> Even though onions aren't perfectly symmetrical

The question I have is not about modeling an imperfect object as a perfect abstraction, it's about modeling a 3D object as a 2d object, and assuming that the optimization still holds. I think it's pretty plainly clear that it doesn't. Think about some cross-section of the onion that's closer to you and smaller than the center cross-section. Let's say it's of radius 0.25 instead of 1. The slices you take of it will be much more vertical than the center slice. This changes things. My intuition tells me it means the optimal solution is shallower than the solution found here, since you'd want the "average" cross-section to follow this constant.

The author dealt with this outside the article, and posted a link to his slides in this HN post. The relevant slides begin at [1].

At the end of the day a straight cut is limiting. The next step would be to design the perfect onion dicing knife.

[1] https://drspoulsen.github.io/Onion_Marp/index.html#44

Haven’t had enough coffee to think about this rigorously.

My intuition says that as long as you could get to the desired 3D shape from revolving the 2D shape around an axis, essentially integrating the area into a volume, the results will be valid or equivalent.

I don’t think that’s the entire story, there are probably other ways to simplify 3D shapes. And yes, onions will have non constant variations (or ones that don’t cancel out to 0) along the sweep which is what actually invalidates the real world application.

I believe you are supposed to calculate R*0.55... once for the max onion radius and use the same cut on the smaller disks. That way the smaller disk is cut identically to the inner part of the larger disk.

Isn't that where calculus and intergrals come into to play? As the radius approaches infinity type of stuff?