Why doesn’t he just make the square bigger? That’d be more efficient.
this post was submitted on 01 Jul 2025
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That's not more efficient because the big square is bigger
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.
And the next perfect divisor one that would hold all the ones in the OP pic would be 5x5. 25 > 17, last I checked.
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.
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.
the line of man is straight ; the line of god is crooked
stop quoting Nietzsche you fucking fools
With straight diagonal lines.
Homophobe!
hey it's no longer June, homophobia is back on the menu
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Oh so you're telling me that my storage unit is actually incredibly well optimised for space efficiency?
Nice!
Now, canwe have fractals built from this?
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
"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
Fractal might have meant that when Mandelbrot coined the name, but that is not what it means now.
Here's a much more elegant solution for 17
You may not like it but this is what peak performance looks like.
https://kingbird.myphotos.cc/packing/squares_in_squares.html
Mathematics has played us for absolute fools
Why can't it be stacked up normally? I don't understand.
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. In the solution shown, the length of one side of the outer square is just a bit smaller than 12. If you pack them normally, the length would be larger than 12. (1 = the length of one side of the smaller squares.)
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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.
Bees seeing this: "OK, screw it, we're making hexagons!"
Fun fact: Bees actually make round holes, the hexagon shape forms as the wax dries.
come on now, let them cook, trust the process
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Can someone explain to me in layman's terms why this is the most efficient way?
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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