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I’m pretty sure that waffle could easily fit 5 rows of 5, am I crazy?
It’s still funny
What makes the lower suboptimal?
Probably more unused area
To be honest I would love a waffle maker like this where some parts of the waffle are a little undercooked and other parts crispy.
It’s only more efficient when the containing square is large enough that there would be wasted space on the edges if the inner squares were lined up as a grid. The outer square of the waffle iron is almost but not quite large enough to fit a 4x5 grid. People losing their minds over this weird configuration being “more efficient” think it’s because it’s more efficient than a grid where all the space is used, which is not what this would be.
the joke is about achieving max density of the squares, density as in square per area of the waffle
of course you can make the whole waffle bigger, but it would decrease the density
a better solution is adding smaller squares though
Yeah, if you have extra space but not enough for another row or column, just adjust the size of the inner squares.
Yeah, there’s a lot of unused space there. Or just look at the gap in the middle of that row of 4. A slightly smaller square could have fit a 5x5, even.
It’s a novelty, not an optimization.
Oh my God, I fucking love this. I mean, I absolutely hate that this is the optimal way to pack 17 squares into a larger square such that the size of the larger square is minimised. However, I love that someone went to the effort of making a waffle iron plate for this. High effort shitposts like this give me life
I fucking love this. I mean, I absolutely hate that this is the optimal way to pack 17 squares into a larger square such that the size of the larger square is minimised.
There’s a brain echo in here.
I am sad because these squares look very out of place, unlike hexagons which are beautiful and perfect and never cause problems whatsoever, ever ever!
Hexagons are the bestagons.
I wonder how many people would have understood both references just a few years ago. Yet today, not only someone made a meme out of this, but it also gets a good deal of upvotes. That’s the internet culture I love!
What’s the other reference, for someone not much into Resident Evil?
Oh just that square packing thing from the post. There have been many posts/jokes about it being a mathematically optimal solution that feels irritatingly wrong.
I find the whole thing funny because it’s a very niche scientific concept that somehow made it to popular culture to the same level as a zombie game.
Yeah, it might be optimal for that specific case, but that doesn’t really make it so everywhere.
The item in the post would be fun for novelty though.
The Resident Evil games (at least the few I’ve watched/played) have an inventory management system where each item takes up a certain amount of space, and you have to organize it efficiently in order to maximize how much stuff you can carry.
Oh, is that all there is to it?
I thought it might also have something to do with the personality of the character on the right, or that you get a smaller inventory box when playing as that character.Some items take up multiple slots so sometimes you’re literally playing tetris style packing, and if you didn’t plan ahead around especially weapons you will have to drop stuff before you can take something better
Yeah, I have played Diablo II
It’s more fun thinking about it in hindsight than it was, actually doing that
For the uninitiated: this is the current most-efficient method found of packing 17 unit squares inside another square. You may not like it, but this is what peak efficiency looks like.
(Of course, 16 squares has a packing coefficient of 4, compared to this arrangement’s 4.675, so this is just what peak efficiency looks like for 17 squares)
Isn’t this only true if the outer square’s size is not an integer multiple of the inner square’s size? Meaning, if you have to do this to your waffle iron, you simply chose the dimensions poorly.
The optimisation objective is to fit n smaller squares (in this case, n=17) into the larger square, whilst minimising the size of the outer square. So that means that in this problem, the dimensions of the outer square isn’t a thing that we’re choosing the dimensions of, but rather discovering its dimensions (given the objective of "minimise the dimensions of the outer square whilst fitting 17 smaller squares inside it)
Or maybe you just want waffles with 17 squares in them.
But you can fit 25 squares into the same space. This isn’t efficiency, it’s just wasted space and bad planning.
You raised the packing coefficient by ⅝ to squeeze one extra square in with all that wasted space, so don’t argue that 25 squares has a packing coefficient of 5. Another ⅜ will get you an extra 8 squares, and no wasted space.
