Bees seeing this: "OK, screw it, we're making hexagons!"
this post was submitted on 01 Jul 2025
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4-dimensional bees make rhombic dodecahedrons
Bestagons*
Texagons
Fun fact: Bees actually make round holes, the hexagon shape forms as the wax dries.
the line of man is straight ; the line of god is crooked
stop quoting Nietzsche you fucking fools
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.
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.
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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if I ever have to pack boxes like this I'm going to throw up
I've definitely packed a box like this, but I've never packed boxes like this 😳
Oh so you're telling me that my storage unit is actually incredibly well optimised for space efficiency?
Nice!
If there was a god, I'd imagine them designing the universe and giggling like an idiot when they made math.
Is this a hard limit we’ve proven or can we still keep trying?
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).
Figuring out 1-4 must have been sooo tough
It's the best we've found so far
With straight diagonal lines.
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.
I think this diagram is less accurate. The original picture doesn’t have that gap
You have a point. That's obnoxious. I just wanted straight lines. I'll see if I can find another.
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.
Oh, I see it now. That makes sense.
Homophobe!
hey it's no longer June, homophobia is back on the menu
I love when I have to do research just to understand the question being asked.
Just kidding, I don't really love that.
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).
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
You may not like it but this is what peak performance looks like.
That tiny gap on the right is killing me
That's my favorite part 😆
Unless I’m wrong, it’s not the most efficient use of space but if you impose the square shape restriction, it is.
That's what he said. Pack 17 squares into a square
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
That's what makes it a puzzle. That's what a puzzle is.
I hate this so much
Is this confirmed? Like yea the picture looks legit, but anybody do this with physical blocks or at least something other than ms paint?
Proof via "just look at it"
Visual proofs can be deceptive, e.g. the infinite chocolate bar.
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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.
Now, canwe have fractals built from this?
"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
Say hello to the creation! .-D
(Don't ask about the glowing thing, just don't let it touch your eyes.)
Good job. It'skinda what I expected, except for the glow. But I won't ask about that.
The glow is actually just a natural biproduct of the sheer power of the sq1ua7re
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