The connection between mathematics and art goes back thousands of years. Mathematics has been used in the design of Gothic cathedrals, Rose windows, oriental rugs, mosaics and tilings. Geometric forms were fundamental to the cubists and many abstract expressionists, and award-winning sculptors have used topology as the basis for their pieces. Dutch artist M.C. Escher represented infinity, Möbius bands, tessellations, deformations, reflections, Platonic solids, spirals, symmetry, and the hyperbolic plane in his works.
Mathematicians and artists continue to create stunning works in all media and to explore the visualization of mathematics--origami, computer-generated landscapes, tesselations, fractals, anamorphic art, and more.
"Magic Square 25 Study," by Margaret Kepner (Washington, DC)
First Place Award, 2011 Mathematical Art Exhibition
Archival inkjet print, 12.5" x 12.5", 2010
Magic squares are numerical arrays that have substructures with constant sums. This design is based on a magic square of order 25, containing the numbers from 0 to 624. Each row, column, and main diagonal sums to the “magic constant” of 7800. The numbers in the magic square are represented by a visual base-5 system: four concentric squares serve as the 1, 5, 25, and 125 places, while shades of grey stand for the numerals 0 to 4. Coding the numbers into their base-5 versions yields a pattern of 625 unique, nested-squares in shades of grey. This particular magic square also has a substructure of 25 mini-squares of size 5. Each of these mini-squares is “magic” (although the numbers are not consecutive), with rows, columns, and diagonals summing to 1560. In addition, certain other groups of 5 squares add up to 1560. Examples are the quincunx and the plus-sign shapes (when fully contained in a mini-square). The colored accents are used to indicate a few of these “magic” substructures. --- Margaret Kepner