Wing L. Mui
During the day, I teach geometry to children. When I’m done with that, I make needlework samplers. I am fascinated by the form of traditional needlework samplers, where the artist stitches or embroiders (often exhaustive) collections of symbols and geometric patterns on fabric to demonstrate their skill. But I am also frustrated that the samplers often don’t intend to communicate anything else. So I design patterns based on these traditional forms and use them to intentionally enumerate, demonstrate, or celebrate mathematics.
This blackwork sampler showcases all the possible symmetries that can be stitched on Aida fabric. The outline is the smallest simple perfect squared square, which is 112 stitches on each side and divided into 21 subsquares. The largest square is filled by patterns representing the 7 frieze groups. The 2 smallest squares contain the empty set and a point (a French knot). The last 18 squares contain the 12 wallpaper groups and 6 rosette groups without 3-fold symmetry. Some of the patterns are based on historic designs, though most are original.
This piece was inspired by Susan Goldstine’s challenge for a patient reader to crochet a simple perfect squared sqaure in her chapter in Crafting by Concepts, edited by belcastro and Yackel.