Every fan Friends have their favorite scenes, but if there is one that everyone remembers the most, it is without a doubt the scene from Ross sofa. For those who haven’t watched the show (seriously, what’s wrong with you?), in this scene we see Chandler and Rachel helping Ross carry a couch into his apartment. It seemed like it would be as easy as shelling pears, but no. He turning the stairs This makes their task very difficult.
In 1966, just the year of his birth. David Schwimmer, the actor who played Ross was already a scientist concerned about this. It makes sense that I knew nothing about the series in which this newborn child would rise to fame. But I had an idea of how difficult it is to move an object through L-shaped corridor. This scientist was an Austrian-Canadian mathematician. Leo Moser and the problem he posed was: what is a rigid two-dimensional shape with legs of unit width and greatest area? TO which can move on a flat L-shaped surface? Or said much more to everyone: What is biggest sofa which can move around the corner of an L-shaped corridor?
Two years after Moser posed this mathematical problem, his British colleague John Hammersley offered the first answer. Later, in 1992, two years before the premiere Friendsanother mathematician Joseph Gervergave a much more detailed solution, but it was still a bit unfinished. It was this year when a Korean mathematician Jineon Pack gave what seems to be the most complete solution to Ross’s sofa problem. Well, actually it’s just known as “problem with the sofa” but thinking about the series is inevitable.
The problem with Ross’s sofa…or any sofa.
Let’s imagine that we have a sofa, or rather an armchair, the size of one square unit and we want to move it along a corridor one unit wide. Turning the corner will be easy. However, as the width increases, things get more complicated. This is precisely the problem raised by Leo Moser. What will it be like maximum length What can you do to turn the corner? Width is still a unit of measurement, so we’ll just focus on width.
Hammersley offered to hand them over 2.2074 unitsalthough he later increased his bet to the maximum 2.8284. However, in 1992 Joseph Gerver gave a much more detailed shape to the sofa, with 18 curved sections. At the same time, he calculated that the maximum would be 2.2195 units.
This was the most complete solution in more than 20 years, but in 2018 other mathematicians began working on the problem. In 2018, scientists Yoav Kallus and Dan Romik, from the University of California, Davis, added computational models to the equation. Through computer modeling, taking into account the parameters mentioned by their predecessors, they calculated that the maximum length of the sofa would be 2.37 units
And now the latest solution has just been published in an article, which, it must be said, still requires peer review. This means that a group of scientists specialized in their field, independent of Baek’s research, must verify that everything was done correctly. If this is the case, then the paper can be finally published and its results will not require such careful reading. But, looking forward to this, we can’t deny that the approach turned out to be interesting.
Do we have a final solution?
Scientist Yonsei Universityused in South Korea injective function perform new calculations, starting with the methods described above. This is a function where, given two sets of values, only one value in each set matches the value in the other. This allowed him perform mapping with the ever larger dimensions of the sofa and check at what point it stopped turning the corner.
His conclusion is considered very interesting as it indicates that the maximum would be a long position of 2.2195 units. This is exactly what Gerver already pointed out in 1992.
Therefore, find out if there is a Ross sofa comes around the corneryou will have to measure the width of the stairs and the length of the seat. Perhaps so many failures could have been avoided. But maybe they would also save us some laughs. And laughter, of course, is the last thing we should skimp on.
Source: Hiper Textual
