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)

Edit: For the record, since this blew up, a tiny nitpick in my own explanation above: a smaller value of the packing coefficient is not actually what makes it more efficient (as it is simply the ratio of the larger square's side to the sides of the smaller squares). The optimal efficiency (zero interstitial space) is achieved when 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 this packing of n=17, with a packing coefficient of 4.675. Since sqrt(25)=5, that case is a perfectly efficient packing, equal to the case of n=16 with coefficient of 4. Since sqrt(17)=4.123, this packing above is not perfectly efficient, leaving interstices. Obviously. This also means that we may yet find a packing for n=17 with a packing coefficient closer to sqrt(17), which would be an interesting breakthrough, but more important are the questions "is it possible to prove that a given packing is the most efficient possible packing for that value of n" and "does there exist a general rule which produces the most efficient possible packing for any given value of n unit squares?"

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

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

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

Related:

https://en.wikipedia.org/wiki/Square_packing

Nature is a lot more elegant with spheres:

https://en.wikipedia.org/wiki/Close-packing_of_equal_spheres

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.

Relevant xkcd

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

Mathematicians: makes something with zero practical applications

Waffles:

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.

Is this the new loss?

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

It's still funny

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.

Thanks, I hate it!

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!

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.

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

About damn time.

#WaffleOptimizationCrew

TIHI