from Hacker News

Optimality of Gerver's Sofa

by petters on 12/2/24, 9:05 PM with 36 comments

• by senkora on 12/3/24, 1:25 AM

  Here'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...

  Source: https://www.mdpi.com/2073-8994/14/7/1409

• by doormatt on 12/2/24, 9:21 PM

  For those that don't understand - https://en.wikipedia.org/wiki/Moving_sofa_problem

• by n4r9 on 12/2/24, 9:22 PM

  Looks 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.

• by yoshicoder on 12/2/24, 9:36 PM

  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/proof replication?

• by ks2048 on 12/3/24, 7:29 AM

  I 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

• by ajb on 12/3/24, 8:16 AM

  Interesting, 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.

• by phamilton on 12/3/24, 1:57 PM

  I 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.

• by jonahx on 12/2/24, 9:45 PM

  Wow. This solves a problem that's been open for at least 58 years.

• by robinhouston on 12/3/24, 11:11 AM

  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 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.”

• by parhamn on 12/2/24, 9:29 PM

  Numberphile had a great video on this a few years ago: https://youtu.be/rXfKWIZQIo4

• by jey on 12/3/24, 12:44 AM

  Big if true! But has it been reviewed by experts?

• by amai on 12/3/24, 8:55 AM

  This paper makes use of Mamikons theorem. This theorem is not widely known, but it should be: https://en.m.wikipedia.org/wiki/Visual_calculus

• by nullc on 12/4/24, 10:15 PM

  So 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?

• by bee_rider on 12/3/24, 8:52 AM

  Seems like he could have saved himself a whole lot of trouble by just getting a sectional.

• by polygot on 12/3/24, 1:29 AM

  Pivot!

• by zgs on 12/3/24, 9:38 AM

  My favourite mathematical problem looks to have been solved.

• by bediger4000 on 12/2/24, 10:10 PM

  Dies Ikea offer one of these?

• by nephronaut on 12/3/24, 8:40 AM

  There are more interesting investigations and results This one is ok but not remarkable

• by briandilley on 12/2/24, 10:55 PM

  What is the practical application of this?