Moving Ladder Problem


What is the longest ladder that can be moved around a right-angled hallway of unit width? For a straight, rigid ladder, the answer is 2sqrt(2), which allows the ladder to just pivot around the corner at a 45 degrees angle.

For a smoothly-shaped ladder, the largest diameter is >=2(1+sqrt(2)) (Finch 2003).

See also

Moving Sofa Problem, Piano Mover's Problem

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Finch, S. R. "Moving Sofa Constant." §8.12 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 519-523, 2003.

Referenced on Wolfram|Alpha

Moving Ladder Problem

Cite this as:

Weisstein, Eric W. "Moving Ladder Problem." From MathWorld--A Wolfram Web Resource.

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