Any ‘Friends’ fan knows that there is only one way to get the sofa around a tight corner: Pivot!
However, while this may not have been possible in the pictures, mathematicians have now revealed how Ross Geller could have moved his sofa up the stairs.
Dr Jineon Baek, a mathematician from Yonsei University, Korea, has found a very large sofa that can be rotated at an angle of 90 degrees.
Unlike the Ross sofa, this elegant design looks like an old telephone receiver with a smooth back, rounded corners, and a rounded cutout in the front.
This design was first developed by Joseph Gerber of Rutgers University in 1992 but, until now, no one has been able to prove that a large sofa is not possible.
In a 100-page testimony, Dr Baek has now proven that for a balcony one ‘unit’ large the largest sofa you can reach in this corner has a dimension of exactly 2.2195 units.
This means that, if Friend’s stairs were 2m-wide, the largest sofa Ross could fit into would have an area of 4.439 square meters.
Beyond helping people move into smaller homes, this solution also helps 60-year-old math.
While Ross Gellar might not have been able to get his sofa up the famous Friend’s stairs, mathematicians have now proven how he could have turned his sofa into a corner.
Dr Jineon Baek, a mathematician from Yonsei University, Korea, has found the perfect shape for a sofa that you have to move around in the corner. This shape (pictured) allows for a very large sofa space depending on the size of the corridor
The moving sofa problem was first proposed in 1966 by the Austrian-Canadian mathematician Leo Moser.
This basically set in mathematical terms a puzzle that almost everyone has tried to solve at least once in their life.
The question asks: For a 90 degree corridor, ignoring the length, how big a sofa can you fit in the corner and how big is the sofa?
Although it may seem logical, it turns out that this is a very complicated math.
In the most important cases, you can consider pushing the square out of the way; That square can have a width and length equal to the width of the corridor.
This means that, on only one balcony, your large sofa has only one section.
This is a good start but anyone who has ever moved a sofa can quickly see that you can move a very large sofa.
For example, if you have a round sofa that has the same length and width, you can bump this area up to 1.57 units.
This problem, known as the couch problem, was first proposed in 1966 and has baffled mathematicians ever since. The question is: For a 2D balcony one square, what size sofa can you move around 90 degrees and how big is the sofa? (stock photo)
Mathematicians soon realized that a sofa shaped like a banana or an old telephone could be very large.
In 1992, Professor Joseph Gerver designed the Gerver sofa, made of 18 curved sections.
For more than 30 years, no one has been able to find a shape that allows large spaces but, on the other hand, no one can prove that a large shape is not possible.
Now, after working on his evidence for seven years, Dr Baek can confirm that the Gerver sofa is indeed the perfect model.
Dr Baek’s success came from looking at a small section of the sofa and asking what things they all have in common.
These features include a smooth outer edge, a mathematical element called balance that is similar to symmetry and the ability to rotate 90 degrees around a corner.
By combining all these factors, Dr Baek developed a new mathematical model called Q which was more closely related to the region.
This turned the open question of how the sofa would fit into a problem with one definitive answer.
In 1992, a mathematician named Joseph Gerver designed the ‘Gerver sofa’, a phone-shaped sofa that he believed was the largest sofa you could move around at a 90-degree angle. Photo: Image of what a Gerver sofa would look like
More than 30 years later, Dr Baek confirmed that the Gerver sofa (pictured) is the largest sofa possible. Although his evidence needs to be checked, Dr Baek is confident that he will be proven right
Given the high value of Q, Dr Baek is able to show the shape that will match that value.
And, after calculating the numbers, the perfect shape of the sofa turned out to be exactly the same as the one that Professor Gerver gave thirty years ago.
Dr. Baek said New Scientist: ‘I devoted a lot of time to this, without any publication until now.
‘The fact that I can now say to the world that I did something valuable to the problem is to prove it.’
If Dr Baek is doing the right thing, this will mathematically prove that Professor Gerver was right to say that his sofa was a very large shape.
Professor Gerver said: ‘I am very pleased with all of this. I am 75 years old, and Baek is not yet 30 years old.
‘He’s got more energy, strength and brain cells to survive than me, and I’m glad he took the baton. I am also very happy that I lived long enough to see him finish what I started.’
Dr Baek’s results need to be fully scrutinized by other mathematicians before we know for sure, but he is still confident that his results will be accurate.
