# Teresa Downard

Pattern, abstraction, symmetry, and symbolism are the things that call me to both math and art. In my pieces I try to to create a balance between the mathematical ideas and the creative process, depicting the correct correspondence between objects or highlighting a certain relationship. My favorite subjects are ideas from the intersection of algebra and geometry. I paint in acrylics and oils, and also enjoy doing pencil and ink compositions.

As the title suggest, this piece is about Kuratowski's planarity criterion: A graph is planar if and only if it contains no subdivision of K_5 or K(3,3). I love how this result is shocking at first, makes perfect sense once you are able to prove it, and is fun to use afterward. This definition is from the article "Kuratowski's Theorem" by Carsten Thomassen.

In the painting, we see a representation of a graph that contains K(3,3) : a complete bipartite graph between two sets of three vertices. The last connection cannot be drawn in the plane without crossing through one of the forbidden regions. She has gotten into the problem and has found proof that the graph is not planar!