Ideal knots

In this book, experts in different fields of mathematics, physics, chemistry and biology present unique forms of knots which satisfy certain preassigned criteria relevant to a given field. They discuss the shapes of knotted magnetic flux lines, the forms of knotted arrangements of bistable chemical systems, the trajectories of knotted solitons, and the shapes of knots which can be tied using the shortest piece of elastic rope with a constant diameter. This text discusses topics including: the shapes of knotted magnetic flux lines; the forms of knotted arrangements of bistable chemical systems; the trajectories of knotted solitons; and the shapes of knots which can be tied using the shortest piece of elastic rope with a constant diameter. We present here the concept of ideal geometric representations of knots which are defined as minimal length trajectories of uniform diameter tubes forming a given type of knot.