The Mathematics of a Well-Tied Knot
by Theresa Machemer/Smithsonianmag.com
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.