Now, canwe have fractals built from this?
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
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.
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.
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.
Here’s a much more elegant solution for 17
You may not like it but this is what peak performance looks like.
Oh so you’re telling me that my storage unit is actually incredibly well optimised for space efficiency?
Nice!
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”
Visual proofs can be deceptive, e.g. the infinite chocolate bar.
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 😳
I hate this so much
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.
4-dimensional bees make rhombic dodecahedrons
Bestagons*
Texagons
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.
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
All this should tell us is that we have a strong irrational preference for right angles being aligned with each other.
Lol, the ambidextrous sofa. It’s a butt plug.
For two!
Now I want to rewatch Requiem for a dream.
Requiem is the best movie that I’ve only wanted to watch once.
It’s also a great name for a cover band.
Butt rock covers of gospel songs perhaps?
Thanks for the explanation
Any other configurations results in a larger enclosed square. This is the most optimal way to pack 17 squares that we’ve found
Source?
Try this page if you want to read more about it:
https://erich-friedman.github.io/papers/squares/squares.html
Thank you, that’s very helpful - unlike cretins downvoting me for asking a question.
Upvoted.
That’s because when you just type “source?” and nothing else people perceive it as you challenging/denying the claim in a slightly hostile manner
Thankfully the perceived hostility was then dispelled with a followup comment calling people cretins.
…wait.
Bidwell, J. (1997)
In the meme.
Seriously?
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.
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.
That tiny gap on the right is killing me
That’s my favorite part 😆
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
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.
