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- ItemPattern Transference: Making a ‘Nova Scotia Tartan’ Bracelet Using the Peyote Stitch(Taylor & Francis Ltd., 2009-03-24) Knoll, EvaThe look and style of a hand-crafted object is in many cases closely connected to the specific techniques used in its creation. When designs and patterns are transferred from their traditional medium to a different one, these technical parameters can modify and sometimes even limit the results, as well as pose mathematical challenges. In this article, I examine the parameters under which the Nova Scotia tartan can be transferred into an off-loom beading technique, known as peyote stitch, gourd stitch or twill stitch, by using the concepts from tiling theory, in order to produce a piece of wearable art.
- ItemAn Interactive/Collaborative Su Doku Quilt(Bridges: Mathematical Connections in Art, Music, and Science, 2006) Knoll, Eva; Crowley, MaryAfter introducing Su Doku, a popular number place puzzle, the authors describe a transformation of the puzzle where each number is replaced with a distinct colour. The authors investigate the nature of the experience of solving this transposed version. This, in turn, inspires a design process leading to the creation of an interactive quilt. This process, involving issues of choice of medium, level of interactivity, colour theory and aesthetics, is described. The resulting artefact is a textile diptych accompanied by a collection of coloured buttons, constituting a solvable puzzle and its solution.
- ItemBuilding a Möbius Bracelet Using Safety Pins: A Problem of Modular Arithmetic and Staggered Positions(2008) Knoll, EvaThis article reports on the resolution of a mathematical problem that emerged when two ideas were brought together. The first idea consists of a method for constructing a decorated bracelet made with safety pins that are strung together at both ends, creating a band. The other is suggested by the word band: why not introduce a twist and make the bracelet a Möbius band? As Isaksen and Petrofsky demonstrated in their paper  discussing the knitting of a Möbius band, the endless nature of the band’s single face and edge introduces an additional design constraint, particularly if the connection is to appear seamless. To make the creation appear seamless, the decoration applied to the design must itself be regular, as this helps the eye travel along the endless length. The paper discusses the mathematical and practical constraints of this result for a design that uses a repeating pattern throughout the band, first in the standard design, then in the Möbius bracelet. This resolution involves some simple modular arithmetic and an unusual way to lay out the pins in preparation for their being strung together.
- ItemTransferring Patterns: From Twill to Peyote Stitch(2009) Knoll, EvaCrafts are generally known for pieces whose structure and geometry are derived from the constraints of the techniques used. In particular, the look of specific patterns and textures are the natural product of the structure of the specific medium and technique applied to their production. The transfer of a pattern from its natural medium to another whose constraints may differ can sometimes present interesting mathematical challenges. In this workshop, this is exemplified through the transfer of a classic pattern resulting from Twill weaving, the Hound’s-Tooth Check as it is transferred to a different medium, known as Peyote, Gourd or Twill Stitch, whereby beads are strung in a traditional bricklaying pattern using an off-loom beading technique. This transfer presents the challenge of adapting a structure so that the transferred pattern still resembles the original, in as simple a way as possible. In the workshop, several possible result of this transfer are compared and materials are made available to both design and create Peyote-stitched hound’s tooth surfaces, thereby introducing the participants to some of the mathematical constraints of this type of transfer.
- ItemExploring Some of the Mathematical Properties of Chains(2009) Knoll, Eva; Taylor, TaraThis workshop aims to explore various mathematical topics that emerge from examining classes of chains and their properties. Basic concepts are taken from topology, an area of mathematics that is concerned with notions like connectedness, how many holes there are, and orientability; geometry, including symmetries; and collapsibility and degrees of freedom. These topics are explored through an examination of a small number of chain designs including examples that are not topologically linked at all, examples in which the relative position of the links determine the symmetries, degrees of freedom, and the way in which their structure is analogous to that of a Moebius band, and finally a model of a chain design with a fractal structure. The workshop will include building human models to explore various properties and other activities where the participants will be able to play with necklace models to better understand the theory and to come up with their own questions to investigate.