Developing a mathematical model for bobbin lace

@article{Irvine2014DevelopingAM,
  title={Developing a mathematical model for bobbin lace},
  author={Veronika Irvine and F. Ruskey},
  journal={Journal of Mathematics and the Arts},
  year={2014},
  volume={8},
  pages={110 - 95}
}
Bobbin lace is a fibre art form in which intricate and delicate patterns are created by braiding together many threads. We present an overview of the making of bobbin lace, illustrated with a simple, traditional bookmark design. We briefly summarize research on the topology of textiles and braid theory, which form a base for the current work. We then define a new mathematical model that supports the enumeration and generation of bobbin lace patterns using an intelligent combinatorial search… Expand
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References

SHOWING 1-10 OF 44 REFERENCES
The Book of Bobbin Lace Stitches
This work contains an exhaustive collection of stitches which have been developed in the traditional art of bobbin lacemaking since the 17th century, and is designed to aid all lacemakers in theExpand
Satins and Twills: An Introduction to the Geometry of Fabrics
Weaving is one of the oldest activities of mankind and so it is hardly surprising that there exists a vast literature on the subject. But this literature is almost entirely concerned with theExpand
The theory of braids.
  • E. Artin
  • Mathematics, Medicine
  • American scientist
  • 1950
A theory of braids leading to a classification was given in my paper "Theorie der Zopfe" in vol. 4 of the Hamburger Abhandlungen (quoted as Z). Most of the proofs are entirely intuitive. That of theExpand
Tilings and Patterns
"Remarkable...It will surely remain the unique reference in this area for many years to come." Roger Penrose , Nature "...an outstanding achievement in mathematical education." Bulletin of The LondonExpand
The Technique of Bobbin Lace
Equipment, preparation and other useful information Torchon lace Bedfordshire or Beds-Maltese and Cluny lace Bucks Point lace braids and trimmings for modern use.
A Topological Study of Textile Structures. Part I: An Introduction to Topological Methods
This paper proposes a new systematic approach for the description and classification of textile structures based on topological principles. It is shown that textile structures can be considered as aExpand
Lace: A History
This work covers the period from the early-16th century to World War I and is arranged chronologically to accommodate the underlying changes in fashionable dress and the lace worn with it. WithinExpand
The Knot Book
Are you looking to uncover the knot book Digitalbook. Correct here it is possible to locate as well as download the knot book Book. We've got ebooks for every single topic the knot book accessibleExpand
A Topological Study of Textile Structures. Part II: Topological Invariants in Application to Textile Structures
This paper is the second in the series on topological classification of textile structures. The classification problem can be resolved with the aid of invariants used in knot theory forExpand
Motzkin Numbers
  • M. Aigner
  • Computer Science, Mathematics
  • Eur. J. Comb.
  • 1998
TLDR
Motzkin numbers (which are related to Catalan numbers) are studied and it is shown that the sequenceMnis logarithmically concave with limMn+1/Mn=3. Expand
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