Knots: They Are Really About Math And Physics

MIT researchers develop a mathematical model to predict a knot’s stability with the help of color-changing fibers. (Photo by Joseph Sandt)

The Mathematics of a Well-Tied Knot

by Theresa Machemer/

Knots are some of the oldest and most-used technologies that humanity employs. But knowledge of different knots—their strengths, weaknesses and best applications—has generally come from practical experience. Now, a team of mathematicians and engineers at MIT has combined theoretical and experimental research to explain the math and physics behind popular knots’ stability.

The new study, published last week in the journal Science, paired mathematical knot theory with a color-changing fiber developed in 2013. Because the fiber changes color under pressure, the researchers were able to measure physical properties and add data to their computational knot models. They came up with three rules that determine a knot’s stability.

The improved model allowed the researchers to untangle the reasons that similar-looking knots behave very differently when pulled. Speaking with NPR’s Nell Greenfieldboyce, mathematician Vishal Patil gives the example of the granny knot and the reef knot, both of which loop two ropes together but differ by one overlap.

“If you pull on the reef knot, it tends to hold,” Patil tells Greenfieldboyce. “And if you pull on the granny knot, it tends to slip quite easily.

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  1. I have a collection of knot books.
    From the 1950s, data derived from stringent testing has been published, on the percentage of weakness introduced by all the knots into all the varieties of ropes, (in this case natural fibre) and the different degrees of ease of undoing. The synthetic rope manufacturers have kept up a great body of research. The coloured rope which changes under stress is, (sorry) just a gimmick allowing these researchers to make (if not earn) a living. Knots, however, are beautiful, and still their physics remains to some degree elusive, so I’m glad when the subject is highlighted, thanks Carol.

  2. Good read & information. Ancient history ties all this into how the Geometry of Hindu Steppe’s were actually built using rope as the first measuring devices using knots. Amazing how it’s all connected & synchronizes in many aspects.

  3. From nautical to construction, if you ask anyone with any experience, they’ll tell you the bowline is the best, most dependable, knot.

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