art project reflection

Our group project began with Madison selecting the initial artwork, which gave us a strong foundation to build upon. When we first met as a group, we discussed extending the artwork by incorporating additional prime number concepts. Madison suggested using perfect squares as a visual anchor for viewers, and we explored adding elements like square-free prime signatures and Euler’s totient function to enhance the visualization. After discussing different shapes for clarity, we chose concentric circles to create bands of information, allowing us to visually represent our mathematical concepts effectively. Madison's early contributions and direction-setting allowed us to divide the remaining work: Sahl focused on recreating the original artwork, I delved into the specific mathematical extensions, and Andy worked on coding and visualizing these extensions using Python. Once Andy developed a proof-of-concept for the circular band plots, our group collaborated on selecting textures to highlight perfect squares and prime signatures, eventually finalizing the color and texture schemes. To complete the project, we incorporated Euler’s totient into the artwork, and Madison pulled everything together into a polished slide deck.

Firstly, I found this project very interesting, and I very much enjoy working with Andy, Sahl, and Madison. Overall, I'm super impressed with each of them as individuals and it was definitely a motivating factor for me to step up and contribute in any small way I could. That being said, the finished product and presentation wouldn't have been half as good without those guys. Sahl did an immaculate job of reverse engineering the original piece, Andy was really basically showing off his next-level ability to create computer-generated visualizations, and Madison absolutely crushed it with the presentation and slide deck. Initially however, it was challenging to try and think of ways to extend the original artwork, both in terms of the math as well as the artistic aspects. Once I actually started doing some basic research on prime factorizations, I found it hard not to get sucked into the number theory rabbit hole. Being in a mindset of "how can I represent this concept visually" was an excellent way to keep me extra engaged while poring over various wikipedia articles. It also made me miss my number theory class from my undergrad, and also kind of wish I could take some more math classes. There's so much math out there I've yet to learn! But we'll get back to that one day.

As a teacher bird, my big takeaway from this project is that there is so much room for creativity in how we engage with mathematics. Math and art in particular, is a super interesting interdisciplinary combination. Along those lines however, I think it would be cool to mix math with other subject areas in similar kinds of interdisciplinary assignments. Doing something with music would be interesting I think. The obvious exercise would be to look at a piece of music and analyze the fractions of beats and measures based on the given time signature. However, part of what I enjoyed so much about this project was the open-endedness of it. We were presented with some initial starting points, but then given free reign to develop ideas with our own creative ideas. So, were I to run with this idea of mixing math and music, I would try to do something similar: having some initial examples of ways to relate the two subjects and then open it up to the students to extend those further. As a teaching tool, I am 1000% going to steal this assignment idea and use it my own classroom (will give credit).