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.
"Constructing the Inner Apollonian," by Jeffrey Stewart Ely (Lewis and Clark College, Portland, OR)
Digital print on archival paper, 2014
Unlike pictures of two-dimensional Apollonian gaskets, most renderings of the three-dimensional analogue, Apollonian sphere packing, tend to be disappointing because they do not reveal the interior structure the way that their two-dimensional
cousins do. This image tries to reveal the inner structure in several ways. First, some of the larger spheres that obstruct the view have been removed. The negative spaces caused by their removal are plain to 'see'. Second, the observer has been located in one of these negative spaces, affording a more intimate view. Finally, the process has been deliberately left incomplete, giving a sense of both the coarser and finer stages of the construction. --- Jeffrey Stewart Ely