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Reference Lists: Mathematical Articles on Fiber Arts


Everything Except Weaving: Alphabetical
Everything Except Weaving: Chronological

Weaving: Alphabetical
Weaving: Chronological

Articles appearing in nonacademic publications

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


Articles/chapters appearing in academic publications

Everything Except Weaving: Alphabetical
  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. Ashton, Ted. Fashioning Fine Fractals from Fiber, in Crafting by Concepts, A K Peters (2011), pp. 58--86. (Uses tatting and beading and cross-stitch to create fractals.)
  3. belcastro, s-m; Yackel, Carolyn. About Knitting. Math Horizons, November 2006.
  4. belcastro, sarah-marie. Every Topological Surface Can Be Knit: A Proof, Journal of Mathematics and the Arts 3(2) June 2009, 67–83.
  5. belcastro, sarah-marie. Generalized Helix Striping, in Crafting by Concepts, A K Peters (2011), pp. 28--49. (Focuses on knitting stripes.)
  6. belcastro, s-m; Yackel, Carolyn. Introduction (survey of the field), in Making Mathematics with Needlework, A K Peters (2007), pp. 1--10.
  7. belcastro, s-m; Szczepanski, Amy; Yackel, Carolyn. (K)not Cables, Braids, in Making Mathematics with Needlework, A K Peters (2007), pp. 118--134. Reprinted in Mitt. Dtsch. Math.-Ver. 16 (2008), no. 1, 26--34, and EMS newsletter, Issue 70, December 2008, pp. 19--25. (Focuses on knitting braid words.)
  8. belcastro, s-m. Only Two Knit Stitches Can Create a Torus, in Making Mathematics with Needlework, A K Peters (2007), pp. 53--68.
  9. belcastro, s-m; Yackel, Carolyn. The Seven-Colored Torus: mathematically interesting and nontrivial to construct, in Homage to a Pied Puzzler, ed. by Ed Pegg, Jr., Alan H. Schoen, and Tom Rodgers, A K Peters (2009), pp. 25--32. (Analysis of discretization for creating knitting and crochet patterns.)
  10. belcastro, s-m; Yackel, Carolyn. Stop Those Pants!, in Making Mathematics with Needlework, A K Peters (2007), pp. 154--176. (Focuses on knitting a hyperbolic surface.)
  11. 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)
  12. 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.
  13. 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.
  14. Cochrane, Paul. Knitting Maths. Mathematics Teaching September 1988, pp. 26--28.
  15. 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.)
  16. Curtis, S.A. An Application of Functional Programming: Quilting. in Trends in Functional Programming, edited by Stephen Gilmore, Vol. 2, Intellect, 2000.
  17. Curtis, S.A. Marble Mingling. Journal of Functional Programming, 16 (2006), issue 2, 129--136. (This has a passing mention of a quilting problem.)
  18. DeTemple, Duane. Reflection Borders for Patchwork Quilts. Mathematics Teacher, February 1986, 138–143.
  19. Fisher, Gwen. The Quaternions Quilts. FOCUS 25 (2005), no. 1, 4--5.
  20. 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.
  21. Fisher, Gwen; Mellor, Blake. Using tiling theory to generate angle weaves with beads. Journal of Mathematics and the Arts, Volume 6, Issue 4 (2012), 141--158.
  22. 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.
  23. Goldstine, Susan; Baker, Ellie. Building a better bracelet: wallpaper patterns in bead crochet. Journal of Mathematics and the Arts, Volume 6, Issue 1 (2012), 5--17.
  24. Goldstine, Susan. Fortunatus's Purse, in Making Mathematics with Needlework, A K Peters (2007), pp. 104--117. (Focuses on sewing and topology.)
  25. Goldstine, Susan. Perfectly Simple, in Crafting by Concepts, A K Peters (2011), pp. 140--148. (Focuses on crocheting square dissections.)
  26. Gould, Frank; Gould, S. Louise. Exploring the Projective Plane via Variations on the Faceted Octahedron. Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture (2012), pp. 507--508
