Mathematician Calculates 177,147 Ways to Tie a Tie

By Carl Engelking | February 11, 2014 1:02 pm

tying a tie

Whether they know it or not, most guys stick to the tried-and-true Windsor knot when tying their neckties. The more debonair gentlemen, depending on the occasion, may don exotics like the Eldredge, Trinity or Cape knots.

However, the tie is far more versatile than even the most fashionable male could have previously imagined, according to Swedish mathematician Mikael Vejedemo-Johansson. Vejedemo-Johansson — who prefers the Eldredge knot — recently calculated that there are more than 177,000 different ways to tie a necktie.

All Tied Up

Yes, mathematicians have long been tied up with the algorithms of a necktie. In 1999, researchers from Cambridge University published a mathematical model showing only 85 total knots were possible. That study, however, made two assumptions: All knots are covered by a flat stretch of fabric, and each tuck — folding an end of the tie to make a knot— would only occur at the end of making a knot. They also limited the number of winding motions to eight, or the tie gets too short.

However, Vejedemo-Johansson knew that more exotic presentations expose the knots for effect, require multiple tucks mid-sequence, and feature up to 11 winds — like the Eldredge. And he was inspired to research the math after seeing The Matrix Reloaded, in which villain The Merovingian sports an unusual tie knot.

By expanding the knot parameters, Vejedemo-Johansson found that there are in fact 177,147 ways to tie a tie — enough to try a different one every day of your lifetime and still only make it through a fraction of possibilities. Those findings were recently submitted to the ACM Symposium on Computational Geometry.

Are They Fashionable?

Unfortunately, quantity doesn’t translate into quality when it comes to neckties. In fact, many combinations end up looking a little strange, as Vejdemo-Johansson explained to New Scientist:

“I have tried 10 or 20 of them, and most of them to be quite honest look kind of awkward. This is pure speculation, but it seems to be the fraction of really attractive tie knots goes down when we widen the scope.”

He told New Scientist that he would like to mathematically identify aesthetically pleasing knots. In the meantime, if you’re looking to change things up, he’s created a website that randomly generates knots according to his mathematical formula.

Image credit: katalinks/Shutterstock

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