Navajo Rug Weaver

Cartesian Graph


Navajo sand painting offers many good examples of four-fold symmetry. These are used in healing ceremonies. A medicine man ("hataalii") completes the drawing in one day, using colored powder such as crushed stone. The painting is brushed away later that night, along with the illness.


In the Navajo religion, the hataalii heals through the balance of forces. Sand paintings often use reflection symmetry to show these paired forces. Some of these structures are similar to a Cartesian graph. Navajo tradition does not permit photos of sand paintings, so at left we have shown a Navajo rug based on a sand painting. Here we see four human figures. Figures on the horizontal axis are hunched over with back packs. Those on the vertical axis have straight backs.  As a Cartesian graph:

+X = Right-side up figure with backpack

-X = Upside-down figure with backpack

+Y = White straight figure

-Y = Dark straight figure