Who hasn’t struggled to fit a sofa through a tight corner or a cramped stairwell? Within this seemingly trivial conundrum actually lies one of the most fascinating mathematical problems of our time.
Now, a Korean mathematician claims to have solved this mystery.
Many viewers will have recognised themselves in episode 16, Season 5 of the hit TV show Friends when Ross, Rachel and Chandler struggle to squeeze a large sofa through the stairwell of an apartment building. After many unsuccessful attempts, Ross reluctantly decides to cut the sofa in half – a radical decision that could have been avoided, according to mathematician Jineon Baek.
This researcher from Yonsei University, South Korea, claims to have solved the famous “moving sofa problem”, a mathematical conundrum first formulated in 1966 by Austrian-Canadian mathematician Leo Moser, to find the largest size of sofa that could fit around a corner of a given width.
Baek based his work on the Gerver sofa model, developed in 1992 by Rutgers University professor Joseph Gerver. This theoretical form, with its elaborate design, combines a U-shaped front, a flat back with rounded edges and armrests with straight front faces.
This strange shape makes for the largest possible area that could move around a right-angled corner of a hallway with a unit width of one.
After numerous calculations, Baek determined that the maximum surface area of a Gerver sofa is 2.2195 square units. Beyond this size, a sofa would no longer be able to get past a right-angled corner in a narrow corridor, as he explains in a detailed 100-plus page paper published on the ArXiv platform.
In other words, to avoid getting stuck, it’s best to opt for a horseshoe-shaped sofa.
Baek’s work is not yet complete, however. His proposition must now be scrutinised by other mathematicians to confirm its validity. If his conclusions are approved, they will put an end to an enigma that has fascinated mathematicians for almost 60 years.
Although this discovery may seem highly theoretical, it could have concrete applications. For example, designers could draw inspiration from this research to design sofas specially adapted to these kinds of constraints. And that could make moving house a whole lot easier. – AFP Relaxnews
