Dicing an Onion, the Mathematically Optimal Way
85 comments
·August 16, 20251a527dd5
tptacek
Hopefully you're not bothering to core the top and the bottom of the onion; fussy, a waste of time, and works against his later goal of keeping the root intact while dicing.
finebalance
I do it more or less this way - except I keep the root intact until the end. It keeps the onion structurally intact until I'm done with the dicing. At which point, the root takes a single chop to lop off, and then the whole thing scatters into tiny, mostly uniform dices. It's quite satisfying.
fifilura
I also keep the root. But I am on the radial team!
ndr42
Sorry, but I had to link to this video as you said "effectively": https://www.youtube.com/watch?v=eQgIwwKmjdo
dyauspitr
This is silly. I’ve seen Indian street vendors do it the most efficient way. You tilt the knife with the front part down and the back maybe a quarter inch above the surface. That way as you slice the onion the little quarter inch holds it together as you turn it 90 degrees and make the perpendicular set of cuts.
morninglight
That may be the most useful thing I've seen on the internet in months.
Thanks much!
re
> It turns out that making horizontal cuts almost never helps with consistency.
They made the horizontal cuts evenly spaced between the cutting surface and the top of the onion, which is nonsensical to me. I believe that a single horizontal cut at around 15-20% height would be better for uniformity than a horizontal cut at 50% height.
wkcheng
Yeah, that's the way that I cut onions: you make vertical cuts followed by one single horizontal cut slightly above the cutting board.
This way of calculating doesn't take into account the creative ways you can make cuts. You could also do mostly vertical slices, and then slightly angle inwards when you do the final few cuts. That would get you a more optimal distribution as well.
jaxn
Which is exactly how I was taught to do it while working in kitchens 25 years ago.
The other thing is that this seems to ignore that the onion is round in the other direction too. As far as I can see, it only covers the first dice cut.
dcrazy
The planar cuts just determine the thickness of the dice. You just want to make them equal to the thickness of the rings.
null
indy
Yes! They had all those visualisations and you could see the problem areas from vertical slicing were at the bottom of the onion, a couple of horizontal slices down there would have given the best solution.
tetha
But is uniformitiy the goal?
If you want diced onions, the cook generally wants onion chunks below a certain cubic mass, so they cook and dissolve easily and uniformly. It does not matter if some pieces are 50% of that size, some are 20% and some are 80%.
With that, 1-2 horizontal slices and a bunch of straight downward slices are the safest and easiest way to achieve that.
That technique also expands to onion rings, sauteed onions and such.
null
throwawayffffas
Uniformity matters for even cooking.
If some pieces are twice the size of your average size, these pieces will be raw, when the others are done.
And if you have some pieces that are half the size of the average they will burn by the time the rest are done.
shakna
But you don't want an even flavour profile. You do want things cooked, but not perfectly the same as each other.
sdwr
Yeah, measuring standard deviation from the average isn't an accurate way of scoring - "too big" pieces are worse than "too small"
feoren
This ignores the obvious solution of not cutting all the way through. If every other radial cut is only through half the layers, you avoid making the inner pieces too small. It's funny how common it is for people to claim some sort of optimality with lots of math and analysis while completely failing to consider a better possibility. Never take seriously claims that someone found a "mathematically optimal" way of doing something. They didn't.
dcrazy
I’m not going to try to make consistent partial cuts down through an onion. I’m going through to the cutting board every time.
zeroonetwothree
Standard deviation is a poor measure because you care more about avoiding big pieces than small ones. Penalizing for having a few tiny pieces doesn’t make sense.
crazygringo
Thank you, this exactly! Seems like you want to reduce the standard deviation only considering pieces that are larger than the mean, but still relative to the mean. Would be very curious to see the results redone using that approach.
yunwal
You probably don’t even care about the “standard” deviation at all. You care about the deviation from some desired size. Probably the more accurate problem is “what is the fewest number of straight cuts I can make such that all pieces are below some target size”.
