For decades, mathematicians tried to come up with the optimal sofa shape to move around a corner. Post-doctoral student Jineon Baek posted a 100-page proof that claims to solve the problem.
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DAVID SCHWIMMER: (As Ross) All right.
MATTHEW PERRY: (As Chandler) OK.
SCHWIMMER: (As Ross) Here we go. All right, ready?
ARI SHAPIRO, HOST:
In a scene from the classic sitcom, “Friends,” the characters Ross, Rachel and Chandler struggle to heft a new couch up the stairs of their apartment building. As they try to get the sofa around the first corner, Chandler gets jammed against the railing, and no matter how they angle it, the sofa is stopped.
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SCHWIMMER: (As Ross) Come on, up, up up, up. Up. Yes, here we go. Pivot. Pivot.
SHAPIRO: If you’ve ever moved furniture or helped someone get a couch up a flight of stairs, maybe you have had your own pivot moment of sofa vs. corner. Well, this is not just a furniture-moving problem. It is also a math problem, one that people have puzzled over for decades. What is the largest sofa that can turn a corner of a given width?
JINEON BAEK: As soon as I realized that this was a serious problem that has not been solved completely for more than 50 years, I found the shape interesting.
SHAPIRO: Jineon Baek is a postdoctoral math student from Yonsei University in South Korea. Earlier this month, he posted a 100-page proof that claims to solve the elusive moving-sofa problem.
BAEK: The moving-sofa problem asks us to find the largest two-dimensional shape, a 2D sofa, that you can fit around a 90-degree corner without getting stuck and making its way all through.
SHAPIRO: In 1992, the Rutgers professor Joseph Gerver developed a very specific sofa shape to use in the problem. It’s kind of a U shape with wonky arms and a flat back. Not comfy seating, but this is math, not design.
BAEK: He devised a, like, shape called Gerver’s sofa, which consists of 18 different curves and lines. And there – it’s complicated. Like, you have to write a lot of formulas to describe it.
SHAPIRO: And here comes the math. Based on Gerver’s shape, Jineon Baek determined that for a hall of one unit, the Gerver sofa can’t be bigger than 2.2195 units. That’s the same size that Gerver proposed back in the 1990s. Baek’s work still needs to be vetted by other mathematicians, but it looks like this issue might finally have been put to bed.
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THE REMBRANDTS: (Singing) So no one told you life was…
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