Given an open subset 
in 
-dimensional space and two compact subsets 
and 
of 
, where 
is derived from 
by a continuous motion, is it possible to move 
to 
while remaining entirely inside 
?
Piano Mover's Problem
See also
Moving Ladder Problem, Moving Sofa ProblemExplore with Wolfram|Alpha
References
Buchberger, B.; Collins, G. E.; and Kutzler, B. "Algebraic Methods in Geometry." Annual Rev. Comput. Sci. 3, 85-119, 1988.Feinberg, E. B. and Papadimitriou, C. H. "Finding Feasible Points for a Two-point Body." J. Algorithms 10, 109-119, 1989.Finch, S. R. "Moving Sofa Constant." §8.12 in Mathematical Constants. Cambridge, England: Cambridge University Press, pp. 519-523, 2003.Leven, D. and Sharir, M. "An Efficient and Simple Motion Planning Algorithm for a Ladder Moving in Two-Dimensional Space Amidst Polygonal Barriers." J. Algorithms 8, 192-215, 1987.Referenced on Wolfram|Alpha
Piano Mover's ProblemCite this as:
Weisstein, Eric W. "Piano Mover's Problem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/PianoMoversProblem.html