This year’s Summer of Math Exposition (SoME) judging starts this Wednesday (03 Sep 2025). This year’s version of the contest encourages expositions that would be helpful to high school math classes. I’m submitting this essay about how to visualize the geometric series sum as the area of a right triangle filled in with trapezoid slices, where each trapezoid area represents the value of a term in the geometric series.
I would like to also include a Julia and Makie generated animated GIF that animates the transformation of the series of overlapped similar triangles (whose areas represent the values of the individual terms in the geometric series) into a series of equivalent area non-overlapped trapezoids that fill in a right triangle. The animation would be helpful in visualizing the geometry of the geometric series but it would also be a good chance to show off the animation capabilities of Julia and Makie. However, while I was getting surprisingly helpful feedback from Gemini’s proof reading of the essay, Gemini said that it couldn’t access the full essay when I gave it the story link at medium.com. (So I had to keep copying and pasting the essay text into the Gemini prompt for it to give its thorough critiques.)
So that is my first question: can non-members of medium.com read the full essay or are they limited to seeing just a sample of the essay’s beginning? (I tried to manage that story’s paywall settings, but the only control option for the essay was a cancel button. Do I have to become a member to allow non-members to read the full essay?)