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There are 177,000 ways to tie a tie, mathematicians report

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If you're not wearing a tie right now, you might consider slipping one on just for the sake of trying out one or two of these more than 177,000 gorgeously elaborate tie-tying methods, which a mathematician came up with after viewing The Matrix Reloaded.

Mathematician Mikael Vejdemo-Johansson came up with the idea after learning a knot patterned after the one worn by the elaborately-suited Matrix Reloaded character The Merovingian. After checking out existing mathematical tie-tying research (yep, it's thing), he realized the knot wasn't covered. That's when he set out to come up with a new mathematical model for knotting a tie. He spoke to New Scientist about it:

He first became interested in the subject after a YouTube tutorial caught his eye. It showed you how to copy an exotic-looking knot worn by Matrix villain, The Merovingian . . . "I was hooked," he says. Curious to learn more, he looked up the Fink-Mao paper – and immediately noticed that fancier knots like these weren't included.

It turns out Fink and Mao had made two assumptions about tie knots that drastically reduced the number available. They 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. Those assumptions don't hold for the new set of knots, which can involve making multiple tucks midway through a sequence – and surfaces with many folds and edges.


Vejdemo-Johansson has also created a random-tie generator, which generates one of the 177,000, still mostly obscure tie knots. Here's mine, the zingily named C-96 knot:


Try out the tie-knot generator here or read more about it at theNew Scientist here.