Skylar Cheung

Visual Artist
Political Science Department, University of Toronto
Toronto, Ontario, Canada

My name is Skylar, and I am a visual artist based in Toronto. I usually rely on mathematical formulae to build visual guides for other oil paintings. This time around, I wanted to try my hand at using visual arts to put math at the forefront. I hope that in using a variety of materials and a spectrum of basic colors, viewers will have a clear understanding of which mathematical ideas each piece represents.

Though I like paints and political science (my declared academic discipline) plenty, I do like to exercise my mind with logic puzzles found online. I am also interested in exploring impossible shapes in design making. Ultimately, I hope that my visual art will eliminate the panic so many people associate with mathematics.

Infinite Loop, Thread on Mobius Frame
13 x 30 x 25 cm
Thread on cardstock frame

One can obtain an orientable torus by deforming string wrapped around the non-orientable Mobius strip.Though the torus and the Mobius strip have the same fundamental groups, they are not homotopy equivalent (there is no continuous way to turn one surface into another). This work demonstrates a simple example of a broader topological question: what are the properties of a surface obtained by wrapping-string around a “parent” object and uniting the strands?

Consider two objects A and B. Wrap string around their inner and outer surfaces, and glue the loops of the string together in order to get corresponding surfaces A* and B*. If you can pull and push (without tearing!) A* into B*, then A and B are homotopy equivalent. Can you prove it?