The last two weeks were focused on a study of polyhedra. While not strictly a digital art topic, I thought it important for students to develop a basic three-dimensional vocabulary in the event they wanted to do further study in computer graphics.

We began with the Platonic solids, naturally, looking at enumerating them geometrically and algebraically. The algebraic enumeration involved solving the usual

This proved challenging, especially when I gave some additional, similar Diophantine equations for homework. We also took time to build a dodecahedron and an icosahedron. This occupied us on Day 17, Day 18, and part of Day 19.

Since the first half of the semester was nearing its end, it was time to begin thinking about Final Projects. So I took the rest of Day 19 to help students individually choose a topic, and assigned the Project Proposal over the weekend.

We had a brief discussion of graph theory on Day 20, which involved looking at the adjacency graphs of the vertices of the Platonic solids, such as the one for the dodecahedron.

I introduced much of the basic vocabulary, using the chapter I wrote in my polyhedra textbook as a guide. Of course there is only so much progress to be made during a single class, but I did want to indicate how two apparently different areas in mathematics are related.

The homework involved untangling adjacency graphs, such as the one below.

This is just a triangular prism, although drawn a little unconventionally. This assignment again proved more difficult than I thought, even with Euler’s formula to help in calculating the number of faces. So we spent extra time on Day 21 going over the homework, followed by a very brief discussion of duality. And as students were having difficulty narrowing their focus for their project proposals, I spend the rest of Day 21 talking individually with them as they started building a few rhombic dodecahedra.

Over half of Day 22 was taken up by a quiz on their homework; I didn’t want there to be much time pressure. The last part of this class was spent creating an in-class sculpture with rhombic dodecahedra. I chose this dual model for them to build as it is space-filling.

I was surprised at how much they really got into it! I do hope we have time for a similar project at the end of the semester. We were in a bit of a rush for time, but still managed to create something intriguing.

Last time I mentioned I assigned a short response paper getting feedback from the students about how the course was going so far, and I said I’d share some of their comments. All (anonymous) quotes are from student papers.

I really like how hands-on the course is, and how there is a good balance between lecture and lab time.

This was a common opinion — and validates a major feature of the course design. I am glad students appreciate it! Another student made a similar remark about the lab time.

I enjoy the lab assignments that we get because I like the designs I create. It allows us to put to practice what we have learned with each lesson.

I specifically asked about how students’ attitudes about mathematics changed. I got some encouraging responses.

I was used to thinking of math as just something I had to do, that would probably be useful later in life, but wouldn’t really pertain to whatever I wanted to do with art. I’ve realized that I would actually really like to use this kind of math in my art in the future, because I never realized what kind of things I could make with this medium.

As someone who wasn’t the best at geometry in high school (I’m more of an algebra person), I think this class has given me a practical use for all the things I learned in high school that I found difficult to grasp or uninteresting.

I was pleased to read responses like this, since again, this reflects an overarching purpose of the course — see how mathematics can actually be used in practice. One student even went so far as to say,

I would also like to mention something, though this might not be considered significant, I never thought I would have to use matrices ever again in my life.

A few students remarked on using mathematics in the creative process.

At first, I was a little unsure of the role that mathematics took in graphic design, but as soon as we started playing with Sage, I noticed that it affects almost every aspect brought forth in the image.

Making “rules” for you art was something very different for me…..combining the left brain and the right brain creates incredible pieces of work….

Some students made more specific comments. One student liked the presentations the best.

Looking through the different papers in the Bridges archive and hearing everyone’s presentations really made me realize the extent that mathematics is related to so many other topics.

In addition, I asked for specific suggestions for improvement. By far the most common remark was that students want to learn more about how the Python code in Sage works. I was really encouraged when I read those comments! We will start to learn Processing in a few weeks, and I’ll make sure we discuss the code in more detail.

One student really liked the discussion board I set up for a few of the assignments — it is not difficult to create discussion boards for future assignments, so we’ll try that again. Another remarked that it would be good to learn about the printing process — and I certainly agree! But as I remarked in previous posts, I thought the logistics of this challenging endeavor would be too difficult to implement. It is certainly a future goal.

But overall, I was very glad to read how students were enjoying the course — and also pleased about their suggestions for improvement. So I’ll work hard at making the second half of the course even better than the first!