Knoten

Knoten is the German word for knot and, in English-language contexts, may refer to several related concepts. In everyday use, a knot is formed by tying rope, cord, or string to create a secure fastening, a loop, or a stopper. Knots are chosen according to their stability, load-bearing behavior, and ease of tying and untying.

Common knots include the overhand knot, the square (reef) knot, the bowline, the sheet bend, and the clove hitch. They differ in how easily they slip, how hard they are to untie after being loaded, and whether they can be untied after tension has been applied.

In mathematics, a knot is a closed curve in three-dimensional space that does not intersect itself. Two knots are considered the same if one can be deformed into the other without cutting the loop (ambient isotopy). Knot theory studies properties invariant under such deformations. Important concepts include crossing number, knot polynomials (such as the Alexander and Jones polynomials), knot groups, and the distinction between prime and composite knots. Classic simple knots include the trefoil and the figure-eight knot.

Knots have a long history in sailing, climbing, fishing, surgery, and crafts. They provide mechanisms for securing loads, forming climbing systems, and guiding sutures in medicine, with different knots offering reliability and ease of use. Training and standards in various fields emphasize proper knot selection and safe tying techniques.

See also: knot theory, rope, suture, binding.