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Efficency
Submitted 5 months 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 5 months ago
lemmyng@lemmy.ca 5 months ago
Zagorath@aussie.zone 5 months 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 months ago
How?
magic_lobster_party@kbin.run 5 months ago
7 by 7 matrix isn’t the optimal packing. The square shown is slightly smaller than 7 by 7.
hsdkfr734r@feddit.nl 5 months 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 months 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 months ago
These are optimal packings of n circles in a square shaped container
datelmd5sum@lemmy.world 5 months 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 months 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 5 months ago
Yarr
Neat spacing leave much gap, patterned mess less space between.
intensely_human@lemm.ee 5 months 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 months ago
Should have used hexagons
nephs@lemmygrad.ml 5 months ago
The bestagons.
intensely_human@lemm.ee 5 months ago
That’s what she said 😏
sabreW4K3@lazysoci.al 5 months ago
Maths is a science now?
Tolookah@discuss.tchncs.de 5 months ago
Science is applied math, engineering is applied science, manufacturing is applied engineering, etc. it’s math all the way down.
zarlin@lemmy.world 5 months ago
Relevant XKCD: xkcd.com/435/
fossilesque@mander.xyz 5 months ago
ogeist@lemmy.world 5 months ago
always_has_been.jpg
The_Che_Banana@beehaw.org 5 months ago
Evil_Shrubbery@lemm.ee 5 months ago
smeg@feddit.uk 5 months ago
We’ve got !mathmemes@lemmy.blahaj.zone for maths but it’s a bit quiet compared to here
sabreW4K3@lazysoci.al 5 months ago
Quality over quantity! 😉
JimSamtanko@lemm.ee 5 months ago
I think you forgot the /s
Tlaloc_Temporal@lemmy.ca 5 months ago
The study and discovery of mathematics is, yes.
Bertuccio@lemmy.world 5 months ago
Always has been.
veganpizza69@lemmy.world 5 months 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.
_different_username@lemmy.world 5 months ago
HCP FTW.
boatswain@infosec.pub 5 months ago
[deleted]Enkers@sh.itjust.works 5 months ago
I think you skipped a row.
Also, 6*6+7=???
boatswain@infosec.pub 5 months 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 months ago
You got nothing on the 17 square packing
OrnateLuna@lemmy.blahaj.zone 5 months ago
Can someone explain this?
Enkers@sh.itjust.works 5 months 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 5 months 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 months ago
Mathematics actually hates humanity, and it likes to remind us of it, sometimes. That’s why.
isolatedscotch@discuss.tchncs.de 5 months ago
xkcd.com/2740