Knot theory is the branch of mathematics used to classify and analyze different types of knots. The mathematical focus is primarily on knots that have already formed, but recently two physicists from UC San Diego, Dorian M. Raymer and Douglas E. Smith, examined why knots form. Their article, “Spontaneous knotting of an agitated string,” appeared in the October 16 issue of the Proceeding of the National Academy of Sciences.
This paper has received wide exposure in recent months, but it had humble beginnings: while Dorian Raymer was an undergraduate (!!!), he built a spinning machine with materials that Douglas Smith purchased from Home Depot and a local dairy. They looked at how often a knot formed when a string was placed inside, and also what the resulting knot looked like. Some of the things they discovered were that the string had to be at least 18 inches long, and that the knots formed within seconds. In terms of the why question:
Based on their work, Smith and Raymer developed a simple model to explain knot formation. String makes loops in concentric coils like a garden hose because of its stiffness and confinement in a box. The moving ends of the string weave randomly through the coils, with a 50 percent probability of going over or under any coil. Computer simulations using this formula produced knots similar to those observed in the experiments.
(From “Two UCSD scientists untangle a mystery, shedding light on why long strands tend to become knotted” by Scott LaFee)
[This entry was also posted here on the Young Mathematicians’ Network.]