##
Gwen Fisher

*
"Symmetry 1"*

Gouache (opaque watercolor) and ink on paper. Image size
6" by 8.5". Completed in 2004.

Gwen L. Fisher is in her fourth year as an Assistant Professor of
Mathematics at California Polytechnic State University, San Luis Obispo.
She received her M.A. in Mathematics at the University of California, Santa
Barbara, and her Ph.D. in Curriculum and Instruction, Mathematics Education
at the University of Wisconsin, Madison. Her areas of research include
assessment of students' understandings of mathematics and mathematical art.
*Symmetry 1* is one piece of a larger body of work on the seven border groups
and the 17 wallpaper symmetries groups. She spoke about this
work at the meeting in her talk, "Teaching Students to Illustrate Border and Wallpaper
Patterns".

"I began *Symmetry 1* with an isometric (equilateral triangle) grid lightly
drawn in pencil. Then, I used black micron pens in various sizes to draw the
designs in freehand, which were enhanced with blue and green gouache. I use
gouache and ink because I can create artwork with a high amount of detail.
After the design was mostly drawn, I erased the pencil grid.

"*Symmetry 1* shows representations of five of the 17 wallpaper symmetry
groups. All 17 of the wallpaper groups can be illustrated with the use of
just two grids: the standard square grid and the isometric grid. Symmetry 1
includes the five symmetry groups that are subgroups of the symmetries of
the isometric grid but not of the square grid, namely P3, P3M1, P31M, P6,
and P6M. This work was inspired by M. C. Escher who wrote, 'In Regular
Division of the Plane 1, a process of development takes place. The viewer is
invited to follow this by going through the phases, one after the other, of
a band of images that fills the image plane through stages of growth and
metamorphosis.' Similarly, *Symmetry 1* attempts to guide the viewer through
stages of metamorphosis from one symmetry pattern to another."

For inquiries contact Gwen Fisher at glfisher@calpoly.edu.