Basketry and mathematics
Basketry is an intricate craft that involves weaving materials into various shapes and forms, producing functional and artistic items. It encompasses different weaving techniques, such as coiling, wicker, twining, and plaiting, each with unique characteristics based on the materials used and the methods applied. Coiled baskets utilize a thick cord as a foundation, while flexible strips wrap around to form the structure. Wicker weaving involves stiffer fibers and allows for complex surface patterns achieved through the interlacing of weft and foundation materials.
The mathematical principles underlying basketry are notable, particularly in how different weaves can generate various three-dimensional shapes. For instance, twining and wicker techniques often produce ruled surfaces like cylinders and prisms, while more flexible methods can create spherical forms. This connection between basketry and mathematics highlights the creativity involved in selecting appropriate techniques to realize specific artistic visions. Additionally, the craft reflects cultural significance across diverse communities, showcasing the rich traditions and practices associated with weaving. Overall, basketry serves as a fascinating intersection of art, culture, and mathematics, inviting exploration into its techniques and forms.
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Basketry and mathematics
Summary: Basket shapes and patterns are created by varying the weave.
Weaves
There are several types of basket weaves, each with infinitely many possible patterns. Coiled baskets are made with two types of fiber—one thick, and one soft and pliable. The thick cord or vine forms the coil. Flat, pliable strips of materials such as grass or fabric are wound a number of times around the cord, then a number of times around its previous row or several rows in the coil, connecting the rows. Craftspeople can change patterns and shapes of baskets by varying these weave numbers. Wicker is a type of basket weave consisting of relatively stiff fibers of two types. One material, the foundation, is completely rigid, and the other, the weft, is more pliable. The pattern of individual weft fibers going over and under the foundation spokes determines the look of the basket’s surface. Such patterns can become very complex. Weft fibers are often soaked to make them soft during weaving.
Twining also requires rigid foundation fibers and pliable weft. Several strands of pliable fiber—usually two—go around a foundation spike on either side, cross or twist in the middle, then go around the next spike. Twining patterns are created by changing the number of wefts or formulas of skipping spikes, and introducing braiding between spikes.
Plaited baskets consist of pliable fibers woven over and under one another, typically at right angles. This weave is very similar to how woven textiles are made, and some historians believe that textiles originated from this type of basket. Formulas—whose variables are the number of fibers that go over and under in each row—determine the pattern.
The physical properties of baskets are determined by the weave, the materials, and the pattern. Wicker baskets can be very sturdy, and wicker has been used in making fences, houses, and furniture like baby cradles.
Shapes
Baskets take a variety of three-dimensional shapes, such as cylinders, cubes, and prisms. Properties of weaving often determine the shape. For example, the stiff foundation fibers of twined or wicker baskets are usually straight lines, which only allows so-called ruled surfaces. By definition in analytic geometry, ruled surfaces are generated by straight lines. Cylinders, prisms, and cones are ruled surfaces and can be made by wicker. Spheres cannot be made out of straight lines, but spherical baskets are made by coiling, plaiting, or using bendable foundations in wicker and twining. Mathematicians and mathematical artists who use basket weaving to create striking sculptured models of complex surfaces have to select appropriate weaving techniques for their projects.
Bibliography
Gerdes, Paulus. African Basketry: A Gallery of Twill-Plaited Designs and Patterns. NP: Lulu Publishing, 2008.
University of East Anglia. “Basket Weaving May Have Taught Humans to Count.” ScienceDaily (June 8, 2009). http://www.sciencedaily.com /releases/2009/06/090604222534.htm.
Zaslavsky, Claudia. Multicultural Mathematics: Interdisciplinary Cooperative-Learning Activities. Portland, ME: Walch Education, 1993.