altairprime
To translate the final answer from math to human (as I’m going to be explaining this to my mother when I chat with her next!):
Imagine the half onion is a half rainbow. You know there’s another half rainbow lurking below the surface, the onion’s ghost of the sphere it once was. Place your knife as usual for each of your ten dice cuts, but instead of cutting straight down towards the cutting board, angle it slightly inward towards the end of the onion’s ghostly half-rainbow sphere below the board. Check your fingers for safety and then make your cut. Assuming your knife isn’t a plasma cutter, you’ll be stopped at the cutting board without ever reaching the onion at the end of the rainbow, and that’s cool. Set your knife at the next dice point and try again :)
(This still improves on the other dicing cases and only costs 1% uniformity by using 100% radius as the target.)
fnord77
> Place your knife as usual for each of your ten dice cuts,
what does this mean, exactly? I don't cut onions. Also I assume there is some pre-step where you cut the onion in half on some axis, but I don't know which.
altairprime
If you inspect the onion diagrams in the article carefully, they show various ways to cut an onion, as if origami diagrams but with knives. Still, I think you’ll want to learn the traditional methods of dicing an onion independently first, and then with that knowledge revisit this article and my description; this is last-10% optimization work that hinges on knowing that first-90% of how to dice an onion at all.
zeroonetwothree
If you don’t cut onions you probably shouldn’t bother with this thread. Or at least watch a video
motbus3
This remembers I have a challenge to figure out with some friends.
How to split a round cheese in in 5 perfectly without using any tools except the knife.
Assume you have the ability to cut in half perfectly always
Assume that if you can slice it in 10 equals pieces it is also a valid solution because you can just give two pieces for each
mtklein
Okay, I'll bite: 2 and 5 are prime, this is the perfect fifth problem, only approximate solutions are possible. Make me wrong!
bravesoul2
Cut into 8. Give 1 piece each.
For the remaining 3, repeat this method.
Let epsilon be a number as small as you like...
aidenn0
Measure how many widths of the knife divide the circumference of the cheese. Divide by 5 and make a radial cut at each division.
hashmap
I dislike easily 90%+ of the images I recognize as AI-generated, but the ones on this internet web site I think are a good use of the tech.
jader201
Why limit it to just two horizontal cuts?
I’ve always just made equal horizontal and vertical cuts, then slice the onion crosswise.
This results in pretty much no large pieces, and only some smaller pieces (which I prefer over larger ones, anyway).
I don’t care about standard deviation — I only care about minimizing the maximum size (but still without turning them to mush).
(Also, I know this was more of a fun mathematical look at chopping onions vs. practical. But still the “two horizontal cuts” thing seemed to be practical guidance, when it seemed like just equal horizontal and vertical cuts is far superior. But, granted, it’s a little trickier to do.)
EDIT: looking at Youtube, looks like the 2-cut thing is normal. But adding a few more cuts isn’t that much harder, and eliminates the larger pieces from the 2-cut method. I’ll stick to my method, even if it’s a little more work.
otherme123
Horizontal cuts does next to nothing, the onion is already "cut" horizontally.
In my experience it does worse, as the onion gets unstable to do the vertical cuts.
jader201
I mean, it’s also cut vertically — except for the adjacent edges (true for both horizontal and vertical, since it’s a sphere).
saagarjha
What I want is a cutting technique that’s good enough while still being practical for people to do. I am not sure I’m dexterous enough to slightly and consistently tilt the knife as I go through the onion.
uncletaco
Sure.
First its feet, then its head then split its belly 'til its dead.
1970-01-01
Someone, somewhere, will now spend time growing square onions to fix the problem. Probably someone in Japan.
ginko
Better yet onions that grow in large flat sheets.
buildsjets
I make fresh Pico de Gallo twice a week so I chop a lot of onions. Besides an even dice, I’m interested in not dicing my fingertips. Radial slicing a 180 segment or adding horizontal slices is too unstable.
My method is to cut in quarters, give a quarter a vertical dice, rotate 90, do another vertical dice, then go longitudinal.
This is fun!
I really struggled to effectively cut onions until this: https://www.youtube.com/watch?v=CwRttSfnfcc
Haven't looked back since.