  27. 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.
  28. 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.
  29. 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.
  30. 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.
  31. 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.
  32. 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.
  33. 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.
  34. 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.
  35. Harris, Mary. Mathematics and Fabrics. Mathematics Teaching 120 (1987), 43--45.
  36. Henderson, David W.; Taimina, Daina. Crocheting the hyperbolic plane. Math. Intelligencer 23 (2001), no. 2, 17--28. article (.pdf)
  37. Herrmann, Diane. Diaper Patterns in Needlepoint, in Crafting by Concepts, A K Peters (2011), pp. 87--109.
  38. Holden, Joshua. The Graph Theory of Blackwork Embroidery, in Making Mathematics with Needlework, A K Peters (2007), pp. 135--153.
  39. Holden, Joshua; Holden, Lana. Hyperbolic Tilings with Truly Hyperbolic Crochet Motifs. Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture (2014), pp. 405--408.
  40. Holden, Lana. Picking Up Stitches and Diophantine Equations, in Making Mathematics with Needlework, A K Peters (2007), pp. 29--39. (Focuses on knitting in different directions.)
  41. Igarashi, Yuki; Igarashi, Takeo; Suzuki, Hiromasa. Knitting a 3D Model. Computer Graphics Forum (Proceedings of Pacific Graphics 2008), 27(7), Oct. 2008, 1737–1743.
  42. Irvine, Veronika. Broadening the Palette for Bobbin Lace: A Combinatorial Approach. Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture (2012), pp. 191--198.
  43. Irvine, Veronika; Ruskey, Frank. Developing a mathematical model for bobbin lace. Journal of Mathematics and the Arts, Volume 8, Issue 3--4 (2014), 95--110.
  44. Irving, Claire. Making the Real Projective Plane. Math. Gazette November 2005, 417--423. (This focuses on knitted models.)
  45. 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
  46. 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. two versions of the paper.
  47. Liebscher, U., and Weber, M., Topological Studies of Textiles I. Fundamentals. Textiltechnik 30(1), 58--61 (1980).
  48. Liebscher, U., and Weber, M., Topological Studies of Textiles II. Applications and Examples. Textiltechnik 30(1), 30(3) 176--178 (1980).
  49. Mabbs, Louise. Fabric Sculpture—Jacobs Ladder. In Bridges London: Conference Proceedings 2006, pp. 561–568. Tarquin Publications, 2006.
  50. Mallos, James. Triangle-Strip Knitting. Hyperseeing: Proceedings of ISAMA 2010, Summer 2010, 111–116.
  51. Morton, H.R.; Grishanov, S. Doubly periodic textile patterns. J. Knot Theory Ramifications 18 (2009), 1597--1622.
  52. Osinga, Hinke M.; Krauskopf, Bernd. Crocheting the Lorenz manifold. The Mathematical Intelligencer 26 (2004), no. 4, 25--37. article
  53. Osinga, Hinke M.; Krauskopf, Bernd. Visualizing curvature on the Lorenz manifold. Journal of Mathematics and the Arts 1(2): 113-123, 2007. article
  54. Peters, Emily. A Knitted Cross-Cap, in Crafting by Concepts, A K Peters (2011), pp. 50--57.
  55. Pickett, Barbara Setsu. Sashiko: the Stitched Geometry of Rural Japan, in Bridges London: Conference Proceedings 2006 pp. 211–214. Tarquin Publications, 2006.
  56. Reid, Miles. The Knitting of Surfaces. Eureka - The Journal of the Archimedeans 34 (1971), pp21-26.
  57. Reid, Miles. Needlework Section: Knitting 2-Manifolds, 1. 2-Manifold 2, Autumn 1982, 9--14.
  58. Reid, Miles. Needlework Section: Knitting 2-Manifolds, 2: the Boy's Surface. 2-Manifold, (the next issue), 10--21.
  59. Ross, Joan. How to Make a Mobius Hat by Crocheting. Mathematics Teacher 78, (1985) 268--269.
  60. Shepherd, Mary D.; with belcastro, sarah-marie and Yackel, Carolyn. Group Actions in Cross-Stitch, in Crafting by Concepts, A K Peters (2011), pp. 110--139.
