Bridges 2024 Exhibition of Mathematical Art, Craft, and Design

# Stephen M. Gagola, Jr.

## Artists

## Statement

I am a professor of mathematics at Kent State University with a specialty in algebra, especially group theory. It is always fascinating to see an object, be it a toy, artwork, or manipulative, that can be engaged by the observer at multiple levels of interaction and understanding. (One of the best examples of this is the Rubik Cube.) This is especially true when the object involves apparently unrelated mathematical concepts, interweaving geometry, combinatorics, and abstract algebra—but disguised as a toy!

## Artworks

On display are two 8 by 8 "puzzles" the pieces of which are congruent colored tiles. Each puzzle depicts the multiplication table of a group in which group elements are represented by distinct orientations of the tile. Color matches orientation, making it easier to distinguish the different group elements. The tiles (group elements) appearing in the first row are not in the same order as those in the first column (so that tiles can still fit snugly together). The first group is the dihedral group of order 8, and the second one is the direct product of two cyclic groups. Each display is of course a Latin square. However, they are also simply toy puzzles to be played with, broken apart and reassembled into different patterns.