We go deeper into knots – those fascinating geometrical objects which are very simple to visualise, yet remarkably hard to analyse. Simply considering a piece of string, tying a knot and gluing the two loose ends of the string together forms a knotted loop. Such a knotted loop is called a knot in mathematics. Knot theory delves into answering the question of deciding whether two knotted loops made of flexible, but impenetrable material can be transformed by means of continuous modifications into knotted loops having the same shape. Further, one may ask whether an arbitrary knot is a knot.
To answer such questions, knot invariants are employed. Two knot invariants; the number of components and the path-width of a knot were discussed. Further, the mathematics behind these invariants, the Tutte polynomial were presented.