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posted by on Wednesday January 04 2017, @03:34PM   Printer-friendly
from the dirk-gently dept.

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


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  • (Score: 3, Interesting) by MrGuy on Wednesday January 04 2017, @03:51PM

    by MrGuy (1007) on Wednesday January 04 2017, @03:51PM (#449395)

    If a time traveler is there to open the door. [wikipedia.org]

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  • (Score: 4, Interesting) by choose another one on Wednesday January 04 2017, @04:24PM

    by choose another one (515) Subscriber Badge on Wednesday January 04 2017, @04:24PM (#449420)

    Well I was hoping to be first with that one, but realised that the editors had already done it with "from the dirk-gently dept." right there in the post.

    Sometimes it sucks to be in a forum where nobody thinks like you and gets your clever reference, but it also sucks to be in one where everyone thinks like you and thought of it before you could say it... :-)

    PS: The math problem predates Dirk Gently and it is entirely possible that Douglas Adams knew of it when writing, but it's also possible he just got furniture stuck halfway up his stairs one day.

    • (Score: 0) by Anonymous Coward on Wednesday January 04 2017, @09:25PM

      by Anonymous Coward on Wednesday January 04 2017, @09:25PM (#449534)

      According to the wikipedia page linked by grandparent, he did experience a similar problem in the dorms in college - couches that could no longer be moved through the stairwell after a remodel. Though that doesn't preclude being aware of the math problem.