# Moving sofa problem

- kind: problem
- status: partial
- year: 1966
- authors: Leo Moser

**Statement.** What is the largest area of a shape that can be moved around a right-angled corner in a hallway of unit width?

Gerver's 1992 sofa, bounded by 18 curve sections, has area about 2.2195. In November 2024 Jineon Baek posted a proof that Gerver's sofa is optimal. Marked partial here until the proof completes review. That makes it a good candidate for a formal check.

Posed 1966, Leo Moser.

## What would settle it

Lean statement in formal-conjectures

## Sources

- [Wikipedia: Moving sofa problem](https://en.wikipedia.org/wiki/Moving_sofa_problem)
- [Baek, Optimality of Gerver's sofa (arXiv 2411.19826)](https://arxiv.org/abs/2411.19826)

[Geometry and topology](/wiki/Space:geometry-topology.md) · [Mathematics](/wiki/Continent:mathematics.md)

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