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.

That the length 2 * sqrt (2) is just long enough to not be a possible solution... You can't "Austin Powers" the pole if the given length restricts any movement whatsoever. Theoretically, the length of this hypothetical pole should be just shy (infinitesimally smaller) than 2 * sqrt (2).

Here I have a quick question: are we assuming the width of this pole to be nonexistent--that the pole is just a line? If not, this problem might be practically solved if we also include the smallest measurement we will allow for adjusting the pole back and forth (given a 5 cm diameter cylindrical pole, 1/2 cm rotation shouldn't be too far out of the question...)