Original Artwork: Sudoku without Numbers by Dru Horne and Shannon McKillip
We decided to remake and extend the original art piece using cardstock and markers instead of fabric, as none of us had experience with quilting. This proved challenging in that it was quite time-consuming to cut out every individual piece and glue them all together. Additionally, we needed to glue all background squares together in a way that was structurally sound, taking us 6 hours to make just the extended art piece. Coming up with a unique concept for each layer was also difficult to decide on, as we wanted to select distinct features that layer well on one another and still show the other elements beneath. We ultimately settled on adding features like coloured borders, coloured squares, and hand-drawn icons that could fit around our larger icons without blocking the background.
We first focused on extending the piece mathematically by scaling the canvas to a 7x7 matrix and layering 6 different mutually orthogonal Latin squares. We arrived at this number of layers by using theorem 7 as described by Ballif (2008), which produces 6 as the maximal number of mutually orthogonal Latin squares that can be determined from this matrix, given that 7 is a power of a prime. We also used this theorem to construct a full matrix of six layers in a numbered sequence, by assigning a number of 0 through 6 to each element in each Latin square to construct the full picture that ensured all entries were distinct. This part of the process required some care and could be a point of challenge for others interested in recreating, as any mistakes could result in duplicate entries.
We then extended the art by focusing on how we could tie it into learning from place, specifically by having one of the Latin squares be icons from Coast Salish symbols for different local animals (sources were cited in our presentation). This was beneficial both for ourselves to explore more local Indigenous art and artists, as well as to tie in the BC curriculum’s goal of incorporating Indigenous ways of knowing.
We designed our interactive activity to be a smaller/simpler version of the mutually orthogonal Latin squares that we constructed. Specifically, we created a 4x4 matrix with two fixed elements and a movable third that students can use to layer their own Latin square. We hope this can cement an understanding of orthogonality between Latin squares, as well as spark discussion on how many possible arrangements exist when they compare with other students. We decided on a simpler matrix to have confidence it can be completed during the short allotted time during lecture, while still giving everyone a chance to have hands-on experience with these concepts. It also brought the content difficulty closer to the high school level – as combinatorics is only introduced in Foundations of Math 12 – instead of the university-level math the original piece employs.
Our digital mock-up and recreation of original art piece:
Our progress pictures:
Our completed art piece:
Thank you! Looking forward to your presentation today! This is lovely.
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