On the Gerver sofa, once you round a first corner, you can flip it over and go around the other. Flipping the sofa around to get it to fit is pretty common.

On the Gerver sofa, once you round a first corner, you can flip it over and go around the other. Flipping the sofa around to get it to fit is pretty common.

What if it's taller than the width of the corridor?

You can't flip it over -- that would be a trivial way to solve an otherwise interesting problem.

What if it's taller than the width of the corridor?

It's a 2-D problem. Doesn't anyone read the article?

I've had to install a floor to ceiling cabinet against a wall after bringing it into the room horizontally. The top of the cabinet gets hung up on the ceiling when righting it, but the solution is to cut a radius from the bottom corners at the back of the cabinet. These hypothetical couches are too ugly to make a plausible puzzle.

not even an attempt to describe the method?

The method is simple enough. Just make a rectangle to fill the hallway as long as the hall, three times the width will probably do the job though.

Once the object is hard up against the opposite wall allow it to move into the next path by deleting any parts that would stop it from moving. effectively making an arc inside the curve and on the outside against the wall.

Do the same with the trailing edge and you have the required shape.

By placing another bend in the corridor you repeat the process around the next bend.

What is the sofa constant of the Romik 'bikini top' sofa?

Seems like an ideal problem to tackle with a genetic algorithm.

The method is simple enough. Just make a rectangle to fill the hallway as long as the hall, three times the width will probably do the job though.

Once the object is hard up against the opposite wall allow it to move into the next path by deleting any parts that would stop it from moving. effectively making an arc inside the curve and on the outside against the wall.

Do the same with the trailing edge and you have the required shape.

By placing another bend in the corridor you repeat the process around the next bend.

Yeah, they did that in the first version of the solution, but then someone found an even better shape.

When it becomes a 2D problem, it loses all significance. Relevance matters. Standing the sofa on end happens, and when it happens there is another shape to consider. Flipping the sofa in the hall when approaching another turn also happens, and is relevant. Perhaps 2D only problems can have relevance somewhere somehow, but that relevant somewhere/somehow has got to be very small.

What is the sofa constant of the Romik 'bikini top' sofa?

From the article: ≈ 1.644955218425440.

They even have a closed form expression for it. If you're interested, here's the article: https://arxiv.org...8111.pdf

Oh good grief NoStrings & Zzzzzzzz. It is a mathematical way of solving a geometrical problem!
It might have wider use and application, it really has nothing to do with a physical couch or a corridor.

Yeah, they did that in the first version of the solution

The first version of the solution is a tiiiiiiny bit more complex (it consist of 14 areas with different curvature).
Takeaway message: seemingly simply problems are often a bit more complex than a first "knee-jerk" analysis would suggest