Oh so you’re telling me that my storage unit is actually incredibly well optimised for space efficiency?
Nice!
Cursed
Submitted 2 weeks ago by fossilesque@mander.xyz to science_memes@mander.xyz
https://mander.xyz/pictrs/image/666542a1-1287-4135-a741-2714f76c3fd5.jpeg
Comments
9point6@lemmy.world 2 weeks ago
janus2@lemmy.zip 2 weeks ago
if I ever have to pack boxes like this I’m going to throw up
Midnitte@beehaw.org 2 weeks ago
I’ve definitely packed a box like this, but I’ve never packed boxes like this 😳
a_party_german@hexbear.net 2 weeks ago
https://kingbird.myphotos.cc/packing/squares_in_squares.html
Mathematics has played us for absolute fools
avattar@lemmy.sdf.org 2 weeks ago
If you can put the diagonal squares from the 17 solution in a 2-3-2 configuration, I can almost see a pattern. I wonder what other configurations between 17 and 132 have a similar solution?
WorldsDumbestMan@lemmy.today 2 weeks ago
Why can’t it be stacked up normally? I don’t understand.
bilb@lemmy.ml 2 weeks ago
You could arrange them that way, but the goal is to find the way to pack the small squares in a way that results in the smallest possible outer square. If you pack them normally, the outer square will be bigger.
CuriousRefugee@discuss.tchncs.de 2 weeks ago
If there was a god, I’d imagine them designing the universe and giggling like an idiot when they made math.
Psaldorn@lemmy.world 2 weeks ago
You may not like it but this is what peak performance looks like.
fargeol@lemmy.world 2 weeks ago
Bees seeing this: “OK, screw it, we’re making hexagons!”
raltoid@lemmy.world 2 weeks ago
Fun fact: Bees actually make round holes, the hexagon shape forms as the wax dries.
starman2112@sh.itjust.works 2 weeks ago
But fear not, bees are still smart! Mfs can do math!
FiskFisk33@startrek.website 2 weeks ago
come on now, let them cool, trust the process
brown567@sh.itjust.works 2 weeks ago
4-dimensional bees make rhombic dodecahedrons
Squalia@sh.itjust.works 2 weeks ago
LoreleiSankTheShip@lemmy.ml 2 weeks ago
Can someone explain to me in layman’s terms why this is the most efficient way?
tiramichu@sh.itjust.works 2 weeks ago
These categories of geometric problem are ridiculously difficult to find the definitive perfect solution for, which is exactly why people have been grinding on them for decades, and mathematicians can’t say any more than “it’s the best one found so far”
For this particular problem the diagram isn’t answering “the most efficient way to pack some particular square” but “the smallest square that can fit 17 unit-sized (1x1) squares inside it.” - with the answer here being 4.675 unit length per side.
Trivially for 16 squares they would fit inside a grid of 4x4 perfectly, with four squares on each row, nice and tidy. To fit just one more square we could size up to 5x5, and it would remain nice and tidy, but there is then obviously a lot of empty space, which suggests the solution is in-between. But if the solution is in between, then some squares must start going slanted to enable reduction in size, as it is only by doing this we can utilise the unfilled gaps and start poking corners in there.
So, we can’t answer what the optimal solution is going to look like, but we can certainly demonstrate that it’s going to be very ugly and messy.
Another similar (but less ugly) geometric problem is the moving sofa problem which has again seen small iterations over a long period of time.
DozensOfDonner@mander.xyz 2 weeks ago
Lol, the ambidextrous sofa. It’s a butt plug.
blackbrook@mander.xyz 2 weeks ago
All this should tell us is that we have a strong irrational preference for right angles being aligned with each other.
cyrano@lemmy.dbzer0.com 2 weeks ago
Thanks for the explanation
DominatorX1@thelemmy.club 2 weeks ago
For A problem like this. If I was going to do it with an algorithm I would just place shapes at random locations and orientations a trillion times.
It would be much easier with a discreet tile type system of course
GenderNeutralBro@lemmy.sdf.org 2 weeks ago
It’s not necessarily the most efficient, but it’s the best guess we have. This is largely done by trial and error. There is no hard proof or surefire way to calculate optimal arrangements; this is just the best that anyone’s come up with so far.
It’s sort of like chess. Using computers, we can analyze moves and games at a very advanced level, but we still haven’t “solved” chess, and we can’t determine whether a game or move is perfect in general. There’s no formula to solve it without exhaustively searching through every possible move, which would take more time than the universe has existed, even with our most powerful computers.
