For 25 squares of size 1x1 you’d need a square of size 5x5. The square into 17 squares of size 1x1 fit is smaller than 5x5, so you can’t fit 25 squares into it.
Comment on Just one more square bro
wonderingwanderer@sopuli.xyz 9 hours agoBut 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.
SlurpingPus@lemmy.world 7 hours ago
wonderingwanderer@sopuli.xyz 15 minutes ago
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.
ChaoticNeutralCzech@feddit.org 7 hours ago
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.
wonderingwanderer@sopuli.xyz 16 minutes ago
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.
forestbeasts@pawb.social 9 hours ago
Yeah, it’s not at all an optimal waffle. It’s more a cool math meme waffle. ;3
– Frost
wolframhydroxide@sh.itjust.works 8 hours ago
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.
wonderingwanderer@sopuli.xyz 8 hours ago
My autistic ass can’t comprehend why anyone would want to arrange a prime number in a square pattern…
AnarchistArtificer@slrpnk.net 1 hour ago
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
wonderingwanderer@sopuli.xyz 4 minutes ago
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…
bstix@feddit.dk 2 hours ago
It’s not just primes.
en.wikipedia.org/wiki/Square_packing
wonderingwanderer@sopuli.xyz 3 minutes ago
But it’s especially primes, cause they can’t even fit in a rectangle unless it’s 1×
wolframhydroxide@sh.itjust.works 8 hours ago
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.
Cethin@lemmy.zip 5 hours ago
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.
PolarKraken@lemmy.dbzer0.com 6 hours ago
(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.”)
Zwiebel@feddit.org 7 hours ago
Mathematicians try this with every number