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)
Edit: For the record, since this blew up, a tiny nitpick in my own explanation above: a smaller value of the packing coefficient is not actually what makes it more efficient (as it is simply the ratio of the larger square's side to the sides of the smaller squares). The optimal efficiency (zero interstitial space) is achieved when the packing coefficient is precisely equal to the square root of the number of smaller squares. Hence why the case of n=25, with a packing coefficient of 5, is actually more efficient than this packing of n=17, with a packing coefficient of 4.675. Since sqrt(25)=5, that case is a perfectly efficient packing, equal to the case of n=16 with coefficient of 4. Since sqrt(17)=4.123, this packing above is not perfectly efficient, leaving interstices. Obviously. This also means that we may yet find a packing for n=17 with a packing coefficient closer to sqrt(17), which would be an interesting breakthrough, but more important are the questions "is it possible to prove that a given packing is the most efficient possible packing for that value of n" and "does there exist a general rule which produces the most efficient possible packing for any given value of n unit squares?"
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.
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
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'")
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.
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...
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.
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 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're misrepresenting the problem though, it's not about maximising efficiency of an area, but packing the targeted amount of squares inside the smallest square, who's side lengths are some multiple of the packed squares.
If you posted this under OP then I would agree with you, obviously this is bad efficiency for the waffle for the purposes of syrup filled in holes, but for the definitions of the problem the person you replied to is correct in their explanation.
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)
Specifically, the optimal side length of the larger square for any natural number of smaller squares 'n' is the square root of n (assuming the smaller squares are unit squares). The closer your larger side length gets to sqrt(n), the more efficient your packing.
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!
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.
The downvotes are, I assume, from the *WHOOSH* sound as the point flies over your head.
This is the optimal packing of 17 squares in a minimum-size larger square. Of course it's not optimal everywhere. It's specific to 17 squares packed in a square.
The joke is that there's no reason to choose 17 squares as, clearly, a rectangular* array is optimal.
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
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.
Since a link to a wiki article does not an explanation make:
The optimal efficiency (zero interstitial space) is achieved when the ratio of the side length of the larger square to the sides of the shorter squares (let's call it the "packing coefficient") is precisely equal to the square root of the number of smaller squares. Hence why the case of n=25, with a packing coefficient of 5, is actually more efficient than the packing of n=17 given in the waffle iron, with a packing coefficient of 4.675. Since sqrt(25)=5, that case is a perfectly efficient packing, equivalent to the case of n=16 with coefficient of 4. Since sqrt(17)=4.123, the waffle packing (represented by the orangutan) above is not perfectly efficient, leaving interstices. However, the packing coefficient of the suboptimal solution (represented by the girl) is actually 4.707, slightly further from sqrt(17), and thus less efficient, leaving greater wasted interstitial space.
Trying to understand what this actually means. Since these two diagrams have the same number of squares, does this mean the inefficient packing squares are actually slightly smaller in a way that's difficult to observe?
Ah, no, it's that the more efficient packing takes up less space, so the less efficient square is actually slightly larger than the other, compared to the smaller squares.
If the smaller squares are identical in both sets, then the larger square in the less-efficient set will be slightly bigger than the larger square in the more efficient set.
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.
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.
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.
Pfft, let me know when “Big Waffle” develops its own proprietary 6-nanometer syrup squares. Until then I will defer to the Belgians and their superior waffle technology.
Yeah I know, but it's terrible waffle design, there's big flat chunks without syrup squares. It's a huge amount of wasted area unable to hold syrup in any meaningful volume. It's sad, really.
Edit: not to mention the waffle in the picture is clearly big enough to hold 25 squares the same size as those pictured! I thought these memes were supposed to be scientific...
You can't fit 25 squares of the same size in that space. If you check the top row there's 4 squares and space for slightly less than one more square, you can't fit a 5x5 grid there unless you have smaller squares or a bigger waffle
Maybe you couldn't, I absolutely could. The space just looks smaller because there's a diagonal square butting into it. Doesn't matter anyway, making the squares smaller was my original comment that sparked this conversation, so I'm right both ways.
No, you're not. It's square packing, this is the optimal arrangement of 17 squares inside another square as far as we're currently aware with a side length of 4.6756 inner squares. You cannot fit 5 squares in the space of 4.7 squares of the same size.
It's also a well-known meme and this is a science meme community.
I'm not concerned about the optimal packing of 17 squares, I'm talking about the waffle in the picture, which visually appears to have plenty of room for 25 squares. I'm guessing it's hard to get a waffle to the exact specifications of a complicated mathematical model, given its composition and construction. But just look at it with your eyes, there is very obviously enough room on that bottom row for two more squares. And if squares still work they way they did when I first learned about them as a young child, that makes room for 25 total small squares. 🤷♂️
Idk what you mean about constant grid line thickness, but if that's your sticking point, stop assuming it. The waffle in the post certainly doesn't have it. Regardless, you're incorrect, more squares = more surface area, smaller squares = more squares. If you shrunk a billiards ball to the size of a golf ball, which one would have more surface area?
