Mathematics: Which knot holds best?

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Mathematics: Which knot holds best?
Mathematics: Which knot holds best?
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Which knot holds best?

The shoelace is untied again! But why? Researchers have now found a simple method to check the stability of the most common knots - without any complex calculations or simulations.

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Mathematical research is considered abstract and unrealistic. The field of knot theory is a rare exception. We encounter knots all the time, be it in woven fabrics, when lacing shoes or when climbing mountains. Scientists now assume that humans formed knots half a million years ago - long before the wheel was invented. And even some monkeys, including gorillas, have been shown to knot grass when building their nests.

It is therefore all the more astonishing that these ubiquitous structures still hold a number of mysteries that researchers are unable to solve. For example, a granny knot used to tie shoelaces is similar to the less common reef knot. As experience and experiments show, the latter is much more robust - but so far there has been no simple theoretical model that explains this. The mathematician Vishal Patil from the Massachusetts Institute of Technology and his colleagues have now changed that.

In the paper, published in the journal Science at the beginning of January 2020, the researchers identified three easy-to-determine characteristics that can be used to assess how stable common knots are. Patil and his team then confirmed their theoretical results through computer simulations and laboratory experiments. Finally, scientists have a simple method to explain why some knots hold better than others…

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