Artists
Margaret Kepner
Independent Artist
Washington, District of Columbia, USA
Statement
I have a background in mathematics, which provides me with a never-ending supply of subject matter. My lifelong interest in art gives me a vocabulary and references to utilize in my work. I enjoy expressing mathematical concepts through visual attributes such as color, geometric forms, and patterns. A topic I have explored recently is the visualization of the classification groups defined by complement pairs in 4x4 magic squares. These groups were first described by Dudeney in 1910.
Artworks
Magic Night, Order 4
50.0 x 40.0 cm
Archival Inkjet Print
2026
A magic square of order N is an NxN array of numbers (usually the integers from 1 to N), where the rows, columns, and main diagonals all sum to the same magic constant. There are 880 unique magic squares of order 4, all with a magic constant of 34. They have been classified into groups (12 basic ones, plus a variant) based on their patterns of complementary numbers (number pairs that add to 17). In this piece, a particular magic square representing a group is displayed as an arrangement of 16 color-coded circles against a black background, with white lines joining complementary pairs. There exists a companion diagram for each square based on its magic path. Here, seven complement diagrams alternate with six path representations.
Magic Day, Order 4
50.0 x 40.0 cm
Archival Inkjet Print
2026
This piece is a dual to “Magic Night, Order 4” with the complement and magic path diagrams interchanged. Magic path representations have a white background and show the magic path in black, linking the numbers in the square in consecutive order from 1 to 16, and back to 1. In both artworks, the size of the colored circles in a particular magic square is related to the number of squares in its corresponding group. The arrangement of the 13 squares is based on various properties of the groups that they correspond to. The coloring of the circles and shading of the backgrounds indicate group properties such as magic diagonals (including broken and bent) and compactness (magic sub-squares). Magic path symmetries are highlighted in red.