threeknot

Threeknot is a term that can refer to several different things, primarily in the context of knots and mathematics. In sailing and general knot-tying, a three-knot is not a standard recognized knot name. However, it is possible the term is used informally to describe any knot that involves three distinct loops or passes of the rope. For example, certain decorative knots or securing knots might be colloquially referred to as a "threeknot" by someone who is not a professional rigger or knot historian.

In mathematics, particularly in the field of knot theory, a "three-knot" refers to a knot in three-dimensional Euclidean space. A knot in this context is a closed loop (a circle) embedded in R^3 without self-intersection. Knot theory studies the classification and properties of such embeddings. A three-knot is simply a knot existing in this standard three-dimensional space, as opposed to knots in higher dimensions. The study of three-knots involves concepts such as knot invariants, which are properties that remain unchanged under continuous deformation of the knot, allowing mathematicians to distinguish between different knots.