RANDOM Math FACTS #2

In 1999, two mathematicians, Thomas Yink and Yong Mao, examined the actions involved in tying a necktie and calculated that there were 85 different ways to do so.

However, a new team of mathematicians has trumped their research. Mikael Vejdemo-Johansson of the KTH Royal Institute of Technology in Stockholm and a small team of mathematicians found that Fink and Mao had left out some possibilities. 

"We extend the existing enumeration of neck tie knots to include tie knots with a textured front, tied with the narrow end of a tie," Vejdemo-Johansson wrote in the abstract of the team's paper, "More ties than we thought". 

"These tie knots have gained popularity in recent years, based on reconstructions of a costume detail from The Matrix Reloaded, and are explicitly ruled out in the enumeration by Fink and Mao (2000)."  

With this discovery, the team realised that something wasn't quite right, so they had a look at Fink and Mao's research. They realised that Fink and Mao had restricted the number of tucks that occur at the end of knotting the tie to just one. They had also made the assumption that any knotwork would be covered by a flat section of fabric, and restricted the number of windings to just eight.  

Armed with this information, Vejdemo-Johansson's team adjusted the parameters of Fink and Mao's language and calculated that the number of possible knots is much, much higher than the previous calculations: 177,147, to be precise.

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