I agree that spherical coordinates are not good for the 3D onion. In the slides I linked, I use cylindrical coordinates with appropriate bounds to encompass the problem within a sphere.
47 karma · joined November 26, 2024
I have slides that detail the problem setup and the mathematics, as well as a consideration of three-dimensional onions, here: https://drspoulsen.github.io/Onion_Marp/index.html
I have submitted a formal write-up of the details of the problem and the solution to a recreational mathematics journal.
I'm also happy to answer any questions about this!