CarpetMath: exploring mathematical aspects of Turkmen carpets

Abstract

The exhibition, ‘For Tent and Trade: Masterpieces of Turkmen Weaving’, organized by the M.H. de Young Memorial Museum of the Fine Arts Museums of San Francisco offered new opportunities to explore the aspects of mathematics in Turkmen rugs. We present educational resources developed for the Education Department of the Fine Arts Museums of San Francisco which were initially designed for a teacher-training workshop held in conjunction with this exhibition. Following an introduction to the Turkmen people and their historic dependence on pastoralism, we explore the mathematical aspects of Turkmen carpets. These explorations address various topics within the curriculum and are suggested for different age groups: counting units and fractions (K-5); symmetry and geometry (grades 6–8) and algorithms (high school).

Keywords:

• carpet
• weaving
• geometry
• Islamic pattern
• symmetry
• Turkmen
• Central Asia

AMS Subject Classifications::

• 97-01
• 51-01
• 00A06

Acknowledgements

The author wishes to acknowledge the collegial cooperation of the M.H. de Young Memorial Museum of the Fine Arts Museums of San Francisco for providing curatorial support, photographic materials and rights for reproduction for this article. Inspiration for this project came from the Education Department, with special thanks to Emily K.D. Jennings for inviting my participation in the development of teacher-training materials in January 2008. Thanks also to Susan Grinols, Director, Photo Services and Imaging, and Diane Mott, Curator, The Caroline and H. McCoy Jones Department of Textile Arts.

Notes

Notes

1. The exhibition was on view at the M.H. de Young Memorial Museum in San Francisco from 15 December 2007 to 1 September 2008. Diane Mott, Curator of the Caroline and H. McCoy Jones Department of Textile Arts at the de Young Museum, served as curator for this exhibition. Works on view included gifts from H. McCoy Jones, Caroline McCoy Jones, George and Marie Hecksher, and Wolfgang and Gisela Wiedersperg, principal donors to the carpet collection at the de Young.

2. For images of Turkmen carpets, presented with structural analyses, see 12,16,19,25,26. Moshkova 17 relates Central Asian carpets to cultures and peoples, providing ethnographic attributions. Key early acquisitions in the West are those of Russian collections, for which see 26.

3. For symmetry as expressed in Oriental carpets, see Bier 3,4.

4. 3: http://mathforum.org/geometry/rugs/carpets/knots.html.

5. For border patterns, see 3: http://mathforum.org/geometry/rugs/symmetry/bp.html; for field patterns, see 3: http://mathforum.org/geometry/rugs/symmetry/fp.html.

6. For more detailed discussion of border patterns as line symmetries or friezes, see 21.

7. Definitions for each term are listed in the glossary in 3: http://mathforum.org/geometry/rugs/resources/glossary.html

8. For an exploration of Islamic arts and geometry in other media, see 8–10,18,22,27.