Mathematical Experiments with African Sona Designs
by Darrah Chavey, Beloit College
Bridges Banff: Proceedings of the 12th Annual Bridges Conference, 2009.
Abstract: The sona designs of the Chokwe people of Angola/Congo are a particularly attractive form of “mirror curves,” which can be visualized as a curve drawn through a lattice of dots, bouncing off the edges of the lattice and off “mirrors” placed between some of those dots. Most such designs are drawn as a single, uninterrupted line, and most contain symmetries of some type. The mathematics of the designs reflect issues of common divisors of numbers, Eulerian cycles, and symmetry groups. This talk will investigate ways to use a sona-drawing program to investigate these topics with students from middle school through college, with particular emphasis on the experimental discovery of mathematical facts. The sona program developed by the author is cross-platform and free.
This paper was published in the conference proceedings as a shortened 4 page paper, and included on the conference CD as the full 8 page paper. Both papers are available here for download. Because the two papers include essentially all of the same graphics, there is no real difference in the download size of the papers.