[HN Gopher] Erich's Packing Center
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Erich's Packing Center
Author : amadeuspagel
Score : 141 points
Date : 2021-12-12 12:44 UTC (10 hours ago)
(HTM) web link (erich-friedman.github.io)
(TXT) w3m dump (erich-friedman.github.io)
| eezurr wrote:
| This is lovely and made me smile. Reminds me of the (incredibly
| fun) times I spent on attempting to solve problems that wont
| necessarily have an impact on the real world (e.g. Collatz
| conjecture)
| etaioinshrdlu wrote:
| I love this kind of stuff but am always searching for a good
| engineering application of it, and I can't think of too much.
| Anyone have some ideas?
| kwhitefoot wrote:
| It's not exactly the same but cutting shapes out of pieces of
| material in ways that waste as little as possible is surely
| related. The paper industry is very interested in a specialised
| subset of this kind of thing. So are factories that make
| transformer cores. The cores are made by stacking many
| (sometimes hundreds) of thin sheets of steel cut from rolls.
| Good quality core steel is expensive so it is important to
| waste as little as possible by making the cuts in the proper
| places.
| sidpatil wrote:
| These are specifically known as _cutting stock problems_ [1].
|
| Example of a possible application: I used to work at a home
| improvement retailer, and one of my responsibilities was to
| cut plywood boards for customers, to the dimensions they
| specified. I'd often wonder if the cuts I was making were
| optimal. The constraints were that any cuts I made had to go
| all the way through the entire piece, and that the blade
| itself was 1/8" thick.
|
| [1] https://en.m.wikipedia.org/wiki/Cutting_stock_problem
| sidpatil wrote:
| Which field(s) of engineering did you have in mind?
|
| One obvious application would be to find the minimum dimensions
| for a box to contain a number of identically-shaped physical
| parts. This would be a three-dimensional packing problem.
|
| Another application could be to find out how to run the maximum
| number of VMs on a finite quantity of physical machines. This
| would be a multidimensional packing problem, possibly irregular
| since the VMs could have different memory, CPU, disk storage,
| etc. requirements.
| cycomanic wrote:
| Actually coding theory and modulation formats in communications
| are essentially very closely related to packing theory (in
| particular sphere packing)
| tshaddox wrote:
| I've encountered this lovely site several times over the years,
| but this is the first time I've noticed the animated section.
| These animations of circles are quite satisfying: https://erich-
| friedman.github.io/packing/ciranima/
| pierrec wrote:
| I'm probably not the first one, but I wonder if there's a
| recognizable sequence in the "squares in triangles" packings:
| https://erich-friedman.github.io/packing/squintri/
|
| You'll notice that some of the packings have a threefold
| rotational symmetry, but only for certain numbers of triangles:
| 3, 6, 9, 15, 27, 36... A quick search in OEIS yields cryptic
| results, probably a red herring.
| borepop wrote:
| My stepfather (a retired professor) is endlessly fascinated by
| these kinds of questions. If you ever ask him at dinner "so what
| are you working on?" the result is often a half-hour-long
| explanation of how many polygons could conceivably fit into some
| other polygon, if it's not about how many numbers could be
| derived from some other set of numbers. I've never been able to
| understand any of it, but it makes him happy.
| ptero wrote:
| This is a fascinating collection (especially in-depth plots of
| each type), thank you for posting (and many, many thanks to the
| author for building this)!
| twic wrote:
| Who is Maurizio Morandi? He seems to have come up with a
| significant number of the most devious packings.
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(page generated 2021-12-12 23:01 UTC)