Optimality of Gerver's Sofa
131 points by petters 7 months ago | 36 comments- senkora 7 months agoHere's a fun render of how a real life Gerver's Sofa could look:
https://www.mdpi.com/symmetry/symmetry-14-01409/article_depl...
I kinda want one...
- alkonaut 7 months agoShould be mandatory in the lunch room of any self respecting math department
- robocat 7 months agoIt would have to be custom made because the sofa size depends on your hallway width.
- david-gpu 7 months agoA Gerber sofa would work for all hallways that are X amount wide or wider, wouldn't it? Given how it slides over a corner.
- robocat 6 months agoAlso a Gerber sofa is based on a flat 2D world. Tilting the sofa to get around a 3D corner seems a reasonable solution.
Presumably there's another Sofa design for the maximum that can get around a 3D corridor corner (and what height do you choose for the corridor given humans tend to choose corridors that are taller than they are wide?)
- immibis 7 months agoOf course, but it's only the biggest possible sofa for a certain size hallway
- robocat 6 months ago
- david-gpu 7 months ago
- alkonaut 7 months ago
- doormatt 7 months agoFor those that don't understand - https://en.wikipedia.org/wiki/Moving_sofa_problem
- righthand 7 months agoAnd perhaps expanded upon into 3D space in Dirk Gently’s Holistic Detective Agency (in which the sofa becomes impossibly stuck, at least in human understood physics) -
https://en.m.wikipedia.org/wiki/Dirk_Gently%27s_Holistic_Det...
- m463 7 months agoIn a similar incident that occurred while Douglas Adams attended St John's College, Cambridge, furniture was placed in the rooms overlooking the river in Third Court while the staircases were being refurbished. When the staircases were completed, it was discovered that the sofas could no longer be removed from the rooms, and the sofas remained in those rooms for several decades.
lol
- astrange 7 months agoCouldn't take them out the windows?
- astrange 7 months ago
- m463 7 months ago
- righthand 7 months ago
- n4r9 7 months agoLooks like the author researched this during their PhD which ended this year, obtained a postdoc and then finished it off. Good on them!
I wonder how the result varies if one of the corridors (the second one for simplicity) is given a variable width. And if the angle of turn is variable.
- yoshicoder 7 months agoI am not well versed with mathematics publishing, but has this proof been already been peer reviewed by other mathematicians, or is it still awaiting confirmation/proof replication?
- emptygame 7 months agoThis is just a preprint, so no peer review or anything yet. Putting out a preprint on the Arxiv like this is generally the first step of the author sharing their work for other mathematicians to take a look at, before it gets submitted for peer review and publication
- ccppurcell 7 months agoJust a quick well, actually. It's common at least in my corner of mathematics to put something on arxiv simultaneously with submission to a journal or conference. If I wanted feedback on a paper before submitting I would definitely do that privately. But everyone is different.
- iterance 7 months agoYou'd think most people who put stuff on arXiv would already be reasonably confident it is correct, at least through correspondence with their peers. However...
That said, I've no reason to doubt this proof (it is not within my wheelhouse).
- iterance 7 months ago
- ccppurcell 7 months ago
- emptygame 7 months ago
- ks2048 7 months agoI was trying to search in the paper for a definition of the shape, to, for example, draw it in SVG.
It seems there is no closed-form solution. I saw this paper is maybe easier to follow for the definition:
https://www.math.ucdavis.edu/~romik/data/uploads/papers/sofa...
Quote:
It is worth noting that Gerver’s description of his shape is not fully explicit, in the sense that the analytic formulas for the curved pieces of the shape are given in terms of four numerical constants A, B, φ and θ (where 0 < φ < θ < π/4 are angles with a certain geometric meaning), which are defined only implicitly as solutions of the nonlinear system of four equations
- robinhouston 7 months agoThe downloadable extras at the bottom of https://www.math.ucdavis.edu/~romik/movingsofa/ may be useful – especially the Mathematica package, if you have Mathematica.
- LegionMammal978 7 months agoSpeaking of SVGs, you reminded me of the beautiful SVG documents in David Ellsworth's "Squares in Squares" page [0]. If you view the source of any of them, you'll find the full Mathematica code to generate any constants needed (which is usually simple enough to implement in other CAS software, if you know how to read it), as well as their values listed to dozens of digits within an inline DTD, to be referenced from the actual elements.
[0] https://kingbird.myphotos.cc/packing/squares_in_squares.html
- robinhouston 7 months ago
- ajb 7 months agoInteresting, but not practical. All real furniture movers would make use of the third dimension.
The difficulty of extending the definition to 3 dimensions is that the restriction to 2 separates two classes of constraint: being able to move the sofa round the corner, and the shape of the sofa being comfortable to sit on.
- phamilton 7 months agoI introduced my kids (13 and 11) to the sofa problem last week as we installed this cabinet organizer from IKEA: https://www.ikea.com/us/en/p/utrusta-corner-base-cab-pull-ou...
After showing them a youtube video about the problem they saw clearly how the organizer is a sofa and even made a joke about it a few days later.
Relatable math is pretty great. Also really cool is showing how academia translates to enriching our lives in benign ways.
- jonahx 7 months agoWow. This solves a problem that's been open for at least 58 years.
- klysm 7 months agoThis might solve the problem - gotta stand up to scrutiny first which takes some time
- klysm 7 months ago
- robinhouston 7 months agoAn interesting thing about this proof is that it looks as though an earlier draft relied on computer assistance – see the author’s code repository at https://github.com/jcpaik/sofa-designer – whereas this preprint contains a proof that “does not require computer assistance, except for numerical computations that can be done on a scientific calculator.”
- parhamn 7 months agoNumberphile had a great video on this a few years ago: https://youtu.be/rXfKWIZQIo4
- jey 7 months agoBig if true! But has it been reviewed by experts?
- amai 7 months agoThis paper makes use of Mamikons theorem. This theorem is not widely known, but it should be: https://en.m.wikipedia.org/wiki/Visual_calculus
- nullc 6 months agoSo say you have a hallway shaped like a 5, what is the maximum volume 3d-gerver's that can make it through (by being possible to rotate to swap the turning direction?
- bee_rider 7 months agoSeems like he could have saved himself a whole lot of trouble by just getting a sectional.
- polygot 7 months agoPivot!
- zgs 7 months agoMy favourite mathematical problem looks to have been solved.
- bediger4000 7 months agoDies Ikea offer one of these?
- nephronaut 7 months agoThere are more interesting investigations and results This one is ok but not remarkable
- briandilley 7 months agoWhat is the practical application of this?