  61. Shepherd, Mary D. Groups, Symmetry and Other Explorations with Cross Stitch. Electronic Proceedings of the Missouri MAA, 2007 Meeting. article (.doc)
  62. Shepherd, Mary D. Symmetry Patterns in Cross Stitch, in Making Mathematics with Needlework, A K Peters (2007), pp. 69--89.
  63. Swanson, Irena. Quilting Semiregular Tessellations, in Crafting by Concepts, A K Peters (2011), pp. 186--232.
  64. Szczepanski, Amy. Knit Knit Revolution, in Crafting by Concepts, A K Peters (2011), pp. 1--27.
  65. Szczepanski, Amy. Quilted Möbius Band, in Making Mathematics with Needlework, A K Peters (2007), pp. 11--28.
  66. 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.)
  67. 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.)
  68. Wildstrom, D. Jacob. The Sierpinski Variations, in Making Mathematics with Needlework, A K Peters (2007), pp. 40--52. (Focuses on cellular automata in crochet.)
  69. Wildstrom, D. Jacob. Structural Qualities and Serial Construction of Tournament Braids. Proceedings of Bridges 2012: Mathematics, Music, Art, Architecture, Culture (2012), pp. 463--466. (The mathematics was motivated by constructing braids in crochet.)
  70. 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.
  71. Williams, Mary C. Quilts Inspired by Mathematics, in Meeting Alhambra, ISAMA-BRIDGES Conference Proceedings 2003, ed. R. Sarhangi and C. Sequin, 393--399.
  72. Yackel, C. A. Embroidering Polyhedra on Temari Balls. In Math+Art=X Boulder, CO Conference Proceedings 2005, pp. 183–187.
  73. Yackel, C. A. Marking a Physical Sphere with a Projected Platonic Solid. In Bridges Banff: Proceedings 2009, pp. 123–130. Tarquin Publications, 2009.
  74. Yackel, Carolyn. Socks with Algebraic Structure, in Making Mathematics with Needlework, A K Peters (2007), pp. 90--103. (Focuses on knitting and group theory.)
  75. Yackel, Carolyn; with belcastro, sarah-marie. Spherical Symmetries of Temari, in Crafting by Concepts, A K Peters (2011), pp. 149--185.
  76. Yuksel, Cem; Kaldor, Jonathan; James, Doug L.; Marschner, Steve. Stitch Meshes for Modeling Knitted Clothing with Yarn-level Detail. ACM Transactions on Graphics (Proc. of SIGGRAPH 2012), 31, 3, 37. project page
Everything Except Weaving: Chronological
Prior to 1990
1990--2000
2001--2005
2006--2009
2010--2014
Weaving: Alphabetical
  1. Ahmed, Abdalla G. M. AA Weaving. Proceedings of Bridges 2013: Mathematics, Music, Art, Architecture, Culture (2013), pp. 263--270.
  2. Ahmed, Abdalla G. M. Modular Duotone Weaving Design. Proceedings of Bridges 2014: Mathematics, Music, Art, Architecture, Culture (2014), pp. 27--34.
  3. 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.
  4. Burkholder, Douglas G. Brunnian Weavings. Proceedings of Bridges 2010: Mathematics, Music, Art, Architecture, Culture (2010), pp. 263--270.
  5. Chen, Yen-Lin; Akleman, Ergun; Chen, Jianer; Xing, Qing. Designing Biaxial Textile Weaving Patterns. Hyperseeing: Proceedings of ISAMA 2010, Summer 2010, 53–62.
  6. Clapham, C. R. J. The strength of a fabric. Bull. London Math. Soc. 26 (1994), no. 2, 127--131.
  7. Clapham, C. R. J. The bipartite tournament associated with a fabric. Discrete Math. 57 (1985), no. 1-2, 195--197.
  8. Clapham, C. R. J. When a three-way fabric hangs together. J. Combin. Theory Ser. B 38 (1985), no. 2, 190.
  9. Clapham, C. R. J. When a fabric hangs together. Bull. London Math. Soc. 12 (1980), no. 3, 161--164.
  10. Delaney, Cathy. When a Fabric Hangs Together. Ars Combinatoria 21-A (1986), 71--79.
  11. Enns, T. C. An efficient algorithm determining when a fabric hangs together. Geometriae Dedicata, 15 (1984), 259–260.
  12. 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.
  13. Grünbaum, B.; Shephard, G. C. A catalogue of isonemal fabrics. Discrete Geometry and Convexity, Annals of the New York Academy of Sciences 440 (1985), 279–298.