Precisely. That’s why I wrote the parenthetical about the greater efficiency of 16 as a perfect square. As the other commenter pointed out, this is a meme. This is only the most efficient packing method for 17 squares. It’s the packing efficiency equivalent of the spinal tap “this one goes to 11” quote.
My autistic ass can’t comprehend why anyone would want to arrange a prime number in a square pattern…
Basically just to see if they can. We can think of the problem from multiple angles. The general problem is: “if we have a larger square with side length of a, what’s the maximum number of smaller squares (with side length of b) that we can fit into that larger square?”. If we have a larger square with side length of 4, then we can fit 16 squares in. If the larger square had a side length of 5, then we can fit 25 squares in. So this means that if we want a neat packing solution, and we can control how large the outer square is (in relation to the inner squares), then we want each side of the larger square to be a whole number multiple of the smaller square’s side length.
But what if that isn’t our goal? The fact that packing 25 squares into a 5x5 square is an optimal packing solution with no spare space means that it will be impossible to fit 25 smaller squares into a square that’s less than 5x5 large. But what about if we do have awkward constraints, and the number of smaller squares we have to pack isn’t a square number? The fact that this weird packing solution in the OP has 17 squares isn’t because 17 is prime, but rather that 17 is 1 more than 16 (it’s just that 17 happens to be prime).
This is a long way of saying that because packing 16 squares into a square is easy, the natural next question is “how large does the larger square need to be to be able to pack 17 squares into it?”. If this were a problem in real life where I had to pack 17 squares into a physical box, most people would just get a box that’s at least 5x5 large, and put extra packing material into all the spare space. But asking this question in terms of “what’s the smallest possible box we could use to pack 17 squares in?” is basically just an interesting puzzle, precisely because it’s a bit nonsensical to try to pack 17 squares into the larger square. We know for certain we need a box that’s larger than 4x4, and we also know that we can do it in a 5x5 box (with a heckton of spare space), so that gives us an upper and lower bound for the problem — but what’s the smallest we could use, hypothetically?
As a fellow autistic person, I relate to your confusion. But I’d actually wager that there were a non-zero number of autistic people who were involved in this research. It sort of feels like “extreme sports” for autistic people — doing something that’s objectively baffling, precisely because it feels so unnatural and wrong
Okay, but none of that applies to waffles. They said they wanted more squares for syrup, but they actually got more unused space on the waffle surface.
I guess I’m not the “figure out how to fit a prime number into a square” kind of autistic, I’m the “why would you want to do that” kind of autistic.
To me, square numbers are beautiful because of how harmoniously they can be arranged, and prime numbers are beautiful because of how unique and impossible to neatly arrange they are. Trying to treat one like the other feels like an itch that can’t be scratched…
autistic
surprised at people doing weird shit
???
It’s pretty common for people with autism to prefer things to be efficient and logical.
Some autistics thrive on chaos, some thrive on order. I’m not the “pack a prime number into a square” kind of autistic, I’m the “why would you want to do that” kind
LOL’ed, but also
experiencing the human condition
surprised at people doing weird shit
It’s not just primes.
But it’s especially primes, cause they can’t even fit in a rectangle unless it’s 1×
I mean, the actual answer is severalfold: “sometimes, when you need to fill a space, you don’t end up with simple compound numbers of identical packages” is one, but really, it’s a problem in mathematics which, were we to have a general solution to find the most efficient method of packing n objects with identical properties into the smallest area, we would be able to more effectively predict natural structures, including predicting things like protein folding, which is a huge area of medical research. Simple, seemingly inapplicable cases can often be generalised to more specific cases, and that’s how you get the entire field of applied math, as well as most of scientific and engineering modeling
Even when it can’t be generalized, you still often learn something by trying. You may invent a new way to look at a set of problems that no one’s done before, or you may find a solution to something totally unrelated. There’s a lot to learn even when it looks like you’ll gain nothing.
