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%. Simplification of geometric mapping, for a visual example and understanding of mathematical structures. Thus, students can see the interdependence of sets and edges, for a more accurate analysis, you can refer to 123helpme.org.
Mingjang Chen, Associate Professor, Center for General Education, National Chiao Tung University
"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."