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] 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)

[4] 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.

[5] Cochrane, Paul. Knitting Maths. Mathematics Teaching September 1988, pp. 26--28.

[6] 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.)

[7] Curtis, S.A. An Application of Functional Programming: Quilting. in Trends in Functional Programming, edited by Stephen Gilmore,
Vol. 2, Intellect, 2000.

[8] Curtis, S.A. Marble Mingling. Journal of Functional Programming, 16 ( 2006), issue 2, 129--136. (This has a passing mention of a quilting problem.)

[9] Fisher, Gwen. The Quaternions Quilts. FOCUS 25 (2005), no. 1, 4--5.

[10] 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.

[11] 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.

[12] 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.

[13] Harris, Mary. Mathematics and Fabrics. Mathematics Teaching 120 (1987), 43--45.

[14] Henderson, David W.; Taimina, Daina. Crocheting the hyperbolic plane. Math. Intelligencer 23 (2001), no. 2, 17--28. article (.pdf)

[15] Irving, Claire. Making the Real Projective Plane. Math. Gazette November 2005, 417--423.

[16] 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

[17] Osinga, Hinke M.; Krauskopf, Bernd. Crocheting the Lorenz manifold. The Mathematical Intelligencer 26 (2004), no. 4, 25--37. article

[18] Osinga, Hinke M.; Krauskopf, Bernd. Visualizing curvature on the Lorenz manifold. Journal of Mathematics and the Arts 1(2): 113-123, 2007. article

[19] Reid, Miles. The Knitting of Surfaces. Eureka - The Journal of the Archimedeans 34 (1971), pp21-26.

[20] Ross, Joan. How to Make a Mobius Hat by Crocheting. Mathematics Teacher 78, (1985) 268 - 269.

[21] Shepherd, Mary D. Groups, Symmetry and Other Explorations with Cross Stitch. Electronic Proceedings of the Missouri MAA, 2007 Meeting. article (.doc)

[22] 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.)

[23] 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.

[24] Williams, Mary C. Quilts Inspired by Mathematics, in Meeting Alhambra, ISAMA-BRIDGES Conference Proceedings 2003, ed. R. Sarhangi and C. Sequin, 393--399.

Weaving

[1] Clapham, C. R. J. The strength of a fabric. Bull. London Math. Soc. 26 (1994), no. 2, 127--131.

[2] Clapham, C. R. J. The bipartite tournament associated with a fabric. Discrete Math. 57 (1985), no. 1-2, 195--197.

[3] Clapham, C. R. J. When a three-way fabric hangs together. J. Combin. Theory Ser. B 38 (1985), no. 2, 190.

[4] Clapham, C. R. J. When a fabric hangs together. Bull. London Math. Soc. 12 (1980), no. 3, 161--164.

[5] Delaney, Cathy. When a Fabric Hangs Together. Ars Combinatoria 21-A (1986), 71--79.

[6] Grunbaum, B.; Shephard, G. C. Satins and Twills: Introduction to the Geometry of Fabrics. Mathematics Magazine, vol.53, no. 3, May 1980, p. 139-161.

[7] 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.

[8] 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.

[9] Hoskins, J. A.; Stanton, R. G.; Street, A. P. The compound twillins: reflection at an element. Ars Combin. 17 (1984), 177--190.

[10] 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.

[11] 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.

[12] 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.

[13] Hoskins, Janet A.; Praeger, Cheryl E.; Street, Anne Penfold. Twills with bounded float length. Bull. Austral. Math. Soc. 28 (1983), no. 2, 255--281.

[14] Hoskins, J. A.; Stanton, R. G.; Street, Anne Penfold. Enumerating the compound twillins. Congr. Numer. 38 (1983), 3--22.

[16] Hoskins, J. A.; Hoskins, W. D.; Street, Anne Penfold; Stanton, R. G. Some elementary isonemal binary matrices. Ars Combin. 13 (1982), 3--38.

[18] 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.

[19] 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.

[20] Lucas, E. Application de l'Arithm\'{e}tique \`{a} la Construction de l'Armure des Satins R\'{e}guliers, Paris, 1867.

[21] Lucas, E. Principii fondamentali della geometria dei tessute, L'Ingegneria Civile e le Arti Industriali, 6 (1880) 104--111, 113--115.

[22] Lucas, E. Les principes fondamentaux de la g\'{e}ometrie des tissus, Compte Rendu de L'Association Fran\c{c}aise fpour l'Avancement des Sciences, 40 (1911) 72--88.

[23] Pedersen, Jean. Geometry: the unity of theory and practice. Math. Intelligencer 5 (1983), no. 4, 37--49.

[24] Philips, Tony. Inside-out Frieze Symmetries in Ancient Peruvian Weavings. AMS Feature Column October 2008.

[25] Pedersen, Jean J. Some isonemal fabrics on polyhedral surfaces. The geometric vein, pp. 99--122, Springer, New York-Berlin, 1981.

[26] Shorter, S.A. The Mathematical Theory of the Sateen Arrangement. The Mathematical Gazette. 10, 1920, p.92-97.

[27] Thomas, R.S.D. Isonemal prefabrics with only parallel axes of symmetry. Discrete Mathematics 309 (9), 6 May 2009, 2696--2711. arXiv version

[28] Thomas, R.S.D. Isonemal Prefabrics with Perpendicular Axes of Symmetry. available on the arXiv.

[29] Thomas, R.S.D. Isonemal Prefabrics with No Axes of Symmetry. available on the arXiv.

Articles appearing in nonacademic publications

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 Griffith, 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.

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 which 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...)