Textiles

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https://hdl.handle.net/10587/1240
Publications by Eva Knoll pertaining to Textiles.

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Browsing Textiles by Subject "Geometry"

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    Building a Möbius Bracelet Using Safety Pins: A Problem of Modular Arithmetic and Staggered Positions
    (2008) Knoll, Eva
    This 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 [1] 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.
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    Transferring Patterns: From Twill to Peyote Stitch
    (2009) Knoll, Eva
    Crafts 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.