The kind that people had sex on in the 70s.
if you are using the hallway you are already doing it wrong:
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It’s not that it’s a hard problem, really. It’s just that solving it will make it easier for friends to ask you to help them move.
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Damn, I hate the way most couches and armchairs are built; it’s so dumb.
All that wasted space underneath, where you could otherwise pile a bunch of stuff, and often barely a thought given to cleaning or moving. Dumb.
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The animation shows Hammersley’s sofa, not Gerver’s. [Never mind - BBS view playing tricks on me, yet again.]
Although it hasn’t been proven optimal, Philip Gibbs did a search of possible shapes using numerical methods, and the optimal solution found had an area the same as Gerver’s sofa up to 8 decimal places.
Of course, to a theoretical mathematician, that’s just a hint that you’re on the right path. The proof’s the thing!
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Love these sorts of problems. I’ve no maths beyond high school but still enjoy.
But I’m confused… from the Wikipedia article and elsewhere:
Joseph Gerver found a sofa that further increased the lower bound for the sofa constant to approximately 2.2195.
Hammersley also found an upper bound on the sofa constant, showing that it is at most 2.8284.
Doesn’t this mean there are shapes up to .6 larger (~25% larger), which seems a lot bigger (and therefore easily found)?
Or am I mixing up lower & upper bounds?
It’s more the “easily found” part. I haven’t even read the links, not to speak of the literature on this, but i’d guess that the upper bound proof is pretty theoretical, and may not be taking into account all the things that would cut down on the possible size.
ETA: In other words, that upper bound may be about that much of an overshoot, just because of the limitations of any method of finding such an upper bound. It’s a surprisingly tough problem.
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My house is not ancient but at 60 it’s not like homes built today. We’ve learned the hard way that the best way to get furniture in the house is through the double hung window. The doorways and hallways are just too tight.
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I betcha the Chinese have already solved this problem in order to shave a few ounces off shipping costs. Maybe we can hack their solution to get back at them for the election thing.
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Did that once with a stair roughly like this but then with another 90° angel at the bottom.
Just stand it on it’s end and push it straight up, nothing difficult just really heavy and awkward.
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Couldn’t the angel do a little miracle w/ the sofa? 
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Duh:
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Second part of the problem:
Find me one of those weirdo, curved sofas.
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