177,000 Ways to Knot a Tie

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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.

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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…

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