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Efficency
Submitted 6 days ago by fossilesque@mander.xyz to science_memes@mander.xyz
https://mander.xyz/pictrs/image/891d05b2-5dfe-4cb3-80a1-a8682f1e2b45.jpeg
Comments
jordanlund@lemmy.world 6 days ago
lemmyng@lemmy.ca 5 days ago
Zagorath@aussie.zone 5 days ago
This is about the most efficient way to pack that number of circles. By looking at the bottom row of the 49, you can see that it’s slightly less wide than 7 diameters, because it has 5 circles at the very bottom (taking up 5 diameters of width), but two are slightly raised, which also means they’re slightly inward.
hsdkfr734r@feddit.nl 5 days ago
How?
magic_lobster_party@kbin.run 5 days ago
7 by 7 matrix isn’t the optimal packing. The square shown is slightly smaller than 7 by 7.
hsdkfr734r@feddit.nl 5 days ago
Ah. I thought it was about counting. It all makes a lot more sense now. (And it also doesn’t.)
mexicancartel@lemmy.dbzer0.com 5 days ago
Yeah it can fit almost 7 in a line in the last panel so theese definitely aren’t the same squares
apotheotic@beehaw.org 5 days ago
These are optimal packings of n circles in a square shaped container
datelmd5sum@lemmy.world 5 days ago
I mean it makes sense when you think about how the spheres arrange in an infinte square and e.g. 4r square. There has to be some fuckery between the perfect packing and the small square packing. You can see a triangle of perfect packing in the middle of the 49 sphere square, surrounded by garbage.
Maggoty@lemmy.world 5 days ago
Or, they could do 6x8 with one obviously extra at the end. But this is a funny not a rational thing.
FiniteBanjo@lemmy.today 4 days ago
Yarr
Neat spacing leave much gap, patterned mess less space between.
intensely_human@lemm.ee 4 days ago
Well-put. One perfect pattern at one scale, another perfect pattern at a different scale, and then there has to be a transition between them of optimal steps along the way. I like that.
helpImTrappedOnline@lemmy.world 5 days ago
Should have used hexagons
nephs@lemmygrad.ml 5 days ago
The bestagons.
intensely_human@lemm.ee 4 days ago
That’s what she said 😏
veganpizza69@lemmy.world 4 days ago
This is the kind of stuff the timber mafia needs to know so that they can efficiently pack trees and send them to IKEA.
sabreW4K3@lazysoci.al 6 days ago
Maths is a science now?
Tolookah@discuss.tchncs.de 6 days ago
Science is applied math, engineering is applied science, manufacturing is applied engineering, etc. it’s math all the way down.
zarlin@lemmy.world 6 days ago
Relevant XKCD: xkcd.com/435/
fossilesque@mander.xyz 5 days ago
ogeist@lemmy.world 6 days ago
always_has_been.jpg
The_Che_Banana@beehaw.org 6 days ago
Evil_Shrubbery@lemm.ee 5 days ago
smeg@feddit.uk 5 days ago
We’ve got !mathmemes@lemmy.blahaj.zone for maths but it’s a bit quiet compared to here
sabreW4K3@lazysoci.al 5 days ago
Quality over quantity! 😉
JimSamtanko@lemm.ee 5 days ago
I think you forgot the /s
Tlaloc_Temporal@lemmy.ca 5 days ago
The study and discovery of mathematics is, yes.
Bertuccio@lemmy.world 4 days ago
Always has been.
_different_username@lemmy.world 6 days ago
HCP FTW.
boatswain@infosec.pub 5 days ago
[deleted]Enkers@sh.itjust.works 5 days ago
I think you skipped a row.
Also, 6*6+7=???
boatswain@infosec.pub 5 days ago
I did yeah; deleted my content almost immediately after posting it because I went to double check. Counting is hard!
Zehzin@lemmy.world 5 days ago
You got nothing on the 17 square packing
OrnateLuna@lemmy.blahaj.zone 5 days ago
Can someone explain this?
Enkers@sh.itjust.works 5 days ago
This is the most efficient packing of 17 unit squares inside a square. If you’re asking why it’s like that, that’s above my math proficiency level.
en.wikipedia.org/wiki/Square_packing
Artyom@lemm.ee 4 days ago
We’ve figured out optimal packing methods for any number of squares inside a big square. When a number is below and near a square number like 15, you just leave an empty box, but when it’s far from the next square number, you’ll be able to pack them more efficiently than just leaving empty squares around. Turns out this kind of stuff is hilariously hard to prove that it’s the most efficient method.
nephs@lemmygrad.ml 5 days ago
Mathematics actually hates humanity, and it likes to remind us of it, sometimes. That’s why.
isolatedscotch@discuss.tchncs.de 4 days ago
xkcd.com/2740