Art Project Reflection

 Our art project expanded on Katelyn Owen’s “Her,” a piece centred around the Fano Plane (or PG(2, 2), where “PG” stands for “projective geometry”).  Owen's work features paintings on each edge of the Fano Plane, with each edge representing a theme from her life.  Each of the seven art pieces corresponds to the intersection of three themes, encouraging introspection and the exploration of connections that might not have been considered without the geometric structure of the Fano Plane.  We took this concept further, both artistically and mathematically, by working with PG(3, 2), the three-dimensional extension of the Fano Plane.  This allowed us to explore 35 themes through 15 art pieces, each representing the intersection of seven themes.  We also categorized these themes by colour to simplify brainstorming and connection-forming, though this symmetrical and aesthetically pleasing approach isn’t necessary for constructing PG(3, 2).

My experience with this project reminded me of being an undergraduate, researching mathematics that initially felt out of reach. That being said, once I was able to re-familiarize myself with the basics of projective geometry, the research I did surrounding the Fano Plan was exciting. I found myself excited to convey the beautiful symmetries in this structure, though I I’m unsure if I was successful. The longer I spent time with it, the more my appreciation grew. I saw tremendous potential in leveraging this structure to explore many areas of life – political structures, math curriculum, introspection, and everything in between. Despite my excitement, I’m not sure how well I was able to present the deep symmetry of this structure to the class. I personally take a long time to process definitions in mathematics, and I’m unsure as to how well I explained the axioms in our short presentation. I hope to find better techniques in the future.

As a teacher, I fully expect to execute some variation of this project. However, I plan to place much more importance on ensure the art itself is meaningful to those who are working with/creating it. It is clear that there is value when we project mathematics through a creative lens, but unless you have a feeling for the mathematics, the art feels abstract and out of context. For example, when I initially saw Owen’s ‘Her’, although the symmetry of the Fano Plane was beautiful, the depth of the art was lost on me. It was only after understanding the interconnectedness of the Fano Plane that I was able to appreciate the completeness of the art.

I think given the abstract nature of math, in combination with the vast array of unique creative abilities and hobbies I hope to find in my students, any assigned art project will be highly open-ended. I hope to offer students an opportunity to leverage both art and math so as to better understand something they are already familiar with. I speculate this is most clearly possible after completing the ‘Combinatorics’ unit in Foundations 12.