Week 4 Mathematics and the Arts Introduction (Part 1 of 2)

Reflection:

This week’s activity resonated with me because it emphasized the significance of re-merging these two cultures together.  In Susan’s introduction, she notes that our “society often deals in binary”, portraying mathematics and arts as “polar opposites”. For most of my life, I often thought the same way. I loved fine arts as a child, and as a teen considered pursuing an art degree rather than the science/math route. However, cultural and family pressures dictated that one had greater value than the other, one could provide a stable career, so art had to be placed on the backburner. However, it’s intriguing to learn,  “there was not the concept of such a split between the arts and the sciences, even in mainstream Western society and among the academics, up until the early 20th century.” (p.2). My students are often amused to learn that if I wasn’t a math and science teacher, I’d love to be an art teacher. Through this program, and especially this course, I am realizing there is no need to ‘choose’ either but that both worlds can exist in harmony, and better yet, enhance the beauty in each. 

Activity:
For this week’s activity, I was inspired by Karen Amanda Harris’ “Broken Sphere” (Bridges Exhibition, 2018). I admired the symmetry in the outline of her piece and was captivated by her choice of colours and the filled segments she used to break that symmetry. The rays and angles that deviated from various points prompted me to think of so many questions I could ask my students: 

• What angles are formed? 

• What polygons are formed? 

• Where is the symmetry? Why isn’t it symmetry

Karen Amanda Harris: Broken Sphere

30 x 42 cm

Promarker, gel pen, ink liner, nail varnish and correction fluid on watercolour paper

2016

For my own design, I chose to deviate from her pen and paper medium and challenged myself by constructing a 3D version of her work using a board, nails, and coloured string. I started with a 12 x 12 inch board, nailed a center point, and roughly traced a circle using a plate. With a measuring tape, I marked 4 points, and then divided the difference into thirds, creating a dodecagon. I added nails to the four corners and then two more in between. Mathematically, there are a number of circle theorems, line segments, and tangent points I’m sure I could have discussed. However, I haven’t taught high school math in years so they aren’t popping in right now!

   

Figure 1 & 2: (Left) Nails around the circle template, creating a dodecagon. (Right) Segmenting the quarters into additional thirds by dividing the difference by three. 

I had no idea what I wanted to do with the string but had three different colours to use. There was no set design but I started by simply looping the string between nails. Once I finished with a particular sequence, I would tie off the string, change to a different colour, then proceed with a new pattern. Questions I considered as I attempted this art piece:

• Which points had the most loops of string? 

• What type of polygons am I forming? 

• How do I keep seeing these patterns? 

• Are there patterns or connections that I have missed? Many! But I ran out of string and space on some of the nails

• How much string did I use in total?

• Could this be expressed algebraically? 

Unfortunately, I ran out of two of the strings, so the layers were not as clear. I did realize that as I continued the process, there were even more questions that could be asked, depending on the angle the art was viewed. Perhaps in the future with more mindful planning, I could be strategic with the colours and create a designated colour scheme. 

Figure 3 (left) & 4 (right): Final product based on Karen Amanda Harris' inspiration Broken Sphere.