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Reference List: Mathematical Articles on Fiber Arts

Articles appearing in academic publications

Everything Except Weaving
  1. Adams, Colin; Fleming, Thomas; Koegel, Christopher. Brunnian Clothes on the Runway: Not for the Bashful. American Mathematical Monthly, 111 (November 2004), no. 9, 741--748.
  2. belcastro, s-m; Yackel, Carolyn. About Knitting. Math Horizons November 2006.
  3. belcastro, sarah-marie. Every Topological Surface Can Be Knit: A Proof, Journal of Mathematics and the Arts 3(2) June 2009, 67–83.
  4. Bernasconi, Anna; Bodei, Chiara; Pagli, Linda. Knitting for Fun: A Recursive Sweater. in Fun with Algorithms, Lecture Notes in Computer Science, Volume 4475, Springer, 2007, 53--65. article (.pdf)
  5. Bernasconi, Anna; Bodei, Chiara; Pagli, Linda. On formal descriptions for knitting recursive patterns. Journal of Mathematics and the Arts, 2(1) March 2008, 9–27.
  6. Biedl, Therese; Horton, John D.; Lopez-Ortiz, Alejandro. Cross-Stitching Using Little Thread. Proceedings of the 17th Canadian Conference on Computational Geometry (CCCG'05), 199--202.
  7. Cochrane, Paul. Knitting Maths. Mathematics Teaching September 1988, pp. 26--28.
  8. Conway, J. H. Mrs. Perkins's quilt. Proc. Cambridge Philos. Soc. 60 (1964) 363--368. (This doesn't have even a reference to quilting, but the quilting application of the mathematics is obvious to crafters.)
  9. Curtis, S.A. An Application of Functional Programming: Quilting. in Trends in Functional Programming, edited by Stephen Gilmore,
    Vol. 2, Intellect, 2000.
  10. Curtis, S.A. Marble Mingling. Journal of Functional Programming, 16 ( 2006), issue 2, 129--136. (This has a passing mention of a quilting problem.)
  11. DeTemple, Duane. Reflection Borders for Patchwork Quilts. Mathe- matics Teacher, February 1986, 138–143.
  12. Ellison, Elaine Krajenke. Imaginative Quilted Geometric Assemblages. In Bridges Donostia: Proceedings 2007, pp. 425–426. Tarquin Publi- cations, 2007.
  13. Fisher, Gwen. The Quaternions Quilts. FOCUS 25 (2005), no. 1, 4--5.
  14. Fisher, Gwen. Quilt Designs Using Non-Edge-to-Edge Tilings by Squares, in Meeting Alhambra, ISAMA-BRIDGES Conference Proceedings 2003, ed. R. Sarhangi and C. Sequin, 265--272.
  15. Fisher, Gwen; Medina, Elsa. Cayley Tables as Quilt Designs, in Meeting Alhambra, ISAMA-BRIDGES Conference Proceedings 2003, ed. R. Sarhangi and C. Sequin, 553-554.
  16. Funahashi, Tatsushi; Yamada, Masashi; Seki, Hirohisa; Itoh, Hidenori. A technique for representing cloth shapes and generating 3-dimensional knitting shapes. Forma 14 (1999), no. 3, 239--248.
  17. Grishanov, S.A.; Cassidy, T; Spencer, D.J. A model of the loop formation process on knitting machines using finite automata theory. Applied Mathematical Modelling 21(7) July 1997, 455–465.
  18. Grishanov, Sergei; Meshkov, Vadim; Omelchenko, Alexander. A Topological Study of Textile Structures. Part I: An Introduction to Topological Methods. Textile Research Journal 79 (2009), no. 8, 702--713.
  19. Grishanov, Sergei; Meshkov, Vadim; Omelchenko, Alexander. A Topological Study of Textile Structures. Part II: Topological Invariants in Application to Textile Structures. Textile Research Journal 79 (2009), no. 9, 822--36.
  20. Grishanov, S.A.; Meshkov, V.R.; Vassiliev, V.A. Recognizing textile structures by finite type invariants. J. Knot Theory Ramifications 18 (2011) no. 2, 209--35.
  21. Grishanov, S.A.; Vassiliev, V.A. Invariants of Links in 3-Manifolds and Splitting Problem of Textile Structures. J. Knot Theory Ramifications 20 (2011), 345--370.
  22. Grishanov, Sergei; Meshkov, Vadim; Omelchenko, Alexander. Kauffman-type polynomial invariants of doubly-periodic structures. J. Knot Theory Ramifications Vol. 16, No. 6 (2007) 779--788.
  23. Grishanov, S.;Tausif, M; Russell, S.J. Characterisation of fibre entanglement in nonwoven fabrics based on knot theory. Composites Science and Technology 72 (2012) 1331--1337.
  24. Grünbaum, Branko. Periodic Ornamentation of the Fabric Plane: Lessons from Peruvian Fabrics. In Symmetry Comes of Age: The Role of Pattern in Culture, pp. 18–64. University of Washington Press, 2004.
  25. Harris, Mary. Mathematics and Fabrics. Mathematics Teaching 120 (1987), 43--45.
  26. Henderson, David W.; Taimina, Daina. Crocheting the hyperbolic plane. Math. Intelligencer 23 (2001), no. 2, 17--28. article (.pdf)
  27. Igarashi, Yuki; Igarashi, Takeo; Suzuki, Hiromasa. Knitting a 3D Model. Computer Graphics Forum (Proceedings of Pacific Graphics 2008), 27(7), Oct. 2008, 1737–1743.
  28. Irving, Claire. Making the Real Projective Plane. Math. Gazette November 2005, 417--423.
  29. Isaksen, Daniel; Petrofsky, Al. Mobius knitting, in Bridges: Mathematical Connections in Art, Music, and Science, Conference Proceedings 1999, ed. R. Sarhangi, 1999, 67--76. article