Perhaps someday, someone will figure out a way to prove this mathematically.
Devadander@lemmy.world 2 weeks ago
Any other configurations results in a larger enclosed square. This is the most optimal way to pack 17 squares that we’ve found
red_bull_of_juarez@lemmy.dbzer0.com 2 weeks ago
It crams the most boxes into the given square. If you take the seven angled boxes out and put them back in an orderly fashion, I think you can fit six of them. The last one won’t fit. If you angle them, this is apparently the best solution.
What I wonder is if this has any practical applications.
7bicycles@hexbear.net 2 weeks ago
yeah it vindicates my approach of packing stuff via just throwing it in there. no I’m not lazy and disorderly, this is optimal cargo space usage
fox@hexbear.net 2 weeks ago
There’s very likely applications in algorithms that try to maximize resource usage while minimizing cost
a_party_german@hexbear.net 2 weeks ago
bitjunkie@lemmy.world 2 weeks ago
It’s important to note that while this seems counterintuitive, it’s only the most efficient because the small squares’ side length is not a perfect divisor of the large square’s.
jeff@programming.dev 2 weeks ago
What? No. The divisibility of the side lengths have nothing to do with this.
The problem is what’s the smallest square that can contain 17 identical squares. If there were 16 squares it would be simply 4x4.
Natanael@infosec.pub 2 weeks ago
He’s saying the same thing. Because it’s not an integer power of 2 you can’t have a integer square solution. Thus the densest packing puts some boxes diagonally.
bitjunkie@lemmy.world 2 weeks ago
And the next perfect divisor one that would hold all the ones in the OP pic would be 5x5. 25 > 17, last I checked.
sga@lemmings.world 2 weeks ago
this is regardless of that. The meme explains it a bit wierdly, but we start with 17 squares, and try to find most efficient packing, and outer square’s size is determined by this packing.
curiousaur@reddthat.com 2 weeks ago
Did you comment this because you think the people here are stupid?
dream_weasel@sh.itjust.works 2 weeks ago
Bro, the people here, like the people everywhere, ARE stupid.
It’s always better to be explicit. I’m one of the stupid people who learned some things reading the comments here and I’ve got a doctoral degree in aero astro engineering.
bitjunkie@lemmy.world 2 weeks ago
wise_pancake@lemmy.ca 2 weeks ago
Is this a hard limit we’ve proven or can we still keep trying?
chuckleslord@lemmy.world 2 weeks ago
We actually haven’t found a universal packing algorithm, so it’s on a case-by-case basis. This is the best we’ve found so far for this case (17 squares in a square).
glimse@lemmy.world 2 weeks ago
Figuring out 1-4 must have been sooo tough
Natanael@infosec.pub 2 weeks ago
It’s kinda hilarious when the best formula only handles large numbers, not small. You’d think it would be the reverse, but sometimes it just isn’t (something about the law of large numbers making it easier to approximate good solution, in many cases)
rockerface@lemmy.cafe 2 weeks ago
It’s the best we’ve found so far
selokichtli@lemmy.ml 2 weeks ago
Do you know how inspiring documentaries describe how maths are everywhere, telling is about the golden ratio in art and animal shells, and pi, and perfect circles and Euler’s number and natural growth, etc? Well, this, I can see it in the world.
peteypete420@sh.itjust.works 2 weeks ago
Is this confirmed? Like yea the picture looks legit, but anybody do this with physical blocks or at least something other than ms paint?
deaf_fish@midwest.social 2 weeks ago
It is confirmed. I don’t understand it very well, but I think this video is pretty decent at explaining it.
Mathematicians would be very excited if you could find a better way to pack them such that they can be bigger.
So it’s not like there is no way to improve it. It’s just that we haven’t found it yet.
crmsnbleyd@sopuli.xyz 2 weeks ago
Proof via “just look at it”
CheeseNoodle@lemmy.world 2 weeks ago
Visual proofs can be deceptive, e.g. the infinite chocolate bar.
peteypete420@sh.itjust.works 2 weeks ago
I feel like the pixalation on the rotated squares is enough to say this picture is not proof.
