Originally published in the International Study Group on Ethnomathematics (ISGEm) Newsletter, Volume 13, Number 2, May 1998. Located at: http://web.nmsu.edu/~pscott/isgem132.htm. Article reproduced 2003 with permission of the ISGEm Newsletter editor for use in the Ethnomathematics Digital Library (www.ethnomath.org) developed by Pacific Resources for Education and Learning (www.prel.org).

Symmetry Patterns of Ute Beadwork

Cathy A. Barkley
Mesa State College, Grand Junction, Colorado USA

Funding for this study was provided by a grant from the Council Of Chairs Research Grant, Mesa State College.

The "day-to-day" activities of people, both past and present, involve a large amount of mathematical applications. Most of the applications have not been considered as mathematics because they do not involve lengthy calculations or formulas. However, six universal activities have been identified (Bishop, 1988) as mathematical practices by any culture; these activities are counting, measuring, designing, locating, explaining, and playing.

Designing, or organizing shapes, patterns, and colors, on surfaces is one way that people have used one of these basic mathematical practices. The practicality of an item is not enhanced by the creation of a design on the item. A basket, for example, is no more or less useful for carrying if it is a plain, utilitarian item or if it has an intricately patterned design woven into it. But all people seem to share a need for, and love of, creative designs on their items used for everyday living purposes.

The group of indigenous peoples in the Rocky Mountains beyond Denver and extending into central Utah were know as the Blue Sky people or the Yuuttaa (Utes). Their origin is unclear but Spanish records first mention the Utes in 1626. Their native language belongs to a language group known as Uto-Aztecan; an ancient version of this language is still spoken by some Aztecs in central Mexico, so perhaps their ancestors fled from the warfare and disruption of the Aztec world. The Utes were considered a relatively small tribe, never numbering more than 5,000 to 10,000 at any single time. They were fiercely independent and lived in relative isolation by preference.

Every household item, including utensils, clothing, and weapons, had to be made by hand or obtained by trading. The Utes learned that leather was a good trade commodity and they soon became known for their fine quality tanned deer and elk hides. Leather trade goods from the Utes included moccasins, buckskin shirts, leggings, arm gauntlets, pipe bags, and quivers. Spanish and American settlers provided a ready market for the finely tanned garments made by the Utes. Settlers needed clothing and shelter materials that could be fashioned from the tanned hides. Some of the leather products were even shipped to Europe.

Beautiful and intricate beadwork was incorporated into the leather products made by the Utes. The Utes were a nomadic group of people and all household/living items had to be moved from place to place. Thus, their need for artistic decoration and expression manifested itself through their everyday articles of use. Decoration and pattern were found in carrying pouches, knife cases, moccasins, tobacco pouches, etc. Early decorations were done with quills from the porcupine.

After glass trade beads arrived in the New World, the Iroquois Indians became specialists in intricate patterns and ornamental designs on clothing. The beadwork was a natural adaptation of the quill work produced earlier by Native Americans. Large areas of solid quill work resembling a separate fabric were replaced by solid areas of beading to achieve the same effect. Thin bands of quill work gave way to delicate bands of beading and stitching.

Glass beads brought by the Europeans were not valued for their monetary or exchange value, but rather for their symbolic value related to the existing religious and ideological frameworks of the natives. Many of the Iroquois nation words for glass, mirror, and metal are linked with words for seeing, divining, and the soul. So the combination of the glass beads with totem and ritual passage designs on clothing produced many items of exquisite beadwork. Artifacts can be dated in part by the type of beads used on the articles. During the early l800's, the Venetian "pony beads" (so-called because they were packed into the back country by ponies) were the common beads imported into the New World. They were primarily light colors of white and sky blue. Other light colored beads were available but not in such large quantities. Most of the beadwork done during this time had a light or white background and the tradition continued even as other beads became more popular. Around 1840, the smaller, more delicate "seed beads" were available for trade and more delicate beadwork became popular. This type of beadwork was very popular with the European settlers and beadwork as trade experienced a huge increase. By 1860, beading was extremely popular and the Bohemian beads with their darker colors and bluish tinge were imported and traded to the Indians for their trade beadwork. By 1870, translucent beads were available, and by 1885, glass beads colored silver or gold were brought from Europe. The influx of new types of beads continued to fuel the trade beadwork market. However, like all trends, beadwork was waning, and by 1900, the great beadwork period was finished. Beading continued into the early part of the century, but it never experienced the great popularity it had during the second half of the 1800's.

