Gregory's ServerOh, wow. Just dropped: a 199-page preprint that is claiming a solution of the moving sofa problem!
 9 comments
 @highergeometer @johncarlosbaez Please, please tell me this has to do with Douglas Adams and his stuck sofa problem. @Infoseepage https://en.wikipedia.org/wiki/Moving_sofa_problem Maybe Douglas Adams heard about it, or it's completely reasonable he had the idea independently. Certainly the solution in DGHDA is.... novel! ;-) @highergeometer @johncarlosbaez Adams apparently stumbled across the similar problem while at St John's Cambridge in the early 1970s. There was a staircase being renovated and furniture was moved into a room at the top of the stair to get it out of the way. After the staircase was finished, the sofas would no longer fit down the stairs no matter how you manipulated them, so the furniture was stuck in those upstairs rooms for decades.  @highergeometer there's only one author listed. has this guy just been banging on the sofa problem for years until now @cxberger As usual, it's almost never a lone genius slaving away. Here's the acknowledgements section of the paper:  @highergeometer - nice! I'll check it out. These geometric optimization problems can be fiendishly difficult.  |
The optimal shape is the one already known (due to Gerver), but we didn't know it was the shape with the largest area relative to the size of the hallway.
Here's a picture of it moving around the corner