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.
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.
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.
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
the line of man is straight ; the line of god is crooked
stop quoting Nietzsche you fucking fools
Is this confirmed? Like yea the picture looks legit, but anybody do this with physical blocks or at least something other than ms paint?
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.
Proof via "just look at it"
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.
I was joking about the proof but there's a non-pixelated version in the comments here
Visual proofs can be deceptive, e.g. the infinite chocolate bar.
Here's a much more elegant solution for 17
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