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.
For 25 squares of size 1x1 you’d need a square of size 5x5. The square into which 17 1x1 squares fit is smaller than 5x5, so you can’t fit 25 squares into it.
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. This is only the most efficient packing method for 17 squares. It’s the packing efficiency equivalent of the spinal tap “this one goes to 11” quote.
I mean, the actual answer is severalfold: “sometimes, when you need to fill a space, you don’t end up with simple compound numbers of identical packages” is one, but really, it’s a problem in mathematics which, were we to have a general solution to find the most efficient method of packing n objects with identical properties into the smallest area, we would be able to more effectively predict natural structures, including predicting things like protein folding, which is a huge area of medical research. Simple, seemingly inapplicable cases can often be generalised to more specific cases, and that’s how you get the entire field of applied math, as well as most of scientific and engineering modeling
Even when it can’t be generalized, you still often learn something by trying. You may invent a new way to look at a set of problems that no one’s done before, or you may find a solution to something totally unrelated. There’s a lot to learn even when it looks like you’ll gain nothing.
(this is the part where you tack on a silly harmless lie at the end, like - “this specific packing optimization improvement was actually discovered accidentally, through a small mini-game introduced into Candy Crush in 2013. Players discovered the novel improvement, hundreds of individual times, within the first several minutes of launch. Scholars pursuing novel packing algorithms even colloquially call this event ‘The Crushening’”)
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.
For 25 squares of size 1x1 you’d need a square of size 5x5. The square into which 17 1x1 squares fit is smaller than 5x5, so you can’t fit 25 squares into it.
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.
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. This is only the most efficient packing method for 17 squares. It’s the packing efficiency equivalent of the spinal tap “this one goes to 11” quote.
My autistic ass can’t comprehend why anyone would want to arrange a prime number in a square pattern…
???
LOL’ed, but also
I mean, the actual answer is severalfold: “sometimes, when you need to fill a space, you don’t end up with simple compound numbers of identical packages” is one, but really, it’s a problem in mathematics which, were we to have a general solution to find the most efficient method of packing n objects with identical properties into the smallest area, we would be able to more effectively predict natural structures, including predicting things like protein folding, which is a huge area of medical research. Simple, seemingly inapplicable cases can often be generalised to more specific cases, and that’s how you get the entire field of applied math, as well as most of scientific and engineering modeling
Even when it can’t be generalized, you still often learn something by trying. You may invent a new way to look at a set of problems that no one’s done before, or you may find a solution to something totally unrelated. There’s a lot to learn even when it looks like you’ll gain nothing.
(this is the part where you tack on a silly harmless lie at the end, like - “this specific packing optimization improvement was actually discovered accidentally, through a small mini-game introduced into Candy Crush in 2013. Players discovered the novel improvement, hundreds of individual times, within the first several minutes of launch. Scholars pursuing novel packing algorithms even colloquially call this event ‘The Crushening’”)
Mathematicians try this with every number
Yeah, it’s not at all an optimal waffle. It’s more a cool math meme waffle. ;3
– Frost