Remember when Teacher said you’d use math for . . . everything? Teacher wasn’t wrong. Even knots involve math. Scouts, sailors, and rock climbers know firsthand that some knots are stronger than others. Now mathematics experts at the Massachusetts Institute of Technology have figured out why.
Jörn Dunkel is an associate professor of mathematics at MIT. He and engineering associate professor Mathias Kolle helped develope a knot model. Their model predicts how strong different knots will be. Kolle says usage has long shown people which knots are best. It’s just that “now the model shows why.”
Back in 2018, Kolle helped develop fibers that change color when stretched or pulled, especially at the greatest stress or pressure points.
Kolle’s color-changing fibers got Dunkel wondering, Why not knots? Maybe not exactly, but he did begin thinking that perhaps those strands could be helpful in the study of knot stability, or strength.
You see, knots are serious business with math people. There’s even a branch of geometry known as “knot theory.” (Not knot kidding.)
Knot theory is the study of abstract knots with no ends. These “imaginary” knots form a continuous looping pattern. Mathematicians try to describe abstract knots in all the ways they can be twisted while keeping their knot shapes. (Not knot easy.)
The MIT knot model analyzes several knot features, like number of over/under crossings and how a rope twists when a knot gets tight. “These subtle differences . . . determine whether a knot is strong,” says Dunkel. “With this model, you should be able to look at two knots that are almost identical and be able to say which is the better one.”
Dunkel and Kolle and their doctoral students hoped to identify what makes a knot strong. They tied Kolle’s color-changing fibers into various knots and took pictures. They analyzed where, when, and how the fibers changed color—and how that reflected their strength.
From that information, the team made simple diagrams for the knots. Each drawing shows the pattern of the two strands in a knot before it’s tightened.
By comparing diagrams, researchers hit upon the basic strength features: crossings and twists. The reason has to do with rope-against-rope friction. The more crossings and twists, the more friction . . . and the more knot strength.
Kolle hopes his team’s knot model will help create the right knots for use in everything from medicine to manufacturing. “We can play knots against each other for uses in suturing, sailing, climbing, and construction. It’s wonderful.” (Not knot bad.)