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Just one more square bro

⁨1308⁩ ⁨likes⁩

Submitted ⁨⁨2⁩ ⁨weeks⁩ ago⁩ by ⁨fossilesque@mander.xyz⁩ to ⁨science_memes@mander.xyz⁩

https://mander.xyz/pictrs/image/0835c7d1-73b0-4594-a826-427144f2fd2b.webp

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  • wolframhydroxide@sh.itjust.works ⁨2⁩ ⁨weeks⁩ ago

    For the uninitiated: this is the current most - efficient method found of packing 17 unit squares inside another square. You may not like it, but this is what peak efficiency looks like.

    (Of course, 16 squares has a packing coefficient of 4, compared to this arrangement’s 4.675, so this is just what peak efficiency looks like for 17 squares)

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    • wonderingwanderer@sopuli.xyz ⁨2⁩ ⁨weeks⁩ ago

      But you can fit 25 squares into the same space. This isn’t efficiency, it’s just wasted space and bad planning.

      You raised the packing coefficient by ⅝ to squeeze one extra square in with all that wasted space, so don’t argue that 25 squares has a packing coefficient of 5. Another ⅜ will get you an extra 8 squares, and no wasted space.

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      • wolframhydroxide@sh.itjust.works ⁨2⁩ ⁨weeks⁩ ago

        Precisely. That’s why I wrote the parenthetical about the greater efficiency of 16 as a perfect square. As the other commenter pointed out, this is a meme.

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      • SlurpingPus@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

        For 25 squares of size 1x1 you’d need a square of size 5x5. The square into 17 squares of size 1x1 fit is smaller than 5x5, so you can’t fit 25 squares into it.

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      • ChaoticNeutralCzech@feddit.org ⁨2⁩ ⁨weeks⁩ ago

        You can’t fit 25 squares into a square 4.675x bigger unless you make them smaller. Yes, that will increase the volume available for syrup.

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      • forestbeasts@pawb.social ⁨2⁩ ⁨weeks⁩ ago

        Yeah, it’s not at all an optimal waffle. It’s more a cool math meme waffle. ;3

        – Frost

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      • JPAKx4@piefed.blahaj.zone ⁨2⁩ ⁨weeks⁩ ago

        You’re misrepresenting the problem though, it’s not about maximising efficiency of an area, but packing the targeted amount of squares inside the smallest square, who’s side lengths are some multiple of the packed squares.

        If you posted this under OP then I would agree with you, obviously this is bad efficiency for the waffle for the purposes of syrup filled in holes, but for the definitions of the problem the person you replied to is correct in their explanation.

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    • Cris_Citrus@piefed.zip ⁨2⁩ ⁨weeks⁩ ago

      Thank you I was very lost lmao

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    • red_bull_of_juarez@lemmy.dbzer0.com ⁨2⁩ ⁨weeks⁩ ago

      Isn’t this only true if the outer square’s size is not an integer multiple of the inner square’s size? Meaning, if you have to do this to your waffle iron, you simply chose the dimensions poorly.

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      • AnarchistArtificer@slrpnk.net ⁨2⁩ ⁨weeks⁩ ago

        The optimisation objective is to fit n smaller squares (in this case, n=17) into the larger square, whilst minimising the size of the outer square. So that means that in this problem, the dimensions of the outer square isn’t a thing that we’re choosing the dimensions of, but rather discovering its dimensions (given the objective of "minimise the dimensions of the outer square whilst fitting 17 smaller squares inside it)

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      • deus@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

        Or maybe you just want waffles with 17 squares in them.

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    • chris@links.openriver.net ⁨2⁩ ⁨weeks⁩ ago

      Does coefficient in this context mean the length of the side of the big square?

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      • wolframhydroxide@sh.itjust.works ⁨2⁩ ⁨weeks⁩ ago

        Exactly. It is the length of the side of the bigger square, relative to the sides of the smaller identical squares.

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  • SlurpingPus@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

    Image

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    • blx@piefed.zip ⁨2⁩ ⁨weeks⁩ ago

      I wonder how many people would have understood both references just a few years ago. Yet today, not only someone made a meme out of this, but it also gets a good deal of updates. That’s the internet culture I love!

