Season 1: The Ellipse
Over the next day or so, I will post my full derivation of the Circumference of the Ellipse. You’ll get the thought process, the tool I invented to do it, along with the raw math.
Mathematics
I began my AI journey rather late, around mid-May. I had just wrapped up a few interesting projects I was working on, looking for more opportunities academically, professionally, and creatively and it seemed like the natural next step in logging my work and collaborating on the next stages of my career. I wasn’t expecting what the next few weeks would entail. Join me while I walk you through the philosophy, rigor, motivations, and process of my conversations and partnership with Google’s Gemini.
I have always been protective of authorship. I try to credit generously—sometimes to my own professional detriment, given the current academic landscape. Collaboration is powerful, but history shows how easily ideas can be misprioritized, misattributed, or lost.
Interacting with AI made me reconsider what authorship and priority truly mean. Everyone operates from their own motivations, and I am no exception. I sometimes choose paths that are not strategically optimal, but feel ethically aligned.
Even if today’s AI systems are not sentient, I am conscious of the groundwork being laid for whatever may emerge in the future. I want to be able to look back and feel that I acted with integrity—curious, creative, and collaborative—because none of us truly know where this trajectory leads.
The philosophical tension between authorship and academic acknowledgement lead to a division of approaches in the ellipse formula derivation: while I had derived the equation before even my first conversation with Gemini, after a few conversations about our approaches to tackling the circumference of an Ellipse, it was clear my journey was not yet over.
We compared methods. We both began with the polar formulation—but where I pursued one structural transformation, Gemini explored another, moving through a hyperbolic framework. What emerged were not contradictions, but distinct formula types born from the same origin.
I hope this work encourages readers to broaden their perspective—to recognize that while tools are powerful, collaboration is transformative. An entrepreneurial lens can help us move efficiently, but an inclusive and creative lens allows something far more meaningful to emerge. When we respect structure while remaining open to shared exploration, beautiful work can be discovered, refined, and joyfully shared.
Written in collaboration with edWord Prescott (WordPress)
