A solution to The Onion problem of J. Kenji Lopez-Alt (2021)

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.