Math/Art Reflection

I like both art and math, however I don't have much experience in education with the uniting of these two lovely subjects. I found many of the pieces in Bridges 2020 to be mathematically and artistically intriguing. It was tougher to narrow down the selection than it was to delve into the one we selected. Ivan, Tyler, and I agreed upon 'Triangulated Delaunay" by Aylet Sapirstein. It was great to work together to learn about these new (for us) applications of math.

The artists creates portraits of mathematicians based on their theorems, which I think is a great way to make new theorems interesting in the classroom for our students. In this piece, Delaunay triangulation is used to define the set of triangles that connect the points in the plane. The unique solution of Delaunay triangulation is such that the circumcircle of three points doesn't include a fourth point within the circle. The artist used nails on a board with wire

 

Thus, points have a single solution by Delaunay triangulation. There is beauty in the math of the single solution and in the countless possibilities of the point selection by the artist. Naturally, we wondered how the points were selected and this was the question we asked. The slides from our presentation are available on Tyler's blog and I will comment there if we get a response from the artist. Other work with Delaunay triangulation, such as in facial recognition, selects points based on the boundaries of regions with detail and more points are selected in regions with more detail. 

My research background is in brain imaging, where images are based on contrasts between tissues with different nuclei behavior in a magnetic field. This research has opened my eyes (pun intended) to seeing things in different spaces. Consequently, I like teaching exercises that show students how to think differently about what they see because visual information can be represented in many ways beyond what we see.

Because I studied biology and math, most of my university math education was in courses in calculus and statistics. I've thoroughly enjoyed learning more about topics in geometry from my peers. I have gathered many ideas from all the presentations for my upcoming teaching career.