  30. Kaldor, Jonathan M.; James, Doug L.; Marschner, Steve. Simulating knitted cloth at the yarn level. International Conference on Computer Graphics and Interactive Techniques, ACM SIGGRAPH 2008 papers, Article No. 65. ACM Press, 2008.
  31. Liebscher, U., and Weber, M., Topological Studies of Textiles I. Fundamentals. Textiltechnik 30(1), 58--61 (1980).
  32. Liebscher, U., and Weber, M., Topological Studies of Textiles II. Applications and Examples. Textiltechnik 30(1), 30(3) 176--178 (1980).
  33. Mabbs, Louise. Fabric Sculpture—Jacobs Ladder. In Bridges Lon- don: Conference Proceedings 2006, pp. 561–568. Tarquin Publications, 2006.
  34. Mallos, James. Triangle-Strip Knitting. Hyperseeing: Proceedings of ISAMA 2010, Summer 2010, 111–116.
  35. Morton, H.R.; Grishanov, S. Doubly periodic textile patterns. J. Knot Theory Ramifications 18 (2009), 1597--1622.
  36. Osinga, Hinke M.; Krauskopf, Bernd. Crocheting the Lorenz manifold. The Mathematical Intelligencer 26 (2004), no. 4, 25--37. article
  37. Osinga, Hinke M.; Krauskopf, Bernd. Visualizing curvature on the Lorenz manifold. Journal of Mathematics and the Arts 1(2): 113-123, 2007. article
  38. Osinga, Hinke M.; Krauskopf, Bernd. The Lorenz Manifold: Crochet and Curvature. In Bridges London: Conference Proceedings 2006, pp. 255–260. Tarquin Publications, 2006.
  39. Pickett, Barbara Setsu. Sashiko: the Stitched Geometry of Rural Japan, In Bridges London: Conference Proceedings 2006 pp. 211–214. Tarquin Publications, 2006.
  40. Reid, Miles. The Knitting of Surfaces. Eureka - The Journal of the Archimedeans 34 (1971), pp21-26.
  41. Reid, Miles. Needlework Section: Knitting 2-Manifolds, 1. 2-Manifold 2, Autumn 1982, 9--14.
  42. Reid, Miles. Needlework Section: Knitting 2-Manifolds, 2: the Boy's Surface. 2-Manifold, (the next issue), 10--21.
  43. Ross, Joan. How to Make a Mobius Hat by Crocheting. Mathematics Teacher 78, (1985) 268 - 269.
  44. Shepherd, Mary D. Groups, Symmetry and Other Explorations with Cross Stitch. Electronic Proceedings of the Missouri MAA, 2007 Meeting. article (.doc)
  45. Trustrum, G. B. Mrs Perkins's quilt. Proc. Cambridge Philos. Soc. 61 1965 7--11. (This doesn't have even a reference to quilting, but the quilting application of the mathematics is obvious to crafters.)
  46. Vandermonde, Alexandre-The'ophile. Remarques sur les Probl`emes de Situation. Histoire de l' Acade'mie des Sciences (Paris) (1771), 566--574. (Mainly about knight's tours on chessboards, he does describe paths through space for rows of stockinette.)
  47. Williams, Mary C.; Sharp, John. A Collaborative Parabolic Quilt, in Bridges: Mathematical Connections in Art, Music, and Science, Conference Proceedings 2002, ed. R. Sarhangi, 143--149.
  48. Williams, Mary C. Quilts Inspired by Mathematics, in Meeting Alhambra, ISAMA-BRIDGES Conference Proceedings 2003, ed. R. Sarhangi and C. Sequin, 393--399.
  49. Woolfit, Penelope. The Geometry of Asian Trousers. In Bridges Donos- tia: Proceedings 2007, pp. 427–430. Tarquin Publications, 2007.
  50. Yackel, C. A. Embroidering Polyhedra on Temari Balls. In Math+Art=X Boulder, CO Conference Proceedings 2005, pp. 183–187.
  51. Yackel, C. A. Marking a Physical Sphere with a Projected Platonic Solid. In Bridges Banff: Proceedings 2009, pp. 123–130. Tarquin Publications, 2009.
Weaving
  1. Akleman, Ergun; Chen, Jianer; Xing, Qing; Gross, Jonathan L. Cyclic plain-weaving on polygonal mesh surfaces with graph rotation systems. ACM Transactions on Graphics, Proceedings of ACM SIGGRAPH 2009 28(3) August 2009, Article No. 78.
  2. Chen, Yen-Lin; Akleman, Ergun; Chen, Jianer; Xing, Qing. Designing Biaxial Textile Weaving Patterns. Hyperseeing: Proceedings of ISAMA 2010, Summer 2010, 53–62.
  3. Clapham, C. R. J. The strength of a fabric. Bull. London Math. Soc. 26 (1994), no. 2, 127--131.
  4. Clapham, C. R. J. The bipartite tournament associated with a fabric. Discrete Math. 57 (1985), no. 1-2, 195--197.
  5. Clapham, C. R. J. When a three-way fabric hangs together. J. Combin. Theory Ser. B 38 (1985), no. 2, 190.
  6. Clapham, C. R. J. When a fabric hangs together. Bull. London Math. Soc. 12 (1980), no. 3, 161--164.
  7. Delaney, Cathy. When a Fabric Hangs Together. Ars Combinatoria 21-A (1986), 71--79.
  8. Enns, T. C. An efficient algorithm determining when a fabric hangs together. Geometriae Dedicata, 15 (1984), 259–260.
  9. Grünbaum, B.; Shephard, G. C. Satins and Twills: Introduction to the Geometry of Fabrics. Mathematics Magazine, vol.53, no. 3, May 1980, p. 139-161.
  10. Grünbaum, B.; Shephard, G. C. A catalogue of isonemal fabrics. Dis- crete Geometry and Convexity, Annals of the New York Academy of Sciences 440 (1985), 279–298.
  11. Grünbaum, B.; Shephard, G. C. An extension to the catalogue of isonemal fabrics. Discrete Math. 60 (1986), 155–192.
