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This makes me so angry for reasons I can’t articulate
This actually makes me unreasonably happy, kinda like knowing the secrets of the number 37, which is coincidentally your current number of upvotes.
I don’t know…37 just seems like such a random number, even the 3 and the 7 seem so random, what secrets could there be?
Surprsingly different secrets than 137 despite using two of the same digits.
(smartass 😛)
Now it’s 42
Now its more than 42. How do you feel about being wrong on the internet, genius?
The answer is still 42. If you don’t like it, maybe you’re asking the wrong questions
Now then, let’s not go mixing up then with now, then.
I’m sorry I can’t hear you over the sound of me being right on the internet. You’re gonna have to speak up.
Isn’t there a difference between “the most squares fit into a square” and “a collection of squares optimized for maximum small-square area inside of a larger square”? If there’s a difference in solutions, what would the solution for the latter actually be?
Mathematicians halp plz
I’m sure a big square inside the main square would have a higher surface area than this. Calculations over the top of my head tell me this, but then again, I didn’t publish an article on the subject.
I’m pretty sure that waffle could easily fit 5 rows of 5, am I crazy?
It’s still funny
In the “optimal packing” scenario, it’s slightly too small - like 4.95x4.95
I am sad because these squares look very out of place, unlike hexagons which are beautiful and perfect and never cause problems whatsoever, ever ever!
Hexagons are the bestagons.
It’s only more efficient when the containing square is large enough that there would be wasted space on the edges if the inner squares were lined up as a grid. The outer square of the waffle iron is almost but not quite large enough to fit a 4x5 grid. People losing their minds over this weird configuration being “more efficient” think it’s because it’s more efficient than a grid where all the space is used, which is not what this would be.
Yeah, there’s a lot of unused space there. Or just look at the gap in the middle of that row of 4. A slightly smaller square could have fit a 5x5, even.
It’s a novelty, not an optimization.
Yeah, if you have extra space but not enough for another row or column, just adjust the size of the inner squares.
the joke is about achieving max density of the squares, density as in square per area of the waffle
of course you can make the whole waffle bigger, but it would decrease the density
a better solution is adding smaller squares though
Oh my God, I fucking love this. I mean, I absolutely hate that this is the optimal way to pack 17 squares into a larger square such that the size of the larger square is minimised. However, I love that someone went to the effort of making a waffle iron plate for this. High effort shitposts like this give me life
I fucking love this. I mean, I absolutely hate that this is the optimal way to pack 17 squares into a larger square such that the size of the larger square is minimised.
There’s a brain echo in here.
What about 19, 23, 29, 31?! I need to know!
To be honest I would love a waffle maker like this where some parts of the waffle are a little undercooked and other parts crispy.
Pfft, let me know when “Big Waffle” develops its own proprietary 6-nanometer syrup squares. Until then I will defer to the Belgians and their superior waffle technology.
Those fat Belgian waffles have nothing on the Dutch stroopwafel technology coming out of asml
Mathematicians: makes something with zero practical applications
Waffles:
I forget what this shape is actually a solution for but it is very funny
It’s the square packing in a square for n = 17.
yeah that’s a wild rabbit hole to go down, the shaprs are either extremely satisfying or extremely distressing, there is no in-between.
THERE IS CLEARLY ROOM FOR 25 SQUARES… sorry just so unreasonably upset by this image
There isn’t. The sides are 4.675 long.
To fit more squares, youd need to use smaller squares but by that logic you could fit any number of squares.
Decrease the size of the squares and you could get waaaay more surface area.
*Increase? Assuming constant grid line thickness the fewer squares you have the more surface area you get.
Idk what you mean about constant grid line thickness, but if that’s your sticking point, stop assuming it. The waffle in the post certainly doesn’t have it. Regardless, you’re incorrect, more squares = more surface area, smaller squares = more squares. If you shrunk a billiards ball to the size of a golf ball, which one would have more surface area?
It’s really volume you care about, for filling with syrup.
Good point. Pesky square-cube law gets me again. Having done three minutes of research on Wikipedia pages I didn’t fully understand, I think changing the square divots to spherical ones will give us the smallest surface area-to-volume ratio.
Nooo, Hexagons are the bestagons!
Unrelated, but as a Hungarian, this association of waffles with syrup is so odd to see. Syrup is basically just sugar and water, isn’t it? Sounds pretty boring. As a kid we always put nutella on waffles 🤷
We don’t put plain sugar syrup on waffles, we use maple syrup or sometimes a fruit syrup such as blueberry. Maple syrup has a very distinctive flavor.
I checked out your link: this home made syrup is interesting but I’ve never heard of anyone doing this.
thanks, that’s reassuring to know :D maple syrup is good, but imho nutella is better :9
I can imagine that being really good! Hazelnut is under appreciated in the US.
This comes from a math problem where the squares size is fixed and you try to minimize the area they fit in
Yeah I know, but it’s terrible waffle design, there’s big flat chunks without syrup squares. It’s a huge amount of wasted area unable to hold syrup in any meaningful volume. It’s sad, really.
Edit: not to mention the waffle in the picture is clearly big enough to hold 25 squares the same size as those pictured! I thought these memes were supposed to be scientific…
You can’t fit 25 squares of the same size in that space. If you check the top row there’s 4 squares and space for slightly less than one more square, you can’t fit a 5x5 grid there unless you have smaller squares or a bigger waffle
Maybe you couldn’t, I absolutely could. The space just looks smaller because there’s a diagonal square butting into it. Doesn’t matter anyway, making the squares smaller was my original comment that sparked this conversation, so I’m right both ways.
No, you’re not. It’s square packing, this is the optimal arrangement of 17 squares inside another square as far as we’re currently aware with a side length of 4.6756 inner squares. You cannot fit 5 squares in the space of 4.7 squares of the same size.
It’s also a well-known meme and this is a science meme community.
Where does this picture come from? Is it real? Ive just thought at how absurd an orangutan on a bike chasing a kid actually is.
that bike is absolutely not part of the picture tho
I’m cooked. It looked real
https://knowyourmeme.com/memes/girl-running-from-a-peacock
Orangutan edit in, was peacock.
What makes the lower suboptimal?
Since a link to a wiki article does not an explanation make:
The optimal efficiency (zero interstitial space) is achieved when the ratio of the side length of the larger square to the sides of the shorter squares (let’s call it the “packing coefficient”) is precisely equal to the square root of the number of smaller squares. Hence why the case of n=25, with a packing coefficient of 5, is actually more efficient than the packing of n=17 given in the waffle iron, with a packing coefficient of 4.675. Since sqrt(25)=5, that case is a perfectly efficient packing, equivalent to the case of n=16 with coefficient of 4. Since sqrt(17)=4.123, the waffle packing (represented by the orangutan) above is not perfectly efficient, leaving interstices. However, the packing coefficient of the suboptimal solution (represented by the girl) is actually 4.707, slightly further from sqrt(17), and thus less efficient, leaving greater wasted interstitial space.
Trying to understand what this actually means. Since these two diagrams have the same number of squares, does this mean the inefficient packing squares are actually slightly smaller in a way that’s difficult to observe?
Ah, no, it’s that the more efficient packing takes up less space, so the less efficient square is actually slightly larger than the other, compared to the smaller squares.
If the smaller squares are identical in both sets, then the larger square in the less-efficient set will be slightly bigger than the larger square in the more efficient set.
Probably more unused area
The squares are the same size…
The bottom square is slightly larger than the top square.
slice-of-pie-from-just-off-center-and-carved-out-comma-but-worse.bmp
