Examples/classes:
Types
Related concepts:
The trefoil knot is a