History of knotting History of knotting Knots and knotting have been used and studied throughout history. For example, Chinese knotting is a decorative handicraft art that began as a form of Chinese folk art in the Tang and Song Dynasty (960-1279 AD) in China, later popularized in the Ming. Knot theory is the recent mathematical study of unknots. Knots of ancient origin include the bottle sling, bowline, cat's paw, clove hitch, cow hitch, double fisherman's knot, eskimo bowline, figure-eight knot, fisherman's knot, half hitch, kalmyk loop, one-sided overhand bend, overhand knot, overhand loop, reef knot, running bowline, single hitch, thief knot, Turk's head
Mutation (knot theory) Mutation (knot theory) In the mathematical field of knot theory, a mutation is an operation on a knot that can produce different knots. Suppose "K" is a knot given in the form of a knot diagram. Consider a disc "D" in the projection plane of the diagram whose boundary circle intersects "K" exactly four times. We may suppose that (after planar isotopy) the disc is geometrically round and the four points of intersection on its boundary with "K" are equally spaced. The part of the knot inside the disc is a tangle. There are two reflections that switch pairs of