Math/Art Assignment Group Post

Group members: Alina, Emily K, Keith, Tara

Regina Bittencourt: One by one (The original version)

Our remake of the original

In remaking the artwork, we chose to use acrylic paints on paper. During this process, we wondered about why the artist stopped at a maximum of 9 rows (before descending). Exploring this informed our group activity of attempting to make a 10th row, observing that we no longer have the same palindromic pattern, and discussing why that happens. We tried adding a row ourselves and soon found that the “place holders” get in the way and the pattern breaks. Inspired by the lesson on Babylonian place holders, this prompted us to wonder if there was a maximum number of rows for other bases as well. After trying out a few it became clear that this maximum is one minus the base you’re working in. For example, base 10 has a maximum 9 rows while base 2 has only 1 row before the pattern breaks!

Our extension

The extension that multiplies 9x9, 99x99, 999x999, … does not follow quite the same pattern as with the 1s, and so we worked to find out why this one has a pattern of its own. Of course the painting does not have 90-degree symmetry like the original, so we decided to adapt it slightly, “flipping” the bottom half to produce an image with 180-degree symmetry to give it more visual appeal. In making the extension, we had to make decisions regarding whether the color representative of each number should be the same as the original. We ultimately decided to keep the colors consistent between both works, in the hopes that it would make it easier for viewers to easily switch back and forth between viewing. Since 0 does not appear in the original, we chose the color to represent 0 (burgundy) based on what we thought would look best with the other colors in the piece.

In designing a class activity, we wanted to offer a way to further explore the idea of the One by one piece. At first we considered using sticky-notes or tiles, but decided this would be difficult to manage in the short time for presentation. We decided to create a visual handout with the images of our artworks on one side and an activity on the reverse. Providing this visual handout means the class can see the detail of the painting (the paintings are on 12” x 12” paper, so it would be difficult to see the colours from the back of the room).

For the activity, we ask the class to consider what comes next. That is, what would happen if we attempt to add a tenth row to the painting? We’ll work this out together on the paper and on the whiteboard. Then, we ask the class to consider what would happen if the painting were done in a number system other than base 10.

No action shots available of our painting because we were too in the moment. 🙂 

To set the vibe we played the September 17th NTS Breakfast Show w/ Flo while painting and learned a lot more about each other's interests and hobbies.