Mathematicians have revealed there are over 177,000 distinct ways to knot a neck tie – more than 1000 times the number that was previously thought.

As well as vastly broadening the mathematical definition of a neck tie knot, the discovery means there are now hundreds of thousands of new ties to choose from.

In 1999, Thomas Fink and Yong Mao of the University of Cambridge published a mathematical language describing tie knots in the journal Nature.

The pair used an existing tool from logic – known as formal language theory – to express the basic rules of tying a neck tie as a series of symbols. This included things like the placement of the tie, the direction of the fold and the need to end in a final tuck. They used their tie language to show that only 85 knots were possible.

Fink and Mao assumed that you would only make a tuck – folding one end of the tie under the rest to complete the knot – at the end of a given tying sequence, and that all knots would be covered by a flat stretch of fabric.

Vejdemo-Johansson has created a website that generates random knots according to his rules.

Top photo via Ask Men.
Bottom photo via Will Skinner.

Via NewScientist. Check out the mathematician’s random tie generator site as well.