knotted

Knotted is the past participle and adjective form of knot. It typically describes something that has been tied with one or more knots or a tangle of threads or cords. In everyday use, objects such as ropes, shoelaces, or string can be knotted, and the term can also describe a state of complexity or entanglement, as in a knotted rope or a knotted ball of yarn. The verb sense, to knot, means to tie or secure with knots, or to become tangled.

In mathematics, knotted refers to a closed loop embedded in three-dimensional space that cannot be untangled to a simple circle without cutting. This leads to knot theory, a branch of topology. Knots are considered equivalent if one can be transformed into another via continuous deformation without cutting. A knot that cannot be simplified to a circle is nontrivial. Invariants such as the Jones polynomial or the Alexander polynomial help distinguish knots.

In biology, knotted topology can occur in biomolecules. Proteins may fold into knotted configurations; DNA can become knotted during replication and is managed by topoisomerase enzymes. Knotted structures can influence folding stability, function, and replication dynamics.

Knotted is also used metaphorically to describe situations of difficulty or complexity, such as being in a knotted problem or situation. In textile and craft contexts, knotting techniques are fundamental, including macrame and knot-tying art.