Imagine having to drag a sofa down a narrow hallway and negotiate a 90-degree corner without getting stuck. What seems like a common situation during a move turned out to be a complex mathematical challenge, known as the Moving Sofa Problem. This curious question, formulated over 50 years ago, seeks to determine what is the largest shape a sofa can have to cross a right angle.
Finally, after decades of studies, the mathematician Jineon Baeka researcher at Yonsei University in South Korea, may have found an answer. Last December, Baek published a 100-page document on the online archive arXivdemonstrating that the maximum surface area of a sofa capable of overcoming this challenge is 2.2195 units.
The history of the problem begins with the Austro-Canadian mathematician Leo Moserwho formulated it for the first time. Since then, numerous experts have searched for a permanent solution, without success. In 1992, Joseph Gervera mathematician at Rutgers University, proposed an innovative model: the Gerver sofaa U-shaped figure made up of 18 curves.
Although this design had calculated a maximum area of 2.2195 unitsno one had managed to demonstrate that it was actually the optimal solution. Baek, using modern mathematical tools and detailed analysis, confirmed that Gerver’s sofa is indeed as large as possible to tackle a right angle without blocking.
Why is the sofa issue so important?
While it may seem like a simple theoretical exercise – or a joke to those who hate moving – the sofa problem represents a fundamental challenge in geometry and optimization. Exploring the limits of shape and space opens the door to broader and unexpected mathematical discoveries.
There is no shortage of practical applications: from strategies for moving bulky objects to simulations for autonomous vehicles that must move in confined spaces. The issue demonstrates how seemingly trivial situations can evolve into profound academic questions.
The variant of the problem: the ambidextrous sofa puzzle
In addition to the original problem, there is an even more complex variant: the Ambidextrous Sofa Problemwhich involves passing through two consecutive corners, one on the right and one on the left. The mathematician Dan Romik proposed an intriguing solution to this challenge, a sofa shaped like a “bikini bra”. However, as with Gerver’s model, a definitive proof is still missing.
Although Baek’s work has not yet been peer-reviewed, it has already generated great enthusiasm among mathematicians. Images of Gerver’s sofa and discussions on the topic quickly spread on social media, fueling the curiosity of enthusiasts and scholars. If his theorem is confirmed, it will put an end to a debate that has lasted more than half a century, consolidating a fascinating chapter in the history of mathematics.
