ABSTRACT
Every society exhibits one or more “design themes”—geometric abstractions that are manifested in myriad concrete forms. Fourfold symmetry is a deep design theme in many Native-American cultures. is essay will describe how fourfold (and related bifold) symmetry is used as an organizing principle for religion, society, and technology in many Native-American cultures. It will explore the ways in which this design theme has emerged through native structures analogous to the Cartesian coordinate system, and describe some so ware applications that help teachers make use of this ethnomathematics in the classroom.
