“Pivot, pivot, pivot!” Calm down, Ross… you had bought a sofa from Gerver before. The famous “moving couch problem” – which for years has been a headache for mathematicians and movers – finally has a solution.
It’s the end of one of the biggest headaches in moving: the biggest sofa that can be moved in a L-shaped hallway has been officially discovered: it is the Gerver sofain the shape of a horseshoe, whose maximum area has now been mathematically proven.
O “mobile sofa problem” was first put forward in 1966, by the mathematician Leo Moser. The challenge is to determine the largest area of a two-dimensional sofa that can be transported through an “L” shaped hallway.
Em 1992, Joseph Gerver proposed a solution consisting of 18 curved sections.
Gerver sofa
Despite suspicions that this could actually be the solution, there was still a lack of definitive mathematical proof – which has just emerged.
In a study last week in arXivthe mathematician Jineon Baekfrom Yonsei University in South Korea, proved that Gerver’s sofa is the possible solution.
After seven years of work, its proof, with more than 100 pages, demonstrates that this solution is unique.
As he detailed to New Scientist, Jineon Baek began by studying a selection of possible shapes and identified properties that the ideal sofa should have: a smooth exterior, a quantity called balance that is related to symmetry and, of course, the crucial ability to rotate 90 degrees around a corner.
Getting the Gerver sofa around a corner is difficult, but it is possible
The mathematician also created a new mathematical measurement, called Q, to simplify the problem. This approach transformed the challenge into a scenario of defined solutions, where Baek proved that the largest value of Q corresponds precisely to Gerver’s couch.
Joseph Gerver, now 75 years old, was pleased to see his solution confirmed: “Of course I am very happy. I’m 75 years old and Baek can’t be more than 30. He has a lot more energy, stamina and surviving brain cells than me, and I’m glad he took the baton“, he praised, quoted by New Scientist.
“I’m also very glad I lived long enough to see Baek finish what I started“, he added.
This advance solves a almost 60 year old mathematical problemclosing a fascinating chapter in the history of applied geometry.
Now, it’s too late… but 25 years ago this sofa would have been very useful to Ross and avoided stress for his helpers Chandler and Rachel.
