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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 rts008 on Wednesday January 04 2017, @09:42PM
I have a Sawzall, chainsaw, axe, and sledgehammer. With those, I can save my maths for tricky problems, and still get ANY sofa around ANY corner.
I am proudly doing my part to save the maths!
Hey y'all, watch this.... ;-)
Disclaimer: I feel that I have arrived at this attitude to the problem(from TFA) honestly, because of a bathtub(an OLD cast-iron porcelain-coated monster that weighed a 'metric shit ton') on the second floor of a house during a remodel of that old house. It ended up easier to cut a hole in the bathroom wall, shoving it through onto the first floor roof, and then over the side and into the yard. It half buried itself in the yard on impact. I was too busy excavating it to calculate the force of impact from the crater size and depth(Chicks-a-lube, eat yer heart out!), but was glad the dog saw it coming and fled in time to evade extinction. :-)
(Score: 0) by Anonymous Coward on Thursday January 05 2017, @09:23AM
Last time I faced this problem, I used your hammer and saw idea and managed to get the whole sofa up the chimney except for the springs.