Unrelated, but as a Hungarian, this association of waffles with syrup is so odd to see. Syrup is basically just sugar and water, isn't it? Sounds pretty boring. As a kid we always put nutella on waffles 🤷
Good point. Pesky square-cube law gets me again. Having done three minutes of research on Wikipedia pages I didn't fully understand, I think changing the square divots to spherical ones will give us the smallest surface area-to-volume ratio.
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)
Edit: For the record, since this blew up, a tiny nitpick in my own explanation above: a smaller value of the packing coefficient is not actually what makes it more efficient (as it is simply the ratio of the larger square's side to the sides of the smaller squares). The optimal efficiency (zero interstitial space) is achieved when the packing coefficient is precisely equal to the square root of the number of smaller squares. Hence why the case of n=25, with a packing coefficient of 5, is actually more efficient than this packing of n=17, with a packing coefficient of 4.675. Since sqrt(25)=5, that case is a perfectly efficient packing, equal to the case of n=16 with coefficient of 4. Since sqrt(17)=4.123, this packing above is not perfectly efficient, leaving interstices. Obviously. This also means that we may yet find a packing for n=17 with a packing coefficient closer to sqrt(17), which would be an interesting breakthrough, but more important are the questions "is it possible to prove that a given packing is the most efficient possible packing for that value of n" and "does there exist a general rule which produces the most efficient possible packing for any given value of n unit squares?"
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...
?????
LOL'ed, but also
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
Autistic mathematician would defenitely do this kind of shit
It's pretty common for people with autism to prefer things to be efficient and logical.
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!
The part about predicting protein folding makes sense, but this post was about waffles...
I was just answering your question of why someone would want to arrange a prime number of squares. The waffle is clearly a meme.
Mathematicians try this with every number
It's not just primes.
https://en.wikipedia.org/wiki/Square_packing
But it's especially primes, cause they can't even fit in a rectangle unless it's 1×
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...
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?
Yeah, it's not at all an optimal waffle. It's more a cool math meme waffle. ;3
-- Frost
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're misrepresenting the problem though, it's not about maximising efficiency of an area, but packing the targeted amount of squares inside the smallest square, who's side lengths are some multiple of the packed squares.
If you posted this under OP then I would agree with you, obviously this is bad efficiency for the waffle for the purposes of syrup filled in holes, but for the definitions of the problem the person you replied to is correct in their explanation.
But they added an interesting blurb in the edit, so it wasn't for naught.
Also, OOP phrased it as unheard of syrup density, which it isn't because of the interstitial space...
Thank you I was very lost lmao
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)
Specifically, the optimal side length of the larger square for any natural number of smaller squares 'n' is the square root of n (assuming the smaller squares are unit squares). The closer your larger side length gets to sqrt(n), the more efficient your packing.
Or maybe you just want waffles with 17 squares in them.
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.
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 downvotes are, I assume, from the *WHOOSH* sound as the point flies over your head.
This is the optimal packing of 17 squares in a minimum-size larger square. Of course it's not optimal everywhere. It's specific to 17 squares packed in a square.
The joke is that there's no reason to choose 17 squares as, clearly, a rectangular* array is optimal.
*squares are, of course, rectangles.
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
The sub-game where you supplex monks was pretty good too.
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
There's a brain echo in here.
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?
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.
The answer is still 42. If you don't like it, maybe you're asking the wrong questions
I don't know...37 just seems like such a random number, even the 3 and the 7 seem so random, what secrets could there be?
Surprsingly different secrets than 137 despite using two of the same digits.
(smartass 😛)
Where does this picture come from? Is it real? Ive just thought at how absurd an orangutan on a bike chasing a kid actually is.
https://knowyourmeme.com/memes/girl-running-from-a-peacock
Orangutan edit in, was peacock.
that bike is absolutely not part of the picture tho
I'm cooked. It looked real
What makes the lower suboptimal?
wiki - Square Packing
Probably more unused area
The squares are the same size...
The bottom square is slightly larger than the top square.
Since a link to a wiki article does not an explanation make:
The optimal efficiency (zero interstitial space) is achieved when the ratio of the side length of the larger square to the sides of the shorter squares (let's call it the "packing coefficient") is precisely equal to the square root of the number of smaller squares. Hence why the case of n=25, with a packing coefficient of 5, is actually more efficient than the packing of n=17 given in the waffle iron, with a packing coefficient of 4.675. Since sqrt(25)=5, that case is a perfectly efficient packing, equivalent to the case of n=16 with coefficient of 4. Since sqrt(17)=4.123, the waffle packing (represented by the orangutan) above is not perfectly efficient, leaving interstices. However, the packing coefficient of the suboptimal solution (represented by the girl) is actually 4.707, slightly further from sqrt(17), and thus less efficient, leaving greater wasted interstitial space.
