2026 Joint Mathematics Meetings
Stephen M. Gagola, Jr.
Artists
Stephen M. Gagola, Jr.
Professor of Mathematics
Kent State University
Kent, Ohio, USA
Statement
I am a Professor of Mathematics at Kent State University in Kent, Ohio. My specialty is in algebra, especially group theory. The object on display, ``Three Intertwined Latin Cubes'', uses abstract algebra (at work in the background) to interweave geometry and combinatorics into a pattern that embodies tightly restricted mathematical structures (orthogonal Latin squares).
Artworks
Three Intertwined Latin Cubes
44.0 x 44.0 x 44.0 cm
PLA
2025
THREE INTERTWINED LATIN CUBES
On display are three overlapping Latin cubes of size $4 \times 4 \times 4$. The symbols that are used in each of the three cases are:
(1) the four orientations of a cube decorated by the use of long and short cylinders,
(2) four colors used on the long cylinders (black, red, green and gold),
(3) similarly, four colors used on the short cylinders (blue, violet, orange and pink).
Each of the 64 possibilities (orientation and color arrangements) occurs in the display. This does not guarantee that each of the twelve $4 \times 4$ planar sections be an example of three mutually orthogonal Latin squares. However, in the displayed example this is the case.
The Klein 4-group makes this all possible.