Comment on Just one more square bro
cornshark@lemmy.world 1 day agoWhat makes the lower suboptimal?
CorneliusTalmadge@lemmy.world 1 day ago
cockmushroom@reddthat.com 1 day ago
Probably more unused area
matti@sopuli.xyz 1 day ago
The squares are the same size…
5765313496@lemmy.world 1 day ago
The bottom square is slightly larger than the top square.
wolframhydroxide@sh.itjust.works 14 hours 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.
cornshark@lemmy.world 13 hours ago
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?
wolframhydroxide@sh.itjust.works 12 hours ago
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 larger than the larger square in the more efficient set.