# 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!