The mathematician Leo Moser posed in 1966 the following curious mathematical problem: what is the shape of largest area in the plane that can be moved around a right-angled corner in a two-dimensional hallway of width 1? This question became known as the moving sofa problem, and is still unsolved fifty years after it was first asked.
To understand what makes this question tricky, let's think what kind of "sofa" shapes we can construct that can move around a corner. How about a unit square?
Well, a unit square only has area 1; surely we can do better? For example, a semicircle with radius 1 is another simple example that works.
The semicircular sofa has a larger area than the square one, ᴨ/2 (approximately 1.57). It is also more interesting, because in order to move around the corner it rotates, whereas the square sofa merely translates. Now, if only we could combine rotation and translation, maybe we could construct an even bigger sofa shape? Indeed, the mathematician John Hammersley noticed that if the semicircle is cut into two quarter-circles, which are pulled apart and the gap between them filled with a rectangular block, we get a larger sofa shape, which could be moved around the corner if only a smaller semicircular hole is also removed from the rectangular block. Here is the resulting shape, that is starting to look a bit more like an actual sofa.
The shapes involved are interesting. Not really sofa shaped, but then theory is rarely like reality.
-- submitted from IRC
(Score: 2) by VLM on Wednesday January 04 2017, @04:22PM
A bit of google searching shows motorized sofas peaked in interest about a decade ago and even reports of reports of reports was dying down by 2010.
Possibly solving this problem would help popularity, at least help them park and maneuver in close quarters.
They never really took off, despite being a semi-obvious extension of the motorized scooter / powered wheelchair meme. Its not like Americans have gotten skinnier or healthier, motorized sofas "should" still be cool.
(Score: 3, Funny) by bob_super on Wednesday January 04 2017, @05:23PM
Motorized sofas are still cool, but people decided to add a roof in case of rain, an A/C unit, some trunk space for the food and drinks, a windshield for the bugs, and 21" wheels with chrome rims.