Week 4

 This week I chose to read the article “Bridges Stockholm 2018” by Eve Torrence.  

The article is a summary of the events and exhibits of the 2018 Bridges conference in Stockholm Sweden.  It begins with a detailed description of the location the conference was hosted at, including the mathematical architecture such as the pentagonal tessellation on the ramp leading to the main entrance (see photo below).  

The main events, presenters, workshops and the winners of the art exhibit are all related in great detail.  Events included a play about 3 female mathematicians from different centuries, a family day, formal and informal music nights, a fashion show and a film festival.  I’ve included a few pictures of the events and winning art exhibits below.  The Bridges conference is an amazing representation of what can happen when mathematics and the arts are no longer thought of as separate entities, and instead, are considered to be one and the same.

STOP - I am stunned by the creativity of all the participants in this conference!  It’s amazing how they’ve brought together so many different disciplines with the common theme of mathematics.  It really highlights for me how isolated math is at the highschool level.  It also reminds me of how my own mathematical creativity has stagnated.  I’ve been teaching the same 2 grades for over 10 years.  I used to try really hard to bring in artistic and creative elements into my classroom and I’ve lost that over the last few years.  

Has anyone else brought the arts into their classroom?  What did you do?  How did it go?

  Activity

For this activity, I was assigned to the Bridges 2021 art gallery.  I chose to replicate the piece by Conan Chadbourne, as it reminded me of quilting.  It was also one of the only pieces that I felt I actually understood the gist of the mathematics that were used to create it!  Below is a side by side comparison of the original piece and my own.

The mathematics of symmetry (especially in the forms of rotation and reflection) were used to create these 12 grids.  It turns out that when working with 4 x 4 grids, you can partition the grids into nearly 213,000 different ways.  However, there are exactly 12 that have a four fold dihedral symmetry.  If you're like me and aren’t too sure what exactly four fold dihedral symmetry is, I’ve included a definition below!  

Even though I thought this would be a doable challenge for myself, I still found myself stuck on how to recreate the entire piece.  It seemed overwhelmingly complicated for some reason.  I started by trying to fit the entire piece onto a single sheet of graph paper, and quickly gave up.  My daughter, who was watching me struggle, suggested that I look at it as individual pieces rather than one big picture. This was so much easier!  I ended up creating each individual piece and then cutting them out and arranging them on a table in the same orientation as the original artwork.  This process really helped to solidify the concepts that were used by the original artist.  I had thought about creating a black/white/grey version, but ended up going with coloured grids as well.  I felt it enhanced the symmetry features more than the monochromatic version.

Four fold dihedral symmetry - eight subunits are related to each other by one 4-fold axis and two 2-fold axes.

References

Conan Chadbourne. (2021) Bridges. https://gallery.bridgesmathart.org/exhibitions/2021-bridges-conference/conan-chadbourne

Eve Torrence (2019), Bridges 2018, Nexus Journal