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Mathematicians Find 177,147 Ways to Tie a Necktie

Mathematicians Find 177,147 Ways to Tie a Necktie
In 1999, two mathematicians, Thomas Yink and Yong Mao, examined the actions taken in tying a necktie and calculated that there are 85 different ways to do so.  However, a new team of mathematicians trumped their research, claiming there are 177,147.
Mikael Vejdemo-Johansson and a small team of mathematicians of the KTH Royal Institute of Technology in Stockholm determined that the original number of tucks that occur at the end of knotting the tie had been underestimated.  They also determined that the final knotwork was assumed to be covered by a flat piece of fabric, restricting the number of windings.

The team explains their methods and conclusions as follows:

"We show that the relaxed tie knot description language that comprehensively describes these extended tie knot classes is either context sensitive or context free.  It has a sub-language that covers all the knots that inspired the work, and that is regular.  From this regular sub-language, we enumerate 177,147 distinct tie knots that seem tieable with a normal necktie.  These are found through an enumeration of 2,046 winding patterns that can be varied by tucking the tie under itself at various points along the winding."

The average Australian lifespan for me is about 80.5 years.  You would have to tie over six different knots per day for your entire life to get through them all.


Source:  phys.org


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