06-15-2026, 08:57 AM
Summary
The moving sofa problem is a famous unsolved problem in geometry that asks: What is the largest possible two-dimensional shape that can be moved around a right-angled corner in a hallway of unit width? First posed by Leo Moser in 1966, the problem seeks the shape with the maximum possible area, known as the sofa constant. Over the years, mathematicians have found increasingly better candidate shapes, with the best-known one being Gerver’s sofa, discovered by Joseph L. Gerver, which has area approximately 2.2195.
Although the exact value of the sofa constant remained unknown for decades, a 2024 preprint by Jineon Baek claims to prove that Gerver’s shape is optimal. The problem is celebrated because it arises from a simple real-world question—moving furniture around a corner—yet leads to deep and challenging mathematical analysis.
ARTICLE
The moving sofa problem is a famous unsolved problem in geometry that asks: What is the largest possible two-dimensional shape that can be moved around a right-angled corner in a hallway of unit width? First posed by Leo Moser in 1966, the problem seeks the shape with the maximum possible area, known as the sofa constant. Over the years, mathematicians have found increasingly better candidate shapes, with the best-known one being Gerver’s sofa, discovered by Joseph L. Gerver, which has area approximately 2.2195.
Although the exact value of the sofa constant remained unknown for decades, a 2024 preprint by Jineon Baek claims to prove that Gerver’s shape is optimal. The problem is celebrated because it arises from a simple real-world question—moving furniture around a corner—yet leads to deep and challenging mathematical analysis.
ARTICLE
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