ºÙºÙÊÓƵ

Solving the Moving Sofa Problem

Blogs
A despondent man sits at one end of a sofa wedged in a space too narrow for it.
The moving sofa problem, which deals with the math of how shapes can fit around corners, may have been solved by a Korean mathematician. ºÙºÙÊÓƵ mathematician Dan Romik has made a study of the problem and its variants. (Getty Images)

Korean mathematician Jineon Baek may have come up with a proof for a long-standing problem: What is the largest object that can fit around a corner of a certain size? 

Aptly described as the "moving sofa problem," this question was formally posed in 1966. In 1992, Joseph Gerver came up with a shape rather like an old-fashioned telephone handset as having the largest possible area, 2.2195 units if the hallway is one unit wide. Baek's proof, published as a , shows that Gerver's sofa is indeed the largest possible object that can fit round that corner. 

ºÙºÙÊÓƵ mathematician Dan Romik has worked on the and has a web page dedicated to it. His work is also featured in this . 

, Romik used 3-D printing to address a variation of the problem: What if there are two corners in opposite directions? Romik's solution proposes a dumbell-like shape with two wide sections connected by a pinched-in middle. 

Apart from moving oddly-shaped furniture, what is the application of this? One example could be in understanding how fibers suspended in a fluid behave when they pass through a nozzle. Like most things in mathematics, ideas from the abstract have a way of showing up in the real world sooner or later.  

Media Resources

(preprint, 2024)

(ºÙºÙÊÓƵ news, 2017)

Primary Category

Secondary Categories

Driven by Curiosity

Tags