How can mathematical theory predict the strongest knots in real life?
The answer to that question has remained elusive despite humans relying on knots for thousands of years while fishing, hunting, building shelters and harnessing animal power. By using color-changing fibers to experimentally test a mathematical theory, researchers have begun developing more realistic models that can elucidate the rules governing stability in knots.
The mathematical theory of knots has typically focused on classifying their different entangled structures without accounting for mechanical stress and strain. To better predict knots’ strength, Massachusetts Institute of Technology researchers experimented with those made from special photonic fibers that change color as they stretch. Doing so allowed the team to compare the mechanical-strain predictions of their mathematical models against those of the color-changing fiber experiments and therefore develop more sophisticated models that can simulate the intricacies of knots and, perhaps, more complex tangled structures.