# Improved upper bounds in the moving sofa problem

arXiv: https://arxiv.org/abs/1706.06630 · HTML: https://mlsanity.com/paper/1706.06630/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2017.

## Built on by (most cited first, 1 of 1)

- [Deep Learning Evidence for Global Optimality of Gerver's Sofa](https://mlsanity.com/paper/2407.11106/) (2024)

## Abstract (arXiv)

The moving sofa problem, posed by L. Moser in 1966, asks for the planar shape of maximal area that can move around a right-angled corner in a hallway of unit width. It is known that a maximal area shape exists, and that its area is at least 2.2195... - the area of an explicit construction found by Gerver in 1992 - and at most 2√2=2.82..., with the lower bound being conjectured as the true value. We prove a new and improved upper bound of 2.37. The method involves a computer-assisted proof scheme that can be used to rigorously derive further improved upper bounds that converge to the correct value.