Week 4 - Exploring Mathematical Art through Quilting

 Well, this week was a take-me-down-a-fun-and-twisty-rabbit-hole week for sure! When my creative juices are sparked, I can be like a dog with a bone, playing with the ideas and not letting go, even staying up way past my bedtime. I thought the art activity this week was going to be my one and only exploration and then I started making videos for the reading summary! Ha. But this post is about the art activity.

I was assigned Bridges 2013 (along with Joy). The piece I selected was one of two by Margaret Kepner, an independent artist based in Washington, D.C. (Here is her website: http://mekvisysuals.yolasite.com/

 

Here is the piece from the Bridges 2013 section of Mathematical Art Galleries, specifically on this page:

Trapezia Pastiche
Margaret Kepner, 2013

(click on the image for a larger one you might be able to zoom in and out of on your device to see the tessellation patterns)

This archival inkjet print is an exploration of tessellation of trapezoids/trapezium. The larger trapezoid is made of 4 coloured trapezoids which in turn are made of 4 trapezoids. Then, each trapezoid is tiled with a different pattern of trapezoids. Kepner, in the description of the art, notes that there are infinite possibilities for tiling trapezoids.

I was attracted to this piece for a few reasons. I liked that as simple as it seems on first glance, it is more complicated when you look carefully. It seems so beautiful in its pairing of the simple and the complex. The tessellation was interesting to me, too, because I really enjoy doing projects with tessellation with students. The artwork also makes me think of quilting in how it is pieced together and seemingly stitched with patterns; this is where I decided to go in exploring this piece deeper - to quilt it.

And so began the leap down the rabbit hole!

My mom is a quilter, a hobby she has taken up in retirement and even more so since she moved to a smaller town (Armstrong, BC) that has a quilting store that holds classes.  She gives me her scraps for my classroom projects so I was able to scour through my bin at work for some nice pieces to re-create this artwork in fabric.

I also called my mom for advice on how to piece together trapezoids with sewing. Over the phone it was tricky and she didn't really understand what I was getting at, so I sent her a copy of Kepner's art to see what she would come up with. I thought she might actually try sewing a few trapezoids together, but she just got as far as cutting the printout of the art into pieces.  We were definitely on different wavelengths for what I was asking for because my sister sent me this picture with "Mom says the green and blue have to be trimmed to fit":

Mom's take on re-creating Kepner's art

Whereas my fabric pieces looked like this:

Fabric pieces cut and ready for sewing

When Mom and I talked again (I had sent a picture of mine back), she said, "But you told me I could cut it up into pieces!" Yes, yes, I did. I didn't get any helpful advice for piecing the trapezoids together to form what Kepner's art looks like so I tackled it on my own.

Piecing the trapezoids together was a bit tricky because of the need to sew more than one edge together on 2 pieces at times.  It made me appreciate how many sides are being shared between trapezoids in the tiling pattern for the 16 coloured trapezoids. I was also trying to figure out how to most efficiently sew the pieces together so most of the time I was joining the trapezoids on one edge, rather than two.  I forgot to document that process in pictures - I was in the "zone" or in a state of "flow".

I layered the top piece of trapezoids with a layer of batting and another piece of fabric for the batting and outlined the 16 trapezoids in stitching.

Next came the tiling of each of the 16 trapezoids and I knew this step was not going to get finished for this post - so I will edit another day with an update (or maybe a few along the way).

I had to play with sketching the tiling patterns to understand them and to find the base pattern/root.  I have only done a few so far.

Sketching the tiling patterns

While I was sketching, I asked, "How does Kepner know that there are infinite patterns to tile trapezoids?" and as I was sketching for trapezoid B, I found an answer (see image above).

I spent some time hand-stitching the tiling for parts of trapezoids A, I and F (I didn't sketch F but after stitching A, I understood F).

Stitching trapezoid A

Closer look at the stitching on trapezoid A

Trapezoid F

Trapezoid I - triangles that need fixing for scale

There is a lot more stitching to go!

There is a lot more to do to cover the whole piece in the tiling by stitching. However, the process of just getting started really helped me explore the patterns in the art. For trapezoid A (blue), when I was sketching, I didn't at first see that adjacent "rows" were slightly different and by checking that I could repeat the row, I realized I needed to rotate two trapezoids that form a hexagon on alternate rows. By stitching the A pattern, and then exploring other patterns, I realized I could do the tiling for trapezoid F quite easily based on some of the patterns in A. When I went to stitch trapezoid I, I discovered that the tiling patterns on adjacent trapezoids on Kepner's art feed into each other and though I didn't reflect that in my piece (at least not yet - I may decide to correct it), I wouldn't have noticed that the tiling patterns join together if I hadn't been examining them so closely to figure out where to set up the stitching. I also made an assumption that for pattern I, I could fit it in the same width of "row" that I had done for A and F - and only after stitching it did I realize that my stitched trapezoids were too small and that the "row" for triangles has to be wider than the ones for a hexagon made of 2 trapezoids.

At first I worried that I had chosen a piece that was too simple and wouldn't stretch my thinking but now I continue to uncover new understandings of the tiling patterns each time I work with it. As I continue to work with this piece (I am quite determined to finish it sometime!), I want to explore more explicitly some questions Kepner asks about her patterns:

"Which ones have a primitive-cell size of 4? How many are fault-free? Hexagon-free? Are there tilings with only 1 vertex type? Any with 6? Which patterns have rotational symmetry? Mirror lines? No symmetry?"

Check back for updates!

References

Kepner, M. (2013). Margaret Kepner. Mathematical Art Galleries. http://gallery.bridgesmathart.org/exhibitions/2013-bridges-conference/renpek1010