Assignment #1 - Math Art Project writeup

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, Mark delved into the specific mathematical extensions, and I worked on coding and visualizing these extensions using Python. Once I 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.

Overall, this was a highly satisfying project to work on, particularly because of how well our group collaborated. A team communicating effectively and enjoying the process makes a project like this fun. A lot of effort was involved as we went back and forth to finalize textures and create a clear representation of the prime number concepts. The most challenging part for me was finding a clean way to visually represent Euler’s totient function, which required lots of trial and error. However, despite those challenges, we were all pleased with the final result and felt that our combined efforts paid off.

As I shared in class, this project was something of an epiphany for me. Having spent many years codifying concepts and visualizing data, I've typically attributed my learning to the process of translating ideas into code. However, working on this project made it clear that much of my understanding came from visualizing and connecting these mathematical concepts. For instance, the graph immediately revealed that prime numbers have the highest Euler’s quotient, followed by semi-primes, and then composite numbers, whose repeated prime factors reduce their totient values, a straightforward concept more easily grasped through visual representation. This insight has led me to reflect on how visualizations impact my learning compared to coding, a perspective that could be valuable for my future students. I plan to explore visualization and art as alternatives to traditional math learning, and I believe this approach could also be effective in computer science courses. Additionally, I'm intrigued by the idea of incorporating music as a learning tool in the classroom.