Efficency
Efficency
55 comments
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You got nothing on the 17 square packing
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Can someone explain this?
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This is the most efficient (known) packing of 17 unit squares inside a square. If you're asking why it's like that, that's above my math proficiency level.
https://en.wikipedia.org/wiki/Square_packing
See also: https://kingbird.myphotos.cc/packing/squares_in_squares.html
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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.
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Mathematics actually hates humanity, and it likes to remind us of it, sometimes. That's why.
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?
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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.
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How?
Yes, if you push the circles down a bit, it forms a 7 by 7 matrix. But if pushing the circles into a square matrix is not allowed: how?
Edit: I get it now. It is about (efficient) packing not about counting. I also get the 4th panel now...
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7 by 7 matrix isn’t the optimal packing. The square shown is slightly smaller than 7 by 7.
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Thanks. I thought it was about counting. It all makes a lot more sense now. (And it also doesn't.)
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I mean it makes sense when you think about how the circles 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 almost perfect packing in the middle of the 49 circle square, surrounded by fault lines in the structure and then some more good packing, and garbage in the bottom.
slightly related Steve Mould video
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Or, they could do 6x8 with one obviously extra at the end. But this is a funny not a rational thing.
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Yarr
Neat spacing leave much gap, patterned mess less space between.
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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.
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Should have used hexagons
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The bestagons.
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That’s what she said 😏
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HCP FTW.
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This is the kind of stuff the timber mafia needs to know so that they can efficiently pack trees and send them to IKEA.
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Because it's a smaller area than 7x7.
If you consider the regular packing in an infinite plane, tri/hex packing is the most space efficient (least wasted space), so I'd assume larger packings would tend towards that. But in smaller packings, the efficiency loss from the extra size needed to offset the circles outweighs the efficiency gained by hex packing.
7x7 is the boundary where those efficiency tradeoffs switch.
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I think you skipped a row.
Also, 6*6+7=???
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I did yeah; deleted my content almost immediately after posting it because I went to double check. Counting is hard!
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Maths is a science now?
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Science is applied math, engineering is applied science, manufacturing is applied engineering, etc. it's math all the way down.
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Relevant XKCD: https://xkcd.com/435/
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Math and philosophy are basically interchangeable here. I know there's a maths version I saved somewhere. 😅
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always_has_been.jpg
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We've got !mathmemes@lemmy.blahaj.zone for maths but it's a bit quiet compared to here
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Quality over quantity! 😉
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I think you forgot the /s
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The study and discovery of mathematics is, yes.
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Always has been.
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55 comments