The Journal of Physics runs an occasional series of articles explaining particularly interesting papers which appeared in various series of the Journal. I liked today’s post especially because it deals with problems that I’ve spent a lot of time on– the shape of the tightest overhand (or trefoil) knot, and the shape of the tight ‘simple clasp’ formed by two ropes.
The picture at left is from an amazing series of very high-resolution simulations performed by Piotr Pieranski and Sylwek Przybyl. They reveal some of the amazing tiny and intricate details of the structure.
Maybe someday we’ll understand the whole picture and have a proof. In the meantime, it’s still kind of amazing to think that nobody really knows the shape of a tight knot.