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.
"Ready to Fly High," by Mingjang Chen (National Chiao Tung University, Hsinchu, Taiwan)
Digital print by PowerPoint, 17" x 22", 2008. Complete r-partite graph is the graph with vertices set consisting of r disjoint sets such that any two vertices in different sets are connected by an edge and not for vertices in the same set. The work is a complete bipartite graph, following by a rotation on each line segments. One part of vertices is positioned on two adjacent line segments with equal distance; another part of vertices is positioned on an oval. There are 27 vertices on one part and 24 vertices on the oval. Hence, there are 27*24 line segments in this work. The transparency of these line segments is high up 95%. Structural Cloning Method (SCM) implemented on PowerPoint is a Human Computer Interface which handles geometry transformations on a huge number of drawing elements; it can be used to arrange complicate elements. Based on SCM, we can explore symmetry patterns and fractal patterns in different ways, and so math art becomes interesting. Complete r-partite graph is a common used graph, the number of edges in a complete r-partite graph is very large, and its edges always cover the space among vertices when visualizing. Once we tune up the transparency of these line segments, the transparency of overlapped areas become various degrees, this effect makes overlapped areas look like light-spots or rays if the background is in dark color, however the line segments are in light color. Parts of vertices can be arranged in various structures such that the overlapped transparent line segments can generate various and amazing patterns. --- Mingjang Chen (National Chiao Tung University, Hsinchu, Taiwan)