Plains tribes learned the beadwork craft from trade with the Indians of the northeastern United States, particularly the Iroquois nation. The Plains tribes then traded with the Utes of Colorado and they began to make beautifully beaded trade goods. Earliest evidence of Ute beadwork is 1860; by 1930, beadwork had gone out of fashion among Europeans and Ute beadwork was to become almost a lost art. Much of the Ute beadwork found in museums and private collections was made strictly for the purpose of trade and was never intended to be used by the Utes themselves. Unlike the eastern tribes, both the Plains tribes and the Utes used straight line geometry in their beadwork designs. All floral, irregular designs were done strictly for trade to the Europeans. The evolution of beadwork from quill work is evident in the straight even designs used by the Utes. Backgrounds are always a light color, usually white. Early simple forms include blocks, crosses, and triangles. Triangles, especially equilateral, isosceles, and right angle triangles, are all popular designs. Tall, elegant triangles, and congruent triangles that reflect one another, are found over and over again in the beadwork. Delicate designs using a basic rectangle were often embellished with forks and terraces to form new, similar designs. As the beads replaced the use of quills, designs evolved that used more rounded edges and circular patterns. Many rose floral patterns are found in Ute beadwork designs from the turn of the century.

This study is a brief examination of Ute beadwork and designs. Many fine examples of Ute beadwork are in existence today and there are several items in the collection of the Denver Art Museum, Denver, Colorado. This study examined Ute beadwork articles in two locations: The Museum of Western Colorado, Grand Junction, Colorado, and The Ute Indian Museum, Montrose, Colorado. It is not meant to be an exhaustive study, and with the small number of items examined (119), no conclusions can be drawn about the frequency of patterns used throughout the Ute nations. We were interested in comparing the number of symmetry patterns found in Ute beadwork, and their frequency, with the previously done study of Woodland Indian bead designs.

The discipline of mathematics includes the study of patterns. Patterns can be found everywhere in nature. Often these patterns are copied and adapted by humans to enhance their world. Nowhere is this more evident than in the study of designs by indigenous peoples. The study of mathematical ideas of native or indigenous peoples is referred to as ethnomathematics. One particular aspect of mathematics evident in all cultures is the use of symmetry in strip patterns. These patterns are evident in the use of beading designs done by the Ute Indians.

The structure or balance of a design is described by mathematicians as an isometry or rigid motion. For various figures, there are different motions that will move the figures about the plane but are unchanged except for the new orientation. Because the space in the plane is limited (strip design), there are a limited number of motions that are possible. There are exactly four types of rigid motions possible: a) translation or slide, moving the figure forward repeatedly; b) reflection, mirror image in a vertical, horizontal, or combination line; c) rotation, movement around a fixed center point through 180 degrees; d) glide reflection, a movement that translates the figure and then reflects it. Every strip pattern can be made from one of these four types of rigid motion or a combination of them. But the resulting patterns are limited in number.

The different types of isometries that result are called symmetry groups. For any strip pattern, its symmetries will be classified into one of seven distinctive groups. To refer to the groups, a system for classification was developed by crystallographers who identified three-dimensional patterns found in crystals. The classification system uses a four-character symbol for each strip pattern. The classification system uses this coding scheme:

Character One: If the group contains a translation (which they all do), code p.

Character Two: This indicates a vertical reflection symmetry.
Code m if it has a line of vertical reflection symmetry.
Code 1 if it does not.

Character Three: This indicates a horizontal/glide symmetry.
Code m if it has a horizontal line of symmetry.
Code a if it has a glide reflection but not horizontal line.
Otherwise, code 1.

Character Four: This indicates a 180 degree rotation.
Code 2 if it has a point of 180 degree rotation symmetry.
Code 1 if it does not.

This four-character classification system gives complete information about the symmetry groups of any strip pattern. Using this classification system, we examined and coded several articles from the museums that were examples of Ute beadwork strip patterns. We were comparing the seven types of symmetry strip patterns and their frequency among the beadwork designs. We have examined 33 items from the Museum of Western Colorado in Grand Junction, Colorado. Of these items, 24 represented true strip beadwork specimens. From the Ute Museum in Montrose, Colorado, we examined 86 items, with 72 showing examples of strip patterns. Some of the items, such as the headstall owned by Chipeta, had more than one type of strip pattern represented.

Table 1 summarizes the frequency of symmetry patterns found by Nishimoto and Berken in the analysis of Wisconsin Indian beadwork (1996).

Table 2 summarizes the frequencies of patterns found in the current Ute beadwork study by Barkley and Osborn (1997).

The most common pattern found in both studies is the pmm2, the pattern that exhibits the most symmetrically balanced elements of all the patterns. This pattern has horizontal, vertical, and rotational symmetry. For this pattern to occur, the geometric figures used in the design must have specific symmetries. With the small sample used in the Ute study, it is difficult to detect any other similarities to the Woodland study.

The mathematics imbedded within the artwork of the Ute beadwork is representative of the area of Ethnomathematics study. These Native American artisans had no formal training in classical Euclidean geometry, but it is clear that they had an understanding of basic geometry elements. These beautiful beaded treasures are clearly not done by random design, but rather by people who carefully followed some specific guidelines of geometric principles. It is hoped by the researchers that more study of the Ute beadwork designs can be done during Summer 1998. More examples of this authentic art may enable more specific patterns to emerge.

References

Bishop, A. (1988). Mathematical Enculturation, Dordrecht, North Holland: Kluwer.
Nishimoto, K. & Berken, B. (1996). Symmetry patterns of the Wisconsin Woodland Indians. ISGEm Newsletter, 12(1), 6-8.