A mathematician at Yonsei University, in Korea, claims to have solved the moving sofa problem. Jineon Baek has posted a 100+-page proof of the problem on the arXiv preprint server.
Most people who have moved their place of residence have encountered the the moving sofa problem—it comes up when attempting to carry a couch around a corner. What is the largest couch that can be carried around a given corner without getting stuck? This problem was posited mathematically by mathematician Leo Moser back in 1966, and until now, has remained unsolved.
Moser’s initial thoughts centered on the possibility of developing a proof showing how mathematics could be used to solve any such problem using a given shape of a plane as it was moved around a right-angled corner of an empty space (such as a hallway) that was one unit in width.
In his work, Baek chose the Gerver sofa as a demonstration shape. The Gerver sofa is a mathematical construct developed by Joseph Gerver, a professor at Rutgers University, in 1992. It is basically a cuboid with a U-shaped front, a flat back with rounded edges and flat, front-facing arms.
After first, clearly defining the problem, Baek applies mathematical tools to move through the proof step by step before eventually arriving at the answer: For a hall of 1 unit, a Gerver sofa’s maximum area can only be 2.2195 units. As part of the proof, Baek also narrowly defined the shape of the Gerver sofa he was using. Thus, different interpretations of the sofa shape would result in different answers.
Because the shape of the sofa is clearly defined at the outset, the answer Baek found could conceivably be used in the real world by people attempting to move a couch around a corner—though it would have to conform to the interpretation of a Gerver sofa as defined in the proof.
As with all such math proofs, Baek’s will have to undergo scrutiny by other mathematicians to ensure his proof is correct and actually results in the optimal solution to a given problem.
More information:
Jineon Baek, Optimality of Gerver’s Sofa, arXiv (2024). DOI: 10.48550/arxiv.2411.19826
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Mathematician solves the moving sofa problem (2024, December 11)
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