# Differential equations and exact solutions in the moving sofa problem

arXiv: https://arxiv.org/abs/1606.08111 · HTML: https://mlsanity.com/paper/1606.08111/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jun 2016.

## 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, and is conjectured to have as its solution a complicated shape derived by Gerver in 1992. We extend Gerver's techniques by deriving a family of six differential equations arising from the area-maximization property. We then use this result to derive a new shape that we propose as a possible solution to the "ambidextrous moving sofa problem," a variant of the problem previously studied by Conway and others in which the shape is required to be able to negotiate a right-angle turn both to the left and to the right. Unlike Gerver's construction, our new shape can be expressed in closed form, and its boundary is a piecewise algebraic curve. Its area is equal to X+arctan Y, where X and Y are solutions to the cubic equations x2(x+3)=8 and x(4x2+3)=1, respectively.