13 ms·
The moving sofa problem
- TimeBigot 8y agoPIVAHT!!
- manojlds 8y agoSofa constant should be called Ross Number.
- ourmandave 8y agovar numberOfMovers = (! hideABed) ? 3 : 0;
- Biba89 8y agoIt would be great to someone create a game where you should calculate and create sofa in order to move sofa through the building passages
- SOLAR_FIELDS 8y agoWould proving this advance our knowledge in some related field such as mathematical topology? Since the values have already been brute forced (but unproven) there really isn’t any direct practical application for knowing the solution
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- mabbo 8y ago> there really isn’t any direct practical application for knowing the solution Oh, but math always seems that way. And often, it is. But sometimes, very rarely, your solution to the sofa problem explains a key detail to P vs NP, or allows a breakthrough in transistor design, or improves the airflow calculations allowing for faster jets, etc. Math's true beauty is that it's never done playing games with us as we realize all the strange connections.
- Someone 8y agoDepends on the proof. If it solves this specific problem more or less through perseverance, it won’t be more than a tiny footnote in the history of mathematical. If, on the other hand, some abstract theory contains this as a special case (say by limiting the number of dimensions to 2 and the geometry to Euclidean), that theory could (but isn’t guaranteed to) have wider application, both inside mathematics and outside of it. I would think the former is more likely than the latter, though.
- thomasfedb 8y agoKickstarter idea: Gerver's sofa in Italian leather.
- mkl 8y agoIt doesn't seem very practical as furniture - there's a big hole in the middle. Actual sofas can be moved in three dimensions, so can be more usefully shaped.
- empath75 8y agoIs there a 3 dimensional variant? Or n-dimensional?
- thomasfedb 8y agoOnly found this: https://www.reddit.com/r/math/comments/6hui9p/is_the_sofa_moving_problem_any_different_in_3d/ https://www.reddit.com/r/math/comments/6hui9p/is_the_sofa_mo... I suppose you could have a sofa that your corkscrew around the corner?
- mattkrause 8y agoIt might not be awful if it came with a matching coffee table for the middle section.
- berbec 8y agoEven better - a detachable ottoman. It fills the hole when you want a sofa, and becomes a footrest when you don't.
- gregman1 8y agoAs a wallet
- willvarfar 8y agoIf anyone hasn't read or has forgotten Douglas Adams 'Dirk Gently's Holistic Detective Agency' then I warmly recommend it. It includes, iirc, The Sofa Problem and the solution is classic Adams and all HNers will love it! :)
- noir_lord 8y agoWondered if anyone would mention this, also if you haven't tried it the Netflix version of Dirk Gently is wonderful, departs from the books without departing from the characters.
- bostik 8y agoThe first season is delicious, the second one (unfortunately) veers too far off into the odd mix of fantasy, conspiracy theories and mysticism. I'm curious what the third one brings. Casting-wise, I am not sure Elijah Wood was the best choice. Big name for impact maybe, but the role just feels ill-fitting.
- scrooched_moose 8y agoUnfortunately nothing, it's been cancelled. https://www.google.com/amp/s/deadline.com/2018/03/dirk-gentlys-holistic-detective-agency-will-not-have-a-season-3-producer-1202335666/amp/ https://www.google.com/amp/s/deadline.com/2018/03/dirk-gentl...
- golergka 8y agoSecond season was a huge disappointment, but it also featured the best and most truthful portrayal of MDMA that I've ever seen on screen (under the guise of a "love" magic spell).
- Apocryphon 8y agoIt's sad sack similar enough to his role on Wilfred.
- noir_lord 8y agoI really enjoyed the second season but yes the first season was better bordering on sublime. Much better than the BBC version (and very different). When I heard they where doing an american version I didn't expect much wondering how it would translate...it turns out, very well.
- vinchuco 8y agoKudos to the animation illustrator [0]. See also [1]. I'm collecting these for reasons. [0] https://en.m.wikipedia.org/wiki/User:Rocchini https://en.m.wikipedia.org/wiki/User:Rocchini [1] https://news.ycombinator.com/item?id=15549197 https://news.ycombinator.com/item?id=15549197
- mar77i 8y agoThat particular guy appears to have a knack for geometry, 4-dimensionality and hyperbolic spaces. Topics that I feel like I have a foot in from watching my favorite Parker square videos...
- p1mrx 8y agoThe animation appears to be missing some frames, at the point where the couch starts to turn. Someone with a moderate amount of time on their hands could probably patch it by mirroring frames from the end of the turn.
- chdefrene 8y agoNumberphile did a great video on this topic https://youtu.be/rXfKWIZQIo4 https://youtu.be/rXfKWIZQIo4
- tambourine_man 8y agoNice numberphile vídeo on the subject: https://youtube.com/watch?v=rXfKWIZQIo4 https://youtube.com/watch?v=rXfKWIZQIo4
- mkl 8y agoGibbs's computational approach is really interesting [1]. Keep the sofa still and move the corridor, and the optimal sofa shape is the intersection of all (well n, since it's a numerical approximation) the corridor shapes as they sweep around. [1] https://www.researchgate.net/publication/311900489_A_Computational_Study_of_Sofas_and_Cars https://www.researchgate.net/publication/311900489_A_Computa...
