A solution to The Onion problem of J. Kenji Lopez-Alt (2021)
A math-heavy attempt to solve J. Kenji López-Alt’s “onion problem” — how to cut a halved, roughly spherical onion into pieces of equal size with the fewest knife cuts — prompts debate over both the modeling and the practicality. Commenters probe the validity of treating a 3D onion as a 2D half-disk, note real-world complications like uneven layers and off-center cores, and contrast this idealized solution with kitchen realities such as food processors, grating, safety, cleanup effort, and even the value of intentionally uneven cuts for texture and flavor.
Title and terminology
- Several readers were initially misled by the capitalization, expecting an article about the satire site rather than a mathematical cutting method.
- Once clarified, many expressed genuine interest in optimal onion-cutting techniques.
What “the onion problem” is
- Core goal: cut a (half) onion so resulting pieces have as similar volume/area as possible, mainly so they cook evenly.
- Some note the article’s text under-explains the problem statement and relies heavily on accompanying videos.
Appliances vs knife work
- Some propose blenders or food processors as an “engineering” shortcut.
- Counterpoints: they generate hundreds of cuts, poor uniformity, mushy texture, worse caramelization, and more cleanup.
- Consensus: processors are good for very fine dice or large batches; knives are preferred for texture, control, and lower overhead.
Mathematical modeling debates
- Multiple commenters question modeling a 3D half-sphere onion as a 2D half-disk, doubting that the optimal solution transfers cleanly.
- Concerns: real onions are not symmetric; layers vary in thickness; the biological center rarely matches the geometric center.
- Discussion of using cylindrical vs spherical coordinates, Jacobians as weighting, and stacking slices; some deem the model more of a thought experiment than a practical recipe.
- Slides shared by the article’s author reportedly show the 3D complications and limitations.
Technique details and safety
- Ongoing debate about the necessity and safety of the horizontal cut; some see it as dangerous and largely redundant if vertical cuts are angled.
- Suggestions include cut‑resistant gloves, sharper knives, and alternative cut orders.
- Sharpening advice appears, alongside skepticism that “dull knives are more dangerous” has been empirically studied.
Uniform vs varied cuts
- One popular counter-view: heterogeneity in piece size can be desirable for texture and flavor variation.
- Several argue there is no single “right” way; professional consistency and home-cook preference can justify different goals.
Alternative onion prep methods
- Grating, pulling layers flat to make a “perfect dice,” and other chef-style methods are mentioned as ways to sidestep or refine the problem.