Cursed
Cursed
91 comments
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Initially I thought 4x4 square but this is a square of 4.675 sides. Reasonable. Clever maths though.
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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.
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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.
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And the next perfect divisor one that would hold all the ones in the OP pic would be 5x5. 25 > 17, last I checked.
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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.
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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.
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Did you comment this because you think the people here are stupid?
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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.
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With straight diagonal lines.
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Homophobe!
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hey it's no longer June, homophobia is back on the menu
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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.
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I think this diagram is less accurate. The original picture doesn’t have that gap
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You have a point. That's obnoxious. I just wanted straight lines. I'll see if I can find another.
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Oh so you're telling me that my storage unit is actually incredibly well optimised for space efficiency?
Nice!
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You may not like it but this is what peak performance looks like.
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if I ever have to pack boxes like this I'm going to throw up
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I've definitely packed a box like this, but I've never packed boxes like this 😳
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Here's a much more elegant solution for 17
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Why doesn’t he just make the square bigger? That’d be more efficient.
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That's not more efficient because the big square is bigger
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See, that’s the problem with people nowadays?They want to minimalise everything.
They should just slow down and breathe.
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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.
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If there was a god, I'd imagine them designing the universe and giggling like an idiot when they made math.
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the line of man is straight ; the line of god is crooked
stop quoting Nietzsche you fucking fools
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Bees seeing this: "OK, screw it, we're making hexagons!"
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Fun fact: Bees actually make round holes, the hexagon shape forms as the wax dries.
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come on now, let them cook, trust the process
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But fear not, bees are still smart! Mfs can do math!
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Bestagons*
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Texagons
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4-dimensional bees make rhombic dodecahedrons
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Can someone explain to me in layman's terms why this is the most efficient way?
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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 "what is 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 the container up to 5x5, and it would remain nice and tidy, but there is then obviously a lot of empty space, which suggests the solution must be in-between. But if the solution is in between, then some squares must start going slanted to enable the outer square to reduce in size, as it is only by doing this we can utilise unfilled gaps to save space by poking the corners of other squares into them.
So, we can't answer what the optimal solution exactly is, or prove none is better than this, but we can certainly demonstrate that the solution is 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.
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Thanks for the explanation
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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
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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.
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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.
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Now, canwe have fractals built from this?
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"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
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Fractal might have meant that when Mandelbrot coined the name, but that is not what it means now.
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Is this confirmed? Like yea the picture looks legit, but anybody do this with physical blocks or at least something other than ms paint?
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It is confirmed. I don't understand it very well, but I think this video is pretty decent at explaining it.
The proof is done with raw numbers and geometry so doing it with physical objects would be worse, even the MS paint is a bad way to present it but it's easier on the eyes than just numbers.
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.
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Proof via "just look at it"
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Visual proofs can be deceptive, e.g. the infinite chocolate bar.
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Is this a hard limit we’ve proven or can we still keep trying?
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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).
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Figuring out 1-4 must have been sooo tough
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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)
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It's the best we've found so far
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I hate this so much
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That tiny gap on the right is killing me
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That's my favorite part 😆
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Do you know how inspiring documentaries describe maths are everywhere, telling us 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 really happening in the world.
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Not complete without the sounds
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It is one prove more, why it is important to think literally out of the box. But too much people of this type
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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.In other words: The size relation of the squares makes this weird solution the most efficient (yet discovered).Edit: nvm, I am just an idiot.
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The outer square is not given or fixed, it is the result of the arrangement inside. You pack the squares as tightly as you can and that then results in an enclosing square of some size. If someone finds a better arrangement the outer square will become smaller
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Unless I’m wrong, it’s not the most efficient use of space but if you impose the square shape restriction, it is.
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That's what he said. Pack 17 squares into a square
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I love when I have to do research just to understand the question being asked.
Just kidding, I don't really love that.
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But there are 7 squares in the middle with 10 around it, surely that counts for something
91 comments