Trying to understand what this actually means. Since these two diagrams have the same number of squares, does this mean the inefficient packing squares are actually slightly smaller in a way that's difficult to observe?
Ah, no, it's that the more efficient packing takes up less space, so the less efficient square is actually slightly larger than the other, compared to the smaller squares.
If the smaller squares are identical in both sets, then the larger square in the less-efficient set will be slightly bigger than the larger square in the more efficient set.
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
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.
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.
Yeah, if you have extra space but not enough for another row or column, just adjust the size of the inner squares.
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
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.
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
You lost me at the first part.
Are we talking about the same kind of hole and same kind of area?
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
Relevant xkcd
wanna maximize syrup? just make it a giant one-square cup.
My nephew just drinks the syrup from the bottle.
Thanks, I hate it!
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.
I'm pretty sure that waffle could easily fit 5 rows of 5, am I crazy?
It's still funny
In the "optimal packing" scenario, it's slightly too small - like 4.95x4.95
Is this the new loss?
no this is a gain
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.
Mathematicians: makes something with zero practical applications
Waffles:
Pfft, let me know when “Big Waffle” develops its own proprietary 6-nanometer syrup squares. Until then I will defer to the Belgians and their superior waffle technology.
Those fat Belgian waffles have nothing on the Dutch stroopwafel technology coming out of asml
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
TIHI
THERE IS CLEARLY ROOM FOR 25 SQUARES.... sorry just so unreasonably upset by this image
There isn’t. The sides are 4.675 long.
To fit more squares, youd need to use smaller squares but by that logic you could fit any number of squares.
Who tf uses a 56 years old collectible for breakfast?
Decrease the size of the squares and you could get waaaay more surface area.
This comes from a math problem where the squares size is fixed and you try to minimize the area they fit in
Yeah I know, but it's terrible waffle design, there's big flat chunks without syrup squares. It's a huge amount of wasted area unable to hold syrup in any meaningful volume. It's sad, really.
Edit: not to mention the waffle in the picture is clearly big enough to hold 25 squares the same size as those pictured! I thought these memes were supposed to be scientific...
You can't fit 25 squares of the same size in that space. If you check the top row there's 4 squares and space for slightly less than one more square, you can't fit a 5x5 grid there unless you have smaller squares or a bigger waffle
Maybe you couldn't, I absolutely could. The space just looks smaller because there's a diagonal square butting into it. Doesn't matter anyway, making the squares smaller was my original comment that sparked this conversation, so I'm right both ways.
No, you're not. It's square packing, this is the optimal arrangement of 17 squares inside another square as far as we're currently aware with a side length of 4.6756 inner squares. You cannot fit 5 squares in the space of 4.7 squares of the same size.
It's also a well-known meme and this is a science meme community.
I'm not concerned about the optimal packing of 17 squares, I'm talking about the waffle in the picture, which visually appears to have plenty of room for 25 squares. I'm guessing it's hard to get a waffle to the exact specifications of a complicated mathematical model, given its composition and construction. But just look at it with your eyes, there is very obviously enough room on that bottom row for two more squares. And if squares still work they way they did when I first learned about them as a young child, that makes room for 25 total small squares. 🤷♂️
*Increase? Assuming constant grid line thickness the fewer squares you have the more surface area you get.
Idk what you mean about constant grid line thickness, but if that's your sticking point, stop assuming it. The waffle in the post certainly doesn't have it. Regardless, you're incorrect, more squares = more surface area, smaller squares = more squares. If you shrunk a billiards ball to the size of a golf ball, which one would have more surface area?
It's really volume you care about, for filling with syrup.
Unrelated, but as a Hungarian, this association of waffles with syrup is so odd to see. Syrup is basically just sugar and water, isn't it? Sounds pretty boring. As a kid we always put nutella on waffles 🤷
We don't put plain sugar syrup on waffles, we use maple syrup or sometimes a fruit syrup such as blueberry. Maple syrup has a very distinctive flavor.
I checked out your link: this home made syrup is interesting but I've never heard of anyone doing this.
thanks, that's reassuring to know :D maple syrup is good, but imho nutella is better :9
I can imagine that being really good! Hazelnut is under appreciated in the US.
Good point. Pesky square-cube law gets me again. Having done three minutes of research on Wikipedia pages I didn't fully understand, I think changing the square divots to spherical ones will give us the smallest surface area-to-volume ratio.
Nooo, Hexagons are the bestagons!
About damn time.
#WaffleOptimizationCrew
Took me a while lol
where can i buy one
The density of waffle syrup went down compared to the 16 partition waffle though
slice-of-pie-from-just-off-center-and-carved-out-comma-but-worse.bmp
How Alton Brown makes his waffles
I can't believe someone made this waffle iron and didn't make a YouTube video about making it. It has to be a Photoshop x)