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      • ulterno@programming.dev ⁨2⁩ ⁨weeks⁩ ago

        What’s the other reference, for someone not much into Resident Evil?

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  • AnarchistArtificer@slrpnk.net ⁨2⁩ ⁨weeks⁩ ago

    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

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    • Hossenfeffer@feddit.uk ⁨2⁩ ⁨weeks⁩ ago

      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.

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    • gnarles_snarkley@beehaw.org ⁨2⁩ ⁨weeks⁩ ago

      What about 19, 23, 29, 31?! I need to know!

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  • panda_abyss@lemmy.ca ⁨2⁩ ⁨weeks⁩ ago

    This makes me so angry for reasons I can’t articulate

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    • Deconceptualist@leminal.space ⁨2⁩ ⁨weeks⁩ ago

      This actually makes me unreasonably happy, kinda like knowing the secrets of the number 37.

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      • morto@piefed.social ⁨2⁩ ⁨weeks⁩ ago

        Now it’s 42

        mind blow

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      • Neondragon25@piefed.social ⁨2⁩ ⁨weeks⁩ ago

        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?

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  • AdolfSchmitler@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

    Image

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    • Fizz@lemmy.nz ⁨2⁩ ⁨weeks⁩ ago

      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.

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      • far_university1990@reddthat.com ⁨2⁩ ⁨weeks⁩ ago

        knowyourmeme.com/…/girl-running-from-a-peacock

        Orangutan edit in, was peacock.

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      • dreadbeef@lemmy.dbzer0.com ⁨2⁩ ⁨weeks⁩ ago

        that bike is absolutely not part of the picture tho

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    • cornshark@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

      What makes the lower suboptimal?

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      • CorneliusTalmadge@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

        wiki - Square Packing

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      • cockmushroom@reddthat.com ⁨2⁩ ⁨weeks⁩ ago

        Probably more unused area

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      • wolframhydroxide@sh.itjust.works ⁨2⁩ ⁨weeks⁩ ago

        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 (called 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.

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  • Deceptichum@quokk.au ⁨2⁩ ⁨weeks⁩ ago

    How inefficient, I could fit 100 squares in there easily.

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    • Deconceptualist@leminal.space ⁨2⁩ ⁨weeks⁩ ago

      Right? Wake me up when we reach a 7 nm waffle lithographic process.

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      • j4k3@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

        Gate all around. I expect my waffle and syrup to hug each other. No one likes a lethargic partner.

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  • merc@sh.itjust.works ⁨2⁩ ⁨weeks⁩ ago

    Related:

    en.wikipedia.org/wiki/Square_packing

    Nature is a lot more elegant with spheres:

    en.wikipedia.org/…/Close-packing_of_equal_spheres

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  • bitjunkie@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

    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.

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    • Buddahriffic@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

      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.

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    • eru@mouse.chitanda.moe ⁨2⁩ ⁨weeks⁩ ago

      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

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    • kkj@lemmy.dbzer0.com ⁨2⁩ ⁨weeks⁩ ago

      Yeah, if you have extra space but not enough for another row or column, just adjust the size of the inner squares.

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  • UltraGiGaGigantic@lemmy.ml ⁨2⁩ ⁨weeks⁩ ago

    Im a dipper. You put the syrup where you want it yourself. Do not rely on some fancy designed skillet to feed you the way you deserve.

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    • tetris11@feddit.uk ⁨2⁩ ⁨weeks⁩ ago

      Image

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    • captainlezbian@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

      The big perk of waffles is the surface area results in a lot of crispy with some fluffy. The fact that it holds syrup is just a perk

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  • sqw@lemmy.sdf.org ⁨2⁩ ⁨weeks⁩ ago

    wanna maximize syrup? just make it a giant one-square cup.

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    • Jayve@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

      My nephew just drinks the syrup from the bottle.

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      • AltheaHunter@lemmy.blahaj.zone ⁨2⁩ ⁨weeks⁩ ago

        Image

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  • waldfee@feddit.org ⁨2⁩ ⁨weeks⁩ ago

    Relevant xkcd

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  • Berengaria_of_Navarre@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

    Thanks, I hate it!