(this is the part where you tack on a silly harmless lie at the end, like - “this specific packing optimization improvement was actually discovered accidentally, through a small mini-game introduced into Candy Crush in 2013. Players discovered the novel improvement, hundreds of individual times, within the first several minutes of launch. Scholars pursuing novel packing algorithms even colloquially call this event ‘The Crushening’”)
Are you sure the story is real? I can find anything that points to it, so a link would help a lot
That candy crush story is, as the commenter said, a lie. I don’t know why they would suggest that adding on a lie is in any way good, since we know that this packing was discovered in the late 1990s. It’s on the wikipedia article for square packing (with sources) but I don’t feel like looking it up again.
I’m not sure where I came across it, but it’s out there somewhere. You can do it!
Mathematicians try this with every number
For 25 squares of size 1x1 you’d need a square of size 5x5. The square into which 17 1x1 squares fit is smaller than 5x5, so you can’t fit 25 squares into it.
Do I need to tap the sign?
You raised the packing coefficient by ⅝ to squeeze one extra square in with all that wasted space, so don’t argue that 25 squares has a packing coefficient of 5. Another ⅜ will get you an extra 8 squares, and no wasted space.
You can’t fit 25 squares into a square 4.675x bigger unless you make them smaller. Yes, that will increase the volume available for syrup.
Literally already addressed that, but go off
You raised the packing coefficient by ⅝ to squeeze one extra square in with all that wasted space, so don’t argue that 25 squares has a packing coefficient of 5. Another ⅜ will get you an extra 8 squares, and no wasted space.
Yeah, it’s not at all an optimal waffle. It’s more a cool math meme waffle. ;3
– Frost
Thank you I was very lost lmao
Does coefficient in this context mean the length of the side of the big square?
Exactly. It is the length of the side of the bigger square, relative to the sides of the smaller identical squares.
Im a dipper. You put the syrup where you want it yourself. Do not rely on some fancy designed skillet to feed you the way you deserve.
The big perk of waffles is the surface area results in a lot of crispy with some fluffy. The fact that it holds syrup is just a perk
More square holes = more surface = more syrup in the dip!
not that different now, are we
There ya go. It almost has too many squares.
Final boss
More holes = less area of waffle to dip! Less waffle = less dip overall.
Or, another way of looking at it:
Fewer holes = more waffle = more area = more dip overall.Come on, it’s not rocket seance!!!
You’re right, this is rocket séance!:
Oh my god
Pffffffft. You can tell from the tone of my comment that I obviously meant the old saying of “it’s not rocket silence.”
“it’s not rocket appliances, Ricky, move on, it’s water under the fridge.”
Soudns like you’re about to blow up
More holes = less area of waffle to dip!
You lost me at the first part.
Are we talking about the same kind of hole and same kind of area?
This makes me so angry for reasons I can’t articulate
This actually makes me unreasonably happy, kinda like knowing the secrets of the number 37, which is coincidentally your current number of upvotes.
Now it’s 42
Now its more than 42. How do you feel about being wrong on the internet, genius?
The answer is still 42. If you don’t like it, maybe you’re asking the wrong questions
Now then, let’s not go mixing up then with now, then.
I’m sorry I can’t hear you over the sound of me being right on the internet. You’re gonna have to speak up.
Thanks, I hate it!
How inefficient, I could fit 100 squares in there easily.
Right? Wake me up when we reach a 7 nm lithographic waffle process.
Gate all around. I expect my waffle and syrup to hug each other. No one likes a lethargic partner.
Only 100? Pathetic, with my improved algorithm I could get at least 121 squares.
Psh I could fit like 1 square in there. Tryhards
The most interesting part is that you can make 0 squares and still have a square
Yeah, but you still have 4 edges in a circle. Just make a circle in the circle. Now you basically have an edible plate.
Like what, a platewaffle? Are you some kind of breakfast wizard?
Related:
https://en.wikipedia.org/wiki/Square_packing
Nature is a lot more elegant with spheres:
https://en.wikipedia.org/wiki/Close-packing_of_equal_spheres
The solution is to take a bite of waffle and then take a drink of syrup like it’s a chaser
and this is why I can no longer go to cocktail bars
