By combining culture, skill, and mathematics, Navajo basket weavers create works of art.  (Kirstin Roundy contributed to this story)

The bold, geometric design of the Navajo ceremonial basket is captivating. Two rows of alternating black and white triangles straddle a ribbon of red. It is thought, by some, that the center is the beginning of the world, the red band is the sun's rays, and the triangles represent sacred mountains. Instilled with cultural significance, the design transcends the physical world and captures both the life course of an individual and that of the Navajo people.

It takes Navajo basket weaver Anderson Black days to weave a basket with the symmetrical shapes, each perfectly equidistant from the next. It can take much longer to gather all of the materials to make the basket. "I believe it's not made for everyone. All this patience...doing the same thing over and over everyday." Black, who currently lives in North Salt Lake, has been making baskets since he was ten years old. "It means a lot to me...it never gets old."

When starting a basket, Black coils bundles of sumac branches (rods) and then wraps them with strips of dyed split sumac (laces). As he weaves in the ceremonial pattern, he counts the number of times he wraps the lace around the rods. "The size and the width of my lace...they really do matter. Because once when I start counting it has to be all the same size and about the same amount of wrap. ...It's hard to try and keep it the same size."

Jim Barta, an associate professor of elementary education at Utah State University, says basket weavers are master mathematicians, a fact that often goes unappreciated.

As an ethnomathematician, Barta studies the relationship between mathematics and cultural identity. His training helped him realize that the structured ways in which math is taught in most schools doesn't necessarily resonate with people from different cultures. To help Native Americans understand the relevance of math, he uncovers the mathematical concepts that exist in their cultures, like basket weaving.

Early in his career, Barta was asked to make a basket with rope and yarn while at an educational conference. The instructor then demonstrated that the diameter of each coil of the basket graphed against the number of coils yields a linear function. The mathematical equation offers a way to calculate the diameter of each coil in a basket without actually having to build one.

"It was very profound because I had heard about linear functions before. But I had never really thought of them as illustrated in real objects," says Barta "When I saw that the basis for somebody conjuring up the idea of a linear function exists in real-life, that created a whole new meaning for me."

Barta says while Black is weaving, he is doing mathematics and geometry in his head. "[Black] has to be precise because the basket has to have the 'right' number of shapes to be traditional." While making a ceremonial basket, Black uses the tips of the black triangles as markers to maintain the proper spacing within the design. These markers "allow him to measure and place the other shapes," says Barta. "He also has to calculate the scaling of each shape to make sure they fit."

Black explains that since the basket is bowl-shaped, he also has to adjust his design to create a circular shape with expanding sides. "The basket is round so that design that you put in there kind of spreads out. You know how you inflate a balloon with a design, how it [that design] expands out...That's how it [a basket] works, too."

Math also exists within the design itself. In a traditional Navajo basket, triangles rotate and slide as they move around the basket. Also, the black and white triangles are often mirror images of each other. This is an example of transformational, or motion, geometry, says Barta.

The positions and shapes of the designs that surround the ceremonial Navajo basket tell the stories that explain the Navajo people and their culture. "When people come to me...some of them ask, 'When did you get started on the baskets?'" says Black. "My grandpa says it came with us from the beginning, from the creation. It's in our songs; it's in our prayers."

Weaving A Revolution: A Celebration of Contemporary Navajo Baskets is on exhibit at the Natural History Museum of Utah from now until April 28.

Anderson Black (Copyright NHMU)