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  • mexicancartel@lemmy.dbzer0.com ⁨2⁩ ⁨weeks⁩ ago

    Mathematicians: makes something with zero practical applications

    Waffles:

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  • Spaceballstheusername@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

    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.

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  • Jax@sh.itjust.works ⁨2⁩ ⁨weeks⁩ ago

    I’m pretty sure that waffle could easily fit 5 rows of 5, am I crazy?

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    • Ledivin@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

      In the “optimal packing” scenario, it’s slightly too small - like 4.95x4.95

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  • StellarExtract@lemmy.zip ⁨2⁩ ⁨weeks⁩ ago

    Is this the new loss?

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    • y0kai@anarchist.nexus ⁨2⁩ ⁨weeks⁩ ago

      no this is a gain

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  • ICastFist@programming.dev ⁨2⁩ ⁨weeks⁩ ago

    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!

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    • FilthyHands@sh.itjust.works ⁨2⁩ ⁨weeks⁩ ago

      Hexagons are the bestagons.

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  • VoteNixon2016@lemmy.blahaj.zone ⁨2⁩ ⁨weeks⁩ ago

    The solution is to take a bite of waffle and then take a drink of syrup like it’s a chaser

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    • tetris11@feddit.uk ⁨2⁩ ⁨weeks⁩ ago

      and this is why I can no longer go to cocktail bars

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  • Carl@hexbear.net ⁨2⁩ ⁨weeks⁩ ago

    I forget what this shape is actually a solution for but it is very funny

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    • Kumikommunism@hexbear.net ⁨2⁩ ⁨weeks⁩ ago

      It’s the square packing in a square for n = 17.

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      • Carl@hexbear.net ⁨2⁩ ⁨weeks⁩ ago

        yeah that’s a wild rabbit hole to go down, the shaprs are either extremely satisfying or extremely distressing, there is no in-between.

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  • bulwark@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

    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.

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    • Cort@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

      Those fat Belgian waffles have nothing on the Dutch stroopwafel technology coming out of asml

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  • agamemnonymous@sh.itjust.works ⁨2⁩ ⁨weeks⁩ ago

    TIHI

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  • Deconceptualist@leminal.space ⁨2⁩ ⁨weeks⁩ ago

    About damn time. #WaffleOptimizationCrew

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  • bitjunkie@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

    Image

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  • butter_tart@piefed.ca ⁨2⁩ ⁨weeks⁩ ago

    THERE IS CLEARLY ROOM FOR 25 SQUARES…. sorry just so unreasonably angry right now

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    • webghost0101@sopuli.xyz ⁨2⁩ ⁨weeks⁩ ago

      There isn’t. The sides are 4.675 long (as far as i understand)

      To fit more squares, youd need to use smaller squares but by that logic you could fit any number of squares.

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  • Fokeu@lemmy.zip ⁨2⁩ ⁨weeks⁩ ago

    Took me a while lol

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  • ik5pvx@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

    Who tf uses a 56 years old collectible for breakfast?

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  • PapaStevesy@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

    Decrease the size of the squares and you could get waaaay more surface area.

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    • Zwiebel@feddit.org ⁨2⁩ ⁨weeks⁩ ago

      This comes from a math problem where the squares size is fixed and you try to minimize the area they fit in

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      • PapaStevesy@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

        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.

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    • blackbrook@mander.xyz ⁨2⁩ ⁨weeks⁩ ago

      It’s really volume you care about, for filling with syrup.

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      • kazerniel@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

        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 🤷

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      • PapaStevesy@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

        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.

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  • thatradomguy@lemmy.world ⁨2⁩ ⁨weeks⁩ ago

    star wars palpatine from revenge of sith where he sites with Anakin and the image includes caption reading the dark side of the force is a pathway to abilities some consider to be unnatural

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  • MeetMeAtTheMovies@hexbear.net ⁨2⁩ ⁨weeks⁩ ago

    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

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    • ranzispa@mander.xyz ⁨2⁩ ⁨weeks⁩ ago

      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.

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  • lessthanluigi@lemmy.sdf.org ⁨2⁩ ⁨weeks⁩ ago

    How Alton Brown makes his waffles

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