fossilesqueMar 4

Just one more square bro

https://mander.xyz/post/48352247

Show threadwolframhydroxideMar 4

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)

Show threadred_bull_of_juarez
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.
Mar 4 at 9:12amWeb
Show threaddeusMar 4
Or maybe you just want waffles with 17 squares in them.
Show threadAnarchistArtificerMar 4
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)
Show threadwolframhydroxideMar 5
Specifically, the optimal area side length of the larger square for any integer n is the square root of n. The closer your larger side length gets to sqrt(n), the more efficient your packing.