  14. Grünbaum, B.; Shephard, G. C. An extension to the catalogue of isonemal fabrics. Discrete Math. 60 (1986), 155–192.
  15. Grünbaum, B.; Shephard, G. C. Isonemal fabrics. Amer. Math. Monthly 95 (1988), 5–30.
  16. 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.
  17. 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.
  18. Hoskins, J. A.; Stanton, R. G.; Street, A. P. The compound twillins: reflection at an element. Ars Combin. 17 (1984), 177--190.
  19. 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.
  20. 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.
  21. 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.
  22. Hoskins, Janet A.; Praeger, Cheryl E.; Street, Anne Penfold. Twills with bounded float length. Bull. Austral. Math. Soc. 28 (1983), no. 2, 255--281.
  23. Hoskins, J. A.; Stanton, R. G.; Street, Anne Penfold. Enumerating the compound twillins. Congr. Numer. 38 (1983), 3--22.
  24. Hoskins, J. A.; Hoskins, W. D.; Street, Anne Penfold; Stanton, R. G. Some elementary isonemal binary matrices. Ars Combin. 13 (1982), 3--38.
  25. Hoskins, J. A. Factoring binary matrices: a weaver's approach. in Combinatorial mathematics, IX (Brisbane, 1981), pp. 300--326, Lecture Notes in Math., 952, Springer, Berlin-New York, 1982.
  26. 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.
  27. Lucas, E. Application de l'Arithmétique à la Construction de l'Armure des Satins Réguliers, Paris, 1867.
  28. Lucas, E. Principii fondamentali della geometria dei tessute, L'Ingegneria Civile e le Arti Industriali, 6 (1880) 104--111, 113--115.
  29. 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.
  30. 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.
  31. 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.
  32. Pedersen, Jean. Geometry: the unity of theory and practice. Math. Intelligencer 5 (1983), no. 4, 37--49.
  33. Philips, Tony. Inside-out Frieze Symmetries in Ancient Peruvian Weavings. AMS Feature Column October 2008.
  34. Roth, Richard L. The symmetry groups of periodic isonemal fabrics. Geom. Dedicata 48 (1993), 191–210.
  35. Roth, Richard L. Perfect colorings of isonemal fabrics using two colors. Geom. Dedicata 56 (1995), 307–326.
  36. Shorter, S.A. The Mathematical Theory of the Sateen Arrangement. The Mathematical Gazette. 10 (1920), p.92--97.
  37. Thomas, R.S.D. Isonemal prefabrics with only parallel axes of symmetry. Discrete Mathematics 309 (9), 6 May 2009, 2696--2711. arXiv version
  38. Thomas, R.S.D. Isonemal Prefabrics with Perpendicular Axes of Symmetry. Utilitas Mathematica, 82 (2010), 33--70. arXiv version.
  39. Thomas, R.S.D. Isonemal Prefabrics with No Axes of Symmetry. Discrete Mathematics 310 (2010), 1307--1324. arXiv version.
  40. Thomas, R.S.D. Perfect colourings of isonemal fabrics by thin striping. Bulletin of the Australian Mathematical Society, 83, No. 1, 63-86 (2011).
  41. 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.
  42. Thomas, Robert S.D. Colouring Isonemal Fabrics with more than two Colours by Thick Striping. Contributions to Discrete Mathematics. Vol 8, No 1 (2013).
  43. Thomas, Robert S.D. Colouring Isonemal Fabrics with more than two Colours by Thin Striping. Contributions to Discrete Mathematics. Vol 9, No 2 (2014).
  44. Woods, H. J. The geometrical basis of pattern design. Part II—Nets and Sateens. Textile Institute of Manchester Journal, 26 (1935), T293–T308.
  45. Zelinka, Bohdan. Isonemality and mononemality of woven fabrics. Applications of Mathematics, 28(3) 1983, 194–198.
  46. Zelinka, Bohdan. Symmetries of woven fabrics. Applications of Mathematics, 29(1) 1984, 14–22.
Weaving: Chronological
Prior to 1980
1980--1984
1985--1989
1990--2000
2001--2010
2011--2014

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.)


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