60-Year-Old Math Puzzle Solved: The Optimal Sofa Size

A 60-year-old mathematical puzzle – the moving sofa problem – has finally been solved! In the 1960s, mathematicians posed a seemingly simple geometric question: What's the largest area of a sofa that can navigate a unit-width hallway? Recently, Jineon Baek, a postdoctoral researcher at Yonsei University in Seoul, proved in a 119-page paper that the sofa shape proposed by Joseph Gerver in 1992 is the optimal solution, with an area of approximately 2.2195. Baek's proof is remarkable because it didn't rely on computers but used elegant mathematical techniques, offering new approaches to solving other optimization problems. The result also illustrates that even the simplest optimization problems can have surprisingly complex answers.
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