Again I am not saying they are wrong, just that it would be extremely easy make a picture where it looks like all the squares are all the same size.
schnokobaer@feddit.org 2 weeks ago
That tiny gap on the right is killing me
friendly_ghost@beehaw.org 2 weeks ago
That’s my favorite part 😆
JoeTheSane@lemmy.world 2 weeks ago
I hate this so much
TimewornTraveler@lemmy.dbzer0.com 2 weeks ago
the line of man is straight ; the line of god is crooked
stop quoting Nietzsche you fucking fools
Melatonin@lemmy.dbzer0.com 2 weeks ago
I love when I have to do research just to understand the question being asked.
Just kidding, I don’t really love that.
Zerush@lemmy.ml 2 weeks ago
It is one prove more, why it is important to think literally out of the box. But too much people of this type
SpongyAneurysm@feddit.org 2 weeks ago
Now, canwe have fractals built from this?
Lemmisaur@lemmy.zip 2 weeks ago
Say hello to the creation! .-D
(Don’t ask about the glowing thing, just don’t let it touch your eyes.)
SpongyAneurysm@feddit.org 2 weeks ago
Good job. It’skinda what I expected, except for the glow. But I won’t ask about that.
mEEGal@lemmy.world 2 weeks ago
“fractal” just means “broken-looking” (as in “fracture”). see Benoît Mandelbrot’s original book on this
I assume you mean “nice looking self-replicating pattern”, which you can easily obtain by replacing each square by the whole picture over and over again
psud@aussie.zone 2 weeks ago
Fractal might have meant that when Mandelbrot coined the name, but that is not what it means now.
Lionel@endlesstalk.org 2 weeks ago
Unless I’m wrong, it’s not the most efficient use of space but if you impose the square shape restriction, it is.
cooligula@sh.itjust.works 2 weeks ago
That’s what he said. Pack 17 squares into a square
Lionel@endlesstalk.org 2 weeks ago
My point was that it doesn’t break my brain at all when considering there’s an artificial constraint that affects efficiency and there’s just not going to be a perfect solution for every number of squares when you consider the problem for more than just 17 squares
RustyNova@lemmy.world 2 weeks ago
nebulaone@lemmy.world 2 weeks ago
To be fair, the large square can not be cleanly divided by the smaller square(s). Seems obvious to most people, but I didn’t get it at first.
Zwiebel@feddit.org 2 weeks ago
The outer square is not given or fixed, it is the result of the arrangement inside. You pack the squares a tightly as you can and that then results in an enclosing square of some size
NigelFrobisher@aussie.zone 2 weeks ago
Why doesn’t he just make the square bigger? That’d be more efficient.
EddoWagt@feddit.nl 2 weeks ago
That’s not more efficient because the big square is bigger
NigelFrobisher@aussie.zone 2 weeks ago
See, that’s the problem with people nowadays?They want to minimalise everything.
They should just slow down and breathe.
JackbyDev@programming.dev 2 weeks ago
I think people have a hard time wrapping their heads around it because it’s very rare to have this sort of problem in the real world. Typically you have a specific size container and need to arrange things in it. You usually don’t get to pick an arbitrary size container or area for storage. Even if you for something like shipping, you’d probably want to break this into a 4x4 and a separate single box to better fit with other things being shipped as well. Or if it is storage you’d want to be able to see the sides or tops. Plus you have 3 dimensions to work with on the real world.
Admetus@sopuli.xyz 2 weeks ago
Initially I thought 4x4 square but this is a square of 4.675 sides. Reasonable. Clever maths though.
Grandwolf319@sh.itjust.works 2 weeks ago
But there are 7 squares in the middle with 10 around it, surely that counts for something
Serinus@lemmy.world 2 weeks ago
With straight diagonal lines.
Image
bleistift2@sopuli.xyz 2 weeks ago
Homophobe!
pyre@lemmy.world 2 weeks ago
hey it’s no longer June, homophobia is back on the menu
davidgro@lemmy.world 2 weeks ago
Why are there gaps on either side of the upper-right square? Seems like shoving those closed (like the OP image) would allow a little more twist on the center squares.
Serinus@lemmy.world 2 weeks ago
Image
superb@lemmy.blahaj.zone 2 weeks ago
I think this diagram is less accurate. The original picture doesn’t have that gap
Serinus@lemmy.world 2 weeks ago
You have a point. That’s obnoxious. I just wanted straight lines. I’ll see if I can find another.
1rre@discuss.tchncs.de 2 weeks ago
there’s a gap on both, just in different places and you can get from one to the other just by sliding. The constraints are elsewhere so wouldn’t allow you to twist.