What is the longest pole I can swing around the 90° corner of a hallway of unit width?

For the simplicity of this problem, the pole must be kept exactly horizontal, while maneuvering it.

and if the pole has width W,

2*[sqrt(2) - W]

I'm picturing the pole at a 45 degree angle with its midpoint touching the corner and its ends touching the outer walls jammed in place.  But by symmetry, if it could jam into that position then it can keep going and jam out of that postion as it completes the turn.   But I think I scratched the paint.

Posted by Larry on 2004-03-13 10:56:59