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Optimality of Gerver's Sofa

131 点作者 petters5 个月前

19 条评论

senkora5 个月前
Here&#x27;s a fun render of how a real life Gerver&#x27;s Sofa could look:<p><a href="https:&#x2F;&#x2F;www.mdpi.com&#x2F;symmetry&#x2F;symmetry-14-01409&#x2F;article_deploy&#x2F;html&#x2F;images&#x2F;symmetry-14-01409-g007.png" rel="nofollow">https:&#x2F;&#x2F;www.mdpi.com&#x2F;symmetry&#x2F;symmetry-14-01409&#x2F;article_depl...</a><p>I kinda want one...<p>Source: <a href="https:&#x2F;&#x2F;www.mdpi.com&#x2F;2073-8994&#x2F;14&#x2F;7&#x2F;1409" rel="nofollow">https:&#x2F;&#x2F;www.mdpi.com&#x2F;2073-8994&#x2F;14&#x2F;7&#x2F;1409</a>
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doormatt5 个月前
For those that don&#x27;t understand - <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Moving_sofa_problem" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Moving_sofa_problem</a>
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n4r95 个月前
Looks like the author researched this during their PhD which ended this year, obtained a postdoc and then finished it off. Good on them!<p>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.
yoshicoder5 个月前
I 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&#x2F;proof replication?
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ks20485 个月前
I was trying to search in the paper for a definition of the shape, to, for example, draw it in SVG.<p>It seems there is no closed-form solution. I saw this paper is maybe easier to follow for the definition:<p><a href="https:&#x2F;&#x2F;www.math.ucdavis.edu&#x2F;~romik&#x2F;data&#x2F;uploads&#x2F;papers&#x2F;sofa.pdf" rel="nofollow">https:&#x2F;&#x2F;www.math.ucdavis.edu&#x2F;~romik&#x2F;data&#x2F;uploads&#x2F;papers&#x2F;sofa...</a><p>Quote:<p>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 &lt; φ &lt; θ &lt; π&#x2F;4 are angles with a certain geometric meaning), which are defined only implicitly as solutions of the nonlinear system of four equations
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ajb5 个月前
Interesting, but not practical. All real furniture movers would make use of the third dimension.<p>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.
phamilton5 个月前
I introduced my kids (13 and 11) to the sofa problem last week as we installed this cabinet organizer from IKEA: <a href="https:&#x2F;&#x2F;www.ikea.com&#x2F;us&#x2F;en&#x2F;p&#x2F;utrusta-corner-base-cab-pull-out-fitting-40265649&#x2F;" rel="nofollow">https:&#x2F;&#x2F;www.ikea.com&#x2F;us&#x2F;en&#x2F;p&#x2F;utrusta-corner-base-cab-pull-ou...</a><p>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.<p>Relatable math is pretty great. Also really cool is showing how academia translates to enriching our lives in benign ways.
jonahx5 个月前
Wow. This solves a problem that&#x27;s been open for at least 58 years.
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robinhouston5 个月前
An 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 <a href="https:&#x2F;&#x2F;github.com&#x2F;jcpaik&#x2F;sofa-designer">https:&#x2F;&#x2F;github.com&#x2F;jcpaik&#x2F;sofa-designer</a> – whereas this preprint contains a proof that “does not require computer assistance, except for numerical computations that can be done on a scientific calculator.”
parhamn5 个月前
Numberphile had a great video on this a few years ago: <a href="https:&#x2F;&#x2F;youtu.be&#x2F;rXfKWIZQIo4" rel="nofollow">https:&#x2F;&#x2F;youtu.be&#x2F;rXfKWIZQIo4</a>
jey5 个月前
Big if true! But has it been reviewed by experts?
amai5 个月前
This paper makes use of Mamikons theorem. This theorem is not widely known, but it should be: <a href="https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;Visual_calculus" rel="nofollow">https:&#x2F;&#x2F;en.m.wikipedia.org&#x2F;wiki&#x2F;Visual_calculus</a>
nullc5 个月前
So say you have a hallway shaped like a 5, what is the maximum volume 3d-gerver&#x27;s that can make it through (by being possible to rotate to swap the turning direction?
bee_rider5 个月前
Seems like he could have saved himself a whole lot of trouble by just getting a sectional.
polygot5 个月前
Pivot!
zgs5 个月前
My favourite mathematical problem looks to have been solved.
bediger40005 个月前
Dies Ikea offer one of these?
nephronaut5 个月前
There are more interesting investigations and results This one is ok but not remarkable
briandilley5 个月前
What is the practical application of this?
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