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.
"Kokabi Stars," by Reza Sarhangi (Towson University, Towson, MD)
Tile, 50 x 50 cm, 2015
I am interested in Persian geometric art and its historical methods of construction. Kokabi Star (the great pentagram) can be constructed using the lines of the 10/3 star polygon. Patterning this star can be achieved using different approaches. Some of the presented stars in this artwork have been made based on the actual tiling on existing buildings. Some others have been constructed based on old treatises and scrolls. Some of the patterns have been created using the traditional compass-straightedge process. Modularity is another approach in this regard. Moreover, the two decorated quasicrystal patterns of Star and Sun (the only two quasicrystal patterns with global five-fold rotational symmetry) and their striking relationships with Kokabi Star have been presented. Is this relationship a theorem? --- Reza Sarhangi