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So Gerver’s 1992 curved “sofa” (area ≈ 2.2195) is not just a good guess but actually optimal. The problem asks for the largest 2D shape that can be slid around

by cm2012 9mo ago

So Gerver’s 1992 curved “sofa” (area ≈ 2.2195) is not just a good guess but actually optimal. The problem asks for the largest 2D shape that can be slid around a right-angle corner in a unit-width hallway. Here is the perfect fitting sofa: https://en.wikipedia.org/wiki/File:Gerver.svg https://en.wikipedia.org/wiki/File:Gerver.svg

plagiarist 9mo ago
I think it would be cool to have a sofa in that shape as a joke. It could go in a room tiled with a single shape non-repeatable pattern.
- intrasight 9mo ago
  A very functional sofa joke as it's the optimal shape for moving.
  - eru 9mo ago
    Not really, because it's only optimal in 2d.
    - pixelpoet 9mo ago
      Most of us don't live in Escheresque labyrinths
      - eru 9mo ago
        If you've ever moved any furniture at all, you'll notice that it's often much easier to get around corners (or through doorways), if you can turn them sideways. That's especially easy to imagine with tables, but sofas also count. There are also sofas that can be easily taken apart. Eg one of our sofas at home, an L-shaped sofa, comes apart into two pieces.
      - lostlogin 9mo ago
        You don’t have to move house many times to realise that yes, we do.
    - zelphirkalt 9mo ago
      Not a problem, we can just shape it like the space covered by rotating the whole thing and make the sofa kind of "bone shaped", then we should be set for 3 dimensions. The only remaining issue would be, where to put the actual sitting area on the bone, but that problem I leave for homework.
      - Enginerrrd 9mo ago
        3dimensions still allows for more freedom than that though since the couch can stand on end. I would contend that it's still useful since you'd be able to turn the corner without over-complicating it by getting it into some weird tilt position.
      - eru 9mo ago
        > Not a problem, we can just shape it like the space covered by rotating the whole thing and make the sofa kind of "bone shaped", then we should be set for 3 dimensions. That might give you a feasible solution, but I doubt it's optimal.

by cm2012 9mo ago

plagiarist 9mo ago

I think it would be cool to have a sofa in that shape as a joke. It could go in a room tiled with a single shape non-repeatable pattern.

intrasight 9mo ago
A very functional sofa joke as it's the optimal shape for moving.
- eru 9mo ago
  Not really, because it's only optimal in 2d.
  - pixelpoet 9mo ago
    Most of us don't live in Escheresque labyrinths
    - eru 9mo ago
      If you've ever moved any furniture at all, you'll notice that it's often much easier to get around corners (or through doorways), if you can turn them sideways. That's especially easy to imagine with tables, but sofas also count. There are also sofas that can be easily taken apart. Eg one of our sofas at home, an L-shaped sofa, comes apart into two pieces.
    - lostlogin 9mo ago
      You don’t have to move house many times to realise that yes, we do.
  - zelphirkalt 9mo ago
    Not a problem, we can just shape it like the space covered by rotating the whole thing and make the sofa kind of "bone shaped", then we should be set for 3 dimensions. The only remaining issue would be, where to put the actual sitting area on the bone, but that problem I leave for homework.
    - Enginerrrd 9mo ago
      3dimensions still allows for more freedom than that though since the couch can stand on end. I would contend that it's still useful since you'd be able to turn the corner without over-complicating it by getting it into some weird tilt position.
    - eru 9mo ago
      > Not a problem, we can just shape it like the space covered by rotating the whole thing and make the sofa kind of "bone shaped", then we should be set for 3 dimensions. That might give you a feasible solution, but I doubt it's optimal.