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Twenty - five days too late to help Ross get his new couch into his flat in"Friends,“a mathematician has finally puzzle out the plaguey " sofa job . "
The mathematics problem limn the largest - size sofa that can fit around a corner of a given breadth — on the dot the problem face by the fiber in an instalment of " Friends " that aired in 1999 . Ross ' plea of " Pivot ! " could have been avoided , it turn out , if he ’d only believe a Gerver ’s sofa with 18 curve sections and a maximum area of 2.2195 units . ( Okay , so maybe it would n’t have been that helpful . )
A top-down view of a sofa squeezing around an L-shaped hallway. The strangely-shaped Gerver’s sofa may be the solution to a 60-year-old math conundrum.
The solution to the sofa job is a first for math . The problem was posited by Austrian - Canadian mathematician Leo Moser in 1966 . Moser asked for the largest possible area of a single shape in one aeroplane that could move around a right - tilt corner of a hallway with a unit breadth of one . While this might seem simple , the math is quite complicated , as the job involves both area maximisation and movement of the shape .
Now , Jineon Baek , a postdoctoral research worker in mathematics at Yonsei University in South Korea , has get at an answer . Baek posted his solution on Dec. 2 on the preprint websiteArXiv . In just over 100 pages of numerical proofs , Baek found that for a hall with a width of 1 unit , the notional sofa ’s maximal area can be 2.2195 unit — narrowing the answer down with precision from the previously known reach of between 2.2195 and 2.37 units . The substantiation has not yet been published in a peer - reviewed diary and will need to be worked through by other mathematicians to determine that it is , indeed , optimum .
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The " Gerver " of Gerver ’s lounge is mathematician Joseph Gerver , an emeritus prof at Rutgers University whoposited the lower truss of 2.2195 in 1992 . But there had been debate over whether the sofa could be larger , with a squad in 2018 using a computer - assisted trial impression to hint that2.37 was actually the upper bind .
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Gerver ’s sofa is a broad U - shaped couch with a curving " buttocks " that can squeeze around the recess without getting pay heed up . The head was whether this painstakingly designed couch — made of 18 separate curves put together — was really the largest , most optimal Supreme Headquarters Allied Powers Europe that could make the twist . Baek worked through the geometry of the shape and its motion and found that Gerver ’s root was , in fact , right .
The proof produce a riffle of interest on societal medium .
" This is the optimal couch , " user@morallawwithinwrote on the social program X on Dec. 6 , posting a picture of the rather wide - armed sofa shape . " You may not care it , but this is what extremum optimisation look like . "
