting from the
same basic plane, there are unlimited possibilities to create different fiber sculptures.
Do these different shapes have anything to do with mathematics or are they just
purely aesthetic forms? All those surfaces are geometric 2-manifolds. Each of
them is covered by the hyperbolic plane and so each is locally isometric to the
hyperbolic plane (and to each other). However, among these geometric 2-manifolds,
only the hyperbolic plane is simply connected—all the other hyperbolic
surfaces have holes or circles that cannot be shrunk on the surface. In the first
/Fiber Arts in Mathematics and Mathematics Education/ session I showed crocheted
hyperbolic octagon that forms a two-manifold. In this talk I will show how to
make two-manifolds from crocheted hyperbolic rectangular hexagons and ideal triangles.

Diane Herrmann

*Diaper Pattern in Needlepoint.*

Informally stated, a diaper pattern in decorative
art is one that has visual diagonals in two different directions. Needlepoint
canvas, because of its evenweave construction, is well suited to the creation
of diaper patterns. The relationship of diaper patterns to the 17 wallpaper
groups will be discussed. Many examples of needlepoint diaper patterns will
be shown, including how the use of color in a single pattern can aid in identification
of the symmetry.

Irena Swanson

*Semiregular tessellations*

A semiregular tessellation of a plane is a tessellation using only regular n-gons
such that each vertex meets an adjacent shape in a vertex, and the configurations
are the same at all vertices (up to rotation). There are only finitely
many semiregular tessellations (eight or nine, in addition to the three regular
tessellations, depending on how you count). I will discuss how to render semiregular
tessellations in quilt form, in particular, what are the geometric shortcuts
that save time but possibly not the fabric.

Joshua Holden

*Braids, Cables, and Cells: An intersection of Mathematics, Computer Science,
and Fiber Arts.*

The mathematical study of braids combines aspects of topology and group theory
to study mathematical representations of one-dimensional strands in three-dimensional
space. These strands are also sometimes viewed as representing the movement through
a time dimension of points in two-dimensional space. On the other hand, the study
of cellular automata usually involves a one- or two-dimensional grid of cells
which evolve through a time dimension according to specified rules. This time
dimension is often represented as an extra spacial dimension. Therefore, it seems
reasonable to ask whether rules for cellular automata can be written in order
to produce depictions of braids. The ideas of representing both strands in space
and cellular automata have also been explored in many artistic media, including
knitting and crochet, where braids are called “cables”. We will view
some examples of braids and their mathematical representations in these media.

Mary Shepherd

*Visualizing Groups and Subgroups in Counted Cross Stitch.*

Symmetry groups have a rich algebraic structure, and since many are non-Abelian,
they comprise a nice set of examples in which to explore general ideas about
groups, free from the hidden pitfalls that students sometimes encounter in Abelian
groups. Using counted cross stitch examples created by the author, this talk
will address: (1) visualizing the individual group elements and the group operation,
(2) visualizing subgroups and cosets in both finite and infinite groups, and (3)
exploring other properties and theorems related to groups and subgroups. We will
begin these explorations looking at the finite group D4 and the infinite wallpaper
group p4m.

sarah-marie belcastro

*Braid words in generalized helix stripe patterns*

When multiple strands of yarn are used in knitting (as, for example, when knitting
with more than one color), a knitter twists a pair of strands when switching
from using one to using another. The yarn strands between the knitting and the
balls of yarn get tangled as the knitting proceeds. In turn, this produces a
braid in the strands. This talk will consider the special case of the braid words
generated by generalized helix stripe patterns. The basic technique produces
spiralling stripes of row-height one. (Standard striping produces cylindrical
or line-segment stripes.) We will first explain how to generalize helix striping
to thicker stripes and different numbers of colors. We will then determine which
braid words are generated using generalized helix stripe patterns. (This has
practical applications in terms of detangling yarn while knitting.)

Ted Ashton

*Don’t Blow a Gasket! *

The beautiful Sierpinski Gasket (also called the Sierpinski Triangle) can be
created in many different ways. In this talk, which grew out of the speaker’s
experience in tatting a Sierpinski triangle, we’ll look at a few of those
ways and how they naturally map into the fiber arts.