This is tremendously fun, thank you!
Your solution seems to assume that all cuts need to be directed towards a single point, but doesn't it seem likely that an even more optimal solution increases h (depth of cut target) as the cuts move outward? Or did I miss a reason that's not the case?
The two cases this solution generalizes are the vertical and radial cut method, which both aim towards a single point (you can think of the vertical method as aiming to a point infinitely far beneath the center of the onion). There may be other more optimal ways (cutting each layer individually for example), but they are not conducive to an ultimately simple strategy.
Hey now, even the practical application of cutting a typical 10 layer onion was left as en excercise for the reader. Quoth:
"So, the best depth for an onion with ten layers would be somewhere between 0 and 0.5573066. I have not investigated this in depth, but this seems like a fun next step."
You are suggesting something even more advanced. :)
Another onion enthusiast has sent me python code that considers finite-layer onions, and that code will be featured in the upcoming journal article.
I think that was just an "arbitrary" constraint of the problem, inspired by the practical constraint of using it to cut an onion?