Mathematicians Solve Infamous ‘Moving Sofa Problem’

Mathematicians solve the evil “problems that move sofa”

By Jack Murtagh Edited Jeanna Bryner

For those who fought a large volume on a narrow salca, “this will also fit?” Mathematicians have heard your pleasures. The geometry asks the “shocking sofa” in a narrow corridor in a narrow angle that can make the right angle without sticking. The problem was almost 60 years old until November, Jineon Baek, a postdoc of Seoul Yonsei University, published Paper online a claim to resolve. Baek’s evidence must still make a deep review of the peer, but the initial passage towards maths known, the problem that peace and a moving sofa seem to be optimistic. Time will only tell you why Baek took 119 pages to write at the Ross Geller’s Sitcom Friend said in a single word.

The solution is hard to help you move the day, but since the limit grows more math, mathematicians have a special love for anyone who can understand problems. In fact, Mathematics Mathematics Keeps a List of Known Mathematics “That no one can understand the problems that are not particularly famous“And the problem that moves sofa today is in the list. However, the techniques used to solve our understanding of the sofa, which is likely to be down the road to other geometric puzzles.

Problem Rules, Canadian Mathematicians in Leo Moser Canada first formally posed In 1966, it involves a rigid form, so the cushions do not turn a proper angle in a hallway. The sofa can be any geometric shape; It doesn’t look like a real couch. Both shapes and hallways are two dimensions. Imagine that the sofa weighs too much to lift, and you can only slip.

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A quick tour made through the history of the problem reveal a wide effort that emits mathematicians, there were no sofa potatoes. In the face of an empty hallway, what is the greatest shape you can squeeze through it? If each leg of the corridor crosses a unit (specific units does not matter), and then we can easily throw a square through the passage. Not having a rectangle forming box immediately fails, once in the marsh, it does not turn around the place.

However, the mathematicians realized that they were greater in curved forms. Suppose a semicircle with a diameter (direct base). When he faces the turn, it still looks like the first leg of the hallway, but the edge leaves the room with enough room to clean the corner.

Remember to find the greatest “sofa” that slides in the corner. By sprinkling high school geometry formulas, we can calculate the area of ​​the semi-circle as π / 2, or approximately 1,571. The circle circle gives significant improvement in the square, the area was only 1. Unfortunately both would be rare in a living room.

Solving the problem that moves the sofa, but also optimizing the size of a form, but way It crosses the shape. The configuration supports two types of movement: Slide and rotate. Square slipped alone on the sofa, when the semicircle slipped, turned around the bend and then slipped again on the other side. But objects can slide and rotate at the same time. Dan Romik Dan Romik at the University of California has Davis warn The solution to the problem should optimize both types of movement at once.

British mathematician John Hammersley They found half-circle in 1968 can Buy a larger sofa, if you sculpt a small piece to deal with that corner. In addition, Hammersley’s sofa takes advantage of a hybrid slider plus a rotary movement. The sofa obtained seems like a mobile phone:

Optimizing different variables gives a sofa π / 2 + 2 / π area, or approximately 2,2074. From the circle seat, it is a foam to move from a series of love seat. But the advances were left there for 24 years. The next significant improvement would be the last. In 1992 Joseph Gerver has introduced Mathematical carpenters master work, which we need to be as much as possible in the sofa today.

Right now you would forgive the feeling of Déjà vu. Gerver’s sofa has the same for Hammersley, but it is much more complicated to construction. Gerver designed 18 different curves to complete its form. You can discern some differences in the narrower inspection, especially the edges at the base of a rounded cut.

Gerver’s victory area on Unit 2,2195. Surprisingly, Hammersley fell only a fairly simple sofa .012 the best short. Although Skosh was greater than his previous one, Gerle suspect that his findings achieved as much as possible. He couldn’t prove. And no one else can be 32 years old.

Baek ended his doctor. In 2024 and he wrote about the problem that moves his thesis sofa, helping various add-ons. In the same year, he made all his fresh ideas spectacular by This does not greater than the sofa that Gerver can squeeze through the hallway. Cracking the long-open problem is a dream for any mathematicians, even in his career so early. If Baek’s work is subject to examinations, it is likely to be found at the high demand of teachers. Unless the furniture structure has entered.