The problem
Determine the supremum of areas of plane regions ("sofas") that can be moved continuously through a right-angled hallway of width 1 (an L-shaped corner), and exhibit a maximiser.
The Moving Sofa Problem
historicHistory & significance
Moser asked in 1966. Dan Romik's research programme systematised candidate shapes; Dan Gerver's 1992 design reached ≈ 2.2195 — long believed optimal, never proven. Lower and upper bounds crept from 2.0929 upward over decades of incremental geometry.
Connected problems
- related Moser's Worm Problem
More in geometry
- same area Heilbronn's Triangle Problem
References
- primaryRead the primary source →
The resolution (human proof)
Settled November 2024 by Jineon Baek (Yonsei University): a 119-page arXiv paper proves Gerver's sofa attains the maximum area ≈ 2.219531… The proof pins down the shape of maximisers via careful analysis of rotation paths and eliminates all rival families — purely human mathematics, no computation heavier than calculus. A rare modern instance of a beloved folkloric problem dying of elegance rather than exhaustion.
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