The moving sofa problem
en.wikipedia.org
en.wikipedia.org
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.
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.
Once I was mobile again, I realized it was a tight fit and the sofa wasn't actually symmetrical. Fortunately, it was asymmetrical in the right way for the room but I had a momentary panic.
>we have a business (the couch doctor)
I also have to say that I just love how businesses get created to deal with especially largely localized problems and do a really good job at it. Even at a national level, I met with a specialist company yesterday to do something in my house and it was very refreshing.
We were stumped until we finally figured out that if we simply unscrewed the two wooden frame pieces that run lengthwise, what remained of the box-spring was wooden pieces that run crosswise and are attached to a network of springs. Then it was possible to fold it into a U shape.
To explain visually, the box-spring was built like this one:
https://mk0mattressclarcyl3h.kinstacdn.com/wp-content/upload...
We removed the two pieces of wood running along the left and right bottom edges, then we folded the whole thing so that the wooden cross pieces at the foot of the bed and head of the bed touched each other. The wire grid at the top was just flexible enough to handle a gentle arc.
Casting-wise, I am not sure Elijah Wood was the best choice. Big name for impact maybe, but the role just feels ill-fitting.
https://www.google.com/amp/s/deadline.com/2018/03/dirk-gentl...
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.
1. https://en.m.wikipedia.org/wiki/Max_Landis#Sexual_assault_ac...
But to be fair, that one was about a regularly shaped sofa getting stuck by violating the laws of physics in the first place.
A quick skim of Amazon doesn't find them so you might have to hunt eBay etc.
[1] https://www.researchgate.net/publication/311900489_A_Computa...
Maybe that one will work for you.
Dan Romik
Someone with a moderate amount of time on their hands could probably patch it by mirroring frames from the end of the turn.
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 ?
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.
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.
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.
I suppose you could have a sofa that your corkscrew around the corner?