Moving sofa problem
On areas of shapes in 2d motion planning
Moving sofa problem
In mathematics, the moving sofa problem or sofa problem is a two-dimensional idealization of real-life furniture-moving problems and asks for the rigid two-dimensional shape of the largest area that can be maneuvered through an L-shaped planar region with legs of unit width. The area thus obtained is referred to as the sofa constant. The exact value of the sofa constant is an open problem. The leading solution, by Joseph L. Gerver, has a value of approximately 2.2195. In November 2024, Jineon Baek posted a 119-page arXiv preprint claiming that Gerver's value is optimal, which if true would solve the moving sofa problem.
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