- cheerlessbog 8y agoThat link does not work for me, but this may be better : https://www.math.ucdavis.edu/~romik/movingsofa/ https://www.math.ucdavis.edu/~romik/movingsofa/
- mkl 8y agoThat is a different article. My link to Gibbs's article came from Wikipedia, but your link points to another copy: http://vixra.org/pdf/1411.0038v2.pdf http://vixra.org/pdf/1411.0038v2.pdf Maybe that one will work for you.
- eboyjr 8y ago> ...describing sofas in terms of the translations and rotations as a function of time is by now a standard way of thinking about the moving sofa problem, and has been used in the attack on the problem by Joseph Gerver in his paper from 1992, and in my own recent paper, where among other thing I made precise your suggested notion of describing the sofa shape that results from the continuous intersection of corridors rotating and translating over time. See my paper (available here: https://www.math.ucdavis.edu/~romik/data/uploads/papers/sofa.pdf https://www.math.ucdavis.edu/~romik/data/uploads/papers/sofa...), and especially Theorem 1 in section 2. Dan Romik
- vignesh_m 8y agoSomewhat related, but more counterintuitive and "solved": https://en.wikipedia.org/wiki/Kakeya_set https://en.wikipedia.org/wiki/Kakeya_set
- lb1lf 8y agoRecycled anecdote from the last time this was discussed on HN: While a student, I looked after the apartment of a friend of mine, who was overseas. When he moved there, we were _just_ able to eke his sofa around the last corner from the stairwell and through the door to his apartment. Just. After much cursing and several failed attempts. So, what does a good (cough) friend do while the owner is overseas? Get some hardwood mouldings/trimmings/whatever you call those long, thin pieces of wood typically put where wall transitions to ceiling or floor and nail them to the exterior doorframes, making both door openings perhaps 3/8" or so narrower, paint them in the color of the doorframe, sit back and wait. Then, years later, as he is about to leave town, moving company comes along and everything runs smoothly until one item remains. The sofa. Obviously, it got in - so it'll (as obviously) come out. Only it doesn't. We (everybody except the owner and the moving guys were in on the joke) managed to keep a straight face for several minutes. The moving guys even laughed as they (eventually) left, mollified by a bottle filled with a Scottish export product which we'd kept on hand to ensure no feelings were hurt afterwards.
- te_platt 8y agoThat especially hurt me too read as just this morning I helped a friend move a couch. We had had to turn it pretty much every way possible and the only reason we kept trying was because we knew somehow she got it moved in. It's interesting that in so many different areas knowing there is a solution makes finding the solution easier. In a related story my dad remodeled his house and put in a new wall blocking in a couch. When it came time to move it (years later) I thought it was going to be a permanent feature of that room. My dad came up with the solution of getting a saw and cutting the couch into pieces.
- fcbrooklyn 8y agoThis is such a common issue in NYC that we have a business (the couch doctor) that does nothing but take apart furniture and reassemble it in place. Friend of mine used them and they were apparently really impressive (he told them what sofa he had, the dimensions of his door, and they knew right away it wouldn't be a problem)
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- kyberias 8y agoPivot!
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- ezequiel-garzon 8y agoYes! https://youtu.be/Tam7KO4qhUI https://youtu.be/Tam7KO4qhUI
- ychen306 8y agoBeat me to it.
- 11235813213455 8y agoreminds me of https://i.imgur.com/IU5aYKi.gif https://i.imgur.com/IU5aYKi.gif
- enriquto 8y agoThis problem seems tame and uninteresting compared to the real-life 3D case. Last christmas, I was moving a sofa on my mother-in-law's home, and it was stuck in the corridor. She told me "i seem to recall that you have to raise this side a bit". I replied something to the effect "no way, i am a mathematician and there's no way that this can possibly make a difference". Of course she was right. I could only move the sofa by rotating it in 3D just so, so that the slightly protruding arm and leg could pass one after the other. So the real question, not dealth with in the wikipedia page, is: what is the largest sofa that we can move through a unit corner, allowing it to rotate in 3D ?
- OscarCunningham 8y agoI guess the answer might be to take the largest 2D sofa and just extrude it upwards 1, so that it fills the height of the corridor.
- enriquto 8y agoIt will depend on how you define the "largest" sofa: total volume? surface area of the ground covered by it? If it is the largest volume, you need to limit the height of the corridor (to be the same as the width? a multiple of it?). Otherwise, you can pass an arbitrarily long L that you turn side-wise on the corner.
- OscarCunningham 8y agoI was thinking of maximising the volume of the sofa in a corridor as tall as it is wide.
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- flingo 8y agoCan someone just put this in an ISO standard already, so I know how wide to make my hallways?