The moving sofa problem
A rigid planar shape must be moved around a right-angled corner in a hallway of width 1. What is the largest possible area of such a shape? Gerver's sofa has area about 2.2195. Prove that no shape with larger area can make the turn.
History and references
Partly solved.
Leo Moser published the problem in 1966, although it had circulated informally before. A half-disk of radius 1 gets around the corner with area , and in 1968 John Hammersley found a shape like a telephone handset with area about 2.2074. In 1992 Joseph Gerver described a sofa bounded by 18 curve sections with area about 2.2195 and conjectured that it is optimal. In November 2024 Jineon Baek posted a 119-page proof that no larger sofa exists, using careful analysis rather than computer search. The proof has been well received, but as of this writing it is still under journal review, so it is marked here as a proof announced and under review.
References
Solutions 0
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