  12. Grünbaum, B.; Shephard, G. C. Isonemal fabrics. Amer. Math. Monthly 95 (1988), 5–30.
  13. Hoskins, J. A.; Thomas, R. S. D. The patterns of the isonemal two-colour two-way two-fold fabrics. Bull. Austral. Math. Soc. 44 (1991), no. 1, 33--43.
  14. Hoskins, J. A.; Hoskins, W. D. An algorithm for color factoring a matrix. Current trends in matrix theory (Auburn, Ala., 1986), 147--154, North-Holland, New York, 1987.
  15. Hoskins, J. A.; Stanton, R. G.; Street, A. P. The compound twillins: reflection at an element. Ars Combin. 17 (1984), 177--190.
  16. Hoskins, Janet A.; Street, Anne Penfold; Stanton, R. G. Binary interlacement arrays, and how to find them. Proceedings of the thirteenth Manitoba conference on numerical mathematics and computing (Winnipeg, Man., 1983). Congr. Numer. 42 (1984), 321--376.
  17. Hoskins, Janet A.; Praeger, Cheryl E.; Street, Anne Penfold. Balanced twills with bounded float length. Proceedings of the fourteenth Southeastern conference on combinatorics, graph theory and computing (Boca Raton, Fla., 1983). Congr. Numer. 40 (1983), 77--89.
  18. Hoskins, J. A. Binary interlacement arrays and structural cross-sections. Proceedings of the fourteenth Southeastern conference on combinatorics, graph theory and computing (Boca Raton, Fla., 1983). Congr. Numer. 40 (1983), 63--76.
  19. Hoskins, Janet A.; Praeger, Cheryl E.; Street, Anne Penfold. Twills with bounded float length. Bull. Austral. Math. Soc. 28 (1983), no. 2, 255--281.
  20. Hoskins, J. A.; Stanton, R. G.; Street, Anne Penfold. Enumerating the compound twillins. Congr. Numer. 38 (1983), 3--22.
  21. Hoskins, J. A.; Hoskins, W. D.; Street, Anne Penfold; Stanton, R. G. Some elementary isonemal binary matrices. Ars Combin. 13 (1982), 3--38.
  22. Hoskins, J. A. Factoring binary matrices: a weaver's approach. Combinatorial mathematics, IX (Brisbane, 1981), pp. 300--326, Lecture Notes in Math., 952, Springer, Berlin-New York, 1982.
  23. Hoskins, Janet A.; Hoskins, W. D. The solution of certain matrix equations arising from the structural analysis of woven fabrics. Ars Combin. 11 (1981), 51--59.
  24. Lucas, E. Application de l'Arithmétique à la Construction de l'Armure des Satins Réguliers, Paris, 1867.
  25. Lucas, E. Principii fondamentali della geometria dei tessute, L'Ingegneria Civile e le Arti Industriali, 6 (1880) 104--111, 113--115.
  26. Lucas, E. Les principes fondamentaux de la géometrie des tissus, Compte Rendu de L'Association Française fpour l'Avancement des Sciences, 40 (1911) 72--88.
  27. Oates-Williams, Sheila; Street, Anne Penfold. Universal fabrics. in Combinatorial Mathematics VIII: Proceedings of the Eighth Australian Conference on Combinatorial Mathematics Held at Deakin University, Geelong, Australia, August 2529, 1980, Lecture Notes in Mathematics 884, pp. 355–359. Springer, 1981.
  28. Pedersen, Jean J. Some isonemal fabrics on polyhedral surfaces. In The Geometric Vein: The Coxeter Festschrift, ed. by Chandler Davis, Branko Grünbaum, and F. A. Sherk, pp. 99–122, Springer-Verlag, 1981.
  29. Pedersen, Jean. Geometry: the unity of theory and practice. Math. Intelligencer 5 (1983), no. 4, 37--49.
  30. Philips, Tony. Inside-out Frieze Symmetries in Ancient Peruvian Weavings. AMS Feature Column October 2008.
  31. Roth, Richard L. The symmetry groups of periodic isonemal fabrics. Geom. Dedicata 48 (1993), 191–210.
  32. Roth, Richard L. Perfect colorings of isonemal fabrics using two colors. Geom. Dedicata 56 (1995), 307–326.
  33. Shorter, S.A. The Mathematical Theory of the Sateen Arrangement. The Mathematical Gazette. 10 (1920), p.92--97.
  34. Thomas, R.S.D. Isonemal prefabrics with only parallel axes of symmetry. Discrete Mathematics 309 (9), 6 May 2009, 2696--2711. arXiv version
  35. Thomas, R.S.D. Isonemal Prefabrics with Perpendicular Axes of Symmetry. available on the arXiv.
  36. Thomas, R.S.D. Isonemal Prefabrics with No Axes of Symmetry. available on the arXiv.
  37. Thomas, R.S.D. Perfect colourings of isonemal fabrics by thin striping. Bulletin of the Australian Mathematical Society, 83, No. 1, 63-86 (2011).
  38. Thomas, R.S.D. Perfect colourings of isonemal fabrics by thick striping. Bulletin of the Australian Mathematical Society,Volume 85, Issue 02 (April 2012), pp 325--349.
  39. Thomas, Robert S.D. Colouring Isonemal Fabrics with more than two Colours by Thick Striping. Contributions to Discrete Mathematics. Vol 8, No 1 (2013).
  40. Thomas, Robert S.D. Colouring Isonemal Fabrics with more than two Colours by Thin Striping. arXiv.
  41. Woods, H. J. The geometrical basis of pattern design. Part II—Nets and Sateens. Textile Institute of Manchester Journal, 26 (1935), T293–T308.
  42. Zelinka, Bohdan. Isonemality and mononemality of woven fabrics. Ap- plications of Mathematics, 28(3) 1983, 194–198.
  43. Zelinka, Bohdan. Symmetries of woven fabrics. Applications of Math- ematics, 29(1) 1984, 14–22.

Articles appearing in nonacademic publications

sarah-marie belcastro, Adventures in Mathematical Knitting. American Scientist, 101(2), March--April 2013, 124–133.

sarah-marie belcastro, You Do the Math. KnitNet, Winter 2001.

Brenda Dayne, Geek chic. Interweave Knits Fall 2003 pp.68--71+118. Now freely available online.

Mary Griffin, Wear Your Own Theory; A Beginner's Guide to Random Knitting. New Scientist, March 26, 1987, pp. 69--70.

Janice Hornicek, Color By Numbers. knitsimple, Spring/Summer 2006, pp. 22--25.

Debbie New, Celluar Automaton Knitting. Knitter's Magazine Number 49, Winter 1997, pp. 82--83.

Meg Swanson, Rita Buchanan, Möbius and Möbius II. Knitter's Magazine Winter 1991, pages 38 and 49.

Rachel Thomas, Career Interview: Fashion Designer, Plus magazine, Issue 53.

Margaret Wertheim, Crocheting the Hyperbolic Plane: An Interview with David Henderson and Daina Taimina. Cabinet: A Quarterly Magazine of Art & Culture Issue 16, Winter 2004. The article is available online here. (There are lots of articles that feature Daina's work, but this is the best one available online.)

(There must be more than just these. If you know of any other articles, either academic or non-, please send me references...)


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