How to you approach solving the moving sofa problem for rectangles only, but given hallway widths a and b? (Not width 1 and 1 as in the original problem)

Guest Jan 6, 2015

#5**+5 **

Don't mind nauseated. He is a very rude troll. He gets out of bed on the wrong side every day.

We are actually quite fond of him but we keep him on a leash and his muzzle is always nearby.

He grows on you after a while but in the meantime it is best to ignore him.

Hi Nauseated now stop snarling and go back to your catacomb. There's a good troll π

Melody
Jan 6, 2015

#2**0 **

To clarify (I thought I only had limited characters for a question or something)

The moving sofa problem requires constructing a shape of greatest possible area, such that it is able to move through a 1 wide hallway that bends at a 90 degree angle. (As you probably already know)

I would like to tackle the simpler problem: Try this problem with the restriction that our shape in question can only be a rectangle. In addition, the widths of both hallways (before, then after the bend) could be any length. For example, the width of the hallway before the turn could be 17, then 0.022 after the right angled turn. Let the widths of said hallways be a and b.

Ive been thinking of the idea that I could first represent the base of the rectangle in terms of slope and length, then find the area of the rectangle, then write a 2 argument function f(s,l) to represent this, then try to take the derivative, then... I'm not even sure if this would work as we would be dealing with 3 dimensional graphs, and as an 8th grader I do not want to go there. Hopefully it does not differ too much from simple 2D calc. Anyways, I am almost certain that this approach is far fetched and may not even work at all. If there a better way to approach this problem?

Guest Jan 6, 2015

#3**+5 **

Perhaps I still do not understand your question properly but it sounds like you have simplified it down to a 2 dimensional problem.

like a rectangular piece of paper beong pushed along the floor.

I think the largest area is just a x b where a and b are the widths of the 2 hallways.

I will think about it more though π

Melody
Jan 6, 2015

#4**+5 **

**The moving sofa problem for eighth grade**? Most students **have mastered** the three-dimensional solution **by third grade**, and many do it by second grade. Certainly the two-dimensional solution is mastered by second grade.

Itβs not a wonder you had a problem determining the limit of character space for a post.

It must be a raging case of untreated CDD. **Try not to spread it around the forum.**

Nauseated
Jan 6, 2015

#5**+5 **

Best Answer

Don't mind nauseated. He is a very rude troll. He gets out of bed on the wrong side every day.

We are actually quite fond of him but we keep him on a leash and his muzzle is always nearby.

He grows on you after a while but in the meantime it is best to ignore him.

Hi Nauseated now stop snarling and go back to your catacomb. There's a good troll π

Melody
Jan 6, 2015