The largest sofa you can move around a corner

Recycled anecdote from an earlier 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.

I never knew this was a real thing math people studied! I wonder if Douglas Adams knew about it when he wrote about the sofa stuck in the staircase in Dirk Gently's Holistic Detective Agency, or if it's a coincidence.

Discussion (131 points, 73 days ago, 36 comments) https://news.ycombinator.com/item?id=42300382

One of the earliest tricks I learned with couches is that if it’s shorter than the ceiling then the arms and back form this U.

Sofas used to be great because they were also shorter than the height of a door frame. Now everything is oversized and you need a 10-15% bigger apartment just to have one of each thing your grandparents had.

With the right design sometimes this still plays out on the diagonal.

Serious request: can someone please solve this for moving furniture around in 3D? Let me take an AR scan of a flight of steps with a corner and another scan of a couch, and tell me if it's possible to do the move.

When someone discovered a new tiling (tesselating?) shape, people made tiles in that shape. Where can I buy this sofa?

Classic example of engineers and mathematicians overthinking something where a mover will just tell you to stand the sofa up on its side.

Pivot! Pivot! PIVOT!

From the article:

> But that was an impossible task: There’s no one formula that can give the area for every kind of shape. (Think about how you use different functions to find the areas of circles versus triangles.)But that was an impossible task: There’s no one formula that can give the area for every kind of shape. (Think about how you use different functions to find the areas of circles versus triangles.)

I don't get it. Am I missing something obvious? I mean, if you have a shape then you can calculate it's area with Green's theorem.

https://en.wikipedia.org/wiki/Green%27s_theorem

If your shape is parameterized then so is your area definition. What's the problem?

Back in my first house, we upgraded our bed and triedto move the old bed into the basement. We had a very small hallway with a door leading ti the basement. The mattress fit, of course, because it flexes. The frame fit because I could disassemble it. The box frame, made of iron and wood slats, could not fit. That day, I cut all the wood slats in half, bent the metal, and got that box spring downstairs. Then I but bracing brackets on the slats and unbent the metal. A few years later, we did the same process over again when moving.

We can measure the angular velocity of mental objects, and it appears to increase linearly with the degree of rotation relative to a reference.

See Shepard, R. N., & Metzler, J. (1971). Mental rotation of three-dimensional objects. Science, 171(3972), 701–703.

https://psycnet.apa.org/record/1971-28060-001

> and that the equations that defined Gerver’s sofa also satisfied those conditions.

> showing that Gerver’s sofa was the biggest possible shape that could move through the hallway without getting stuck at its corner

But there could be other shapes that also satisfy these conditions and could also have the biggest possible shape, correct?

The solution for our real 3d-space looks probably a lot different: https://mathoverflow.net/questions/246914/sofa-in-a-snaky-3d...

may favorite sofa was from Ikea. It disassembled easily. some slots and big bolts took the sides off. then some other big bolts separated the seat from the back. the legs twisted off. now you could carry the two biggest parts, the back and the seat, long and vertical

I'm actually looking forward to doing this with a bed. My prior bed was something I assembled (which I could do gain). Wondering what will work if I want to get a better, e.g. non-IKEA, platform bed. (The mattress will be memory foam so presumably not a problem.)

And this is why modular sofas are so popular now. Whether it be lovesac or another company, sofas these days are coming in multiple boxes and making you do all the work unless you get costco white glove delivery service ;)

Up and Atom has a 2023 youtube video about the moving sofa problem

https://www.youtube.com/watch?v=bUNl_jJMTOw

It just occurred to me that the optimal sofa looks rather uncomfortable. There’s this narrow bit in the middle, which has very little room to sit on. You can’t lie down on it and take nap.

Somehow it doesn’t sit well with me the fact that it’s still quite a complicated shape. I accept that it’s the best one, but I would have expected a simpler shape to be the solution.

Replace sofa with refrigerator and somewhere a Siracusa will get its wings.

Made the sofa modular. Duh!

That has got to be the worst possible navbar imaginable.

PIVOT

Reminds me of 'Pivot' from friends.

Now do it in 3d

Then do it in 4d

Then 24d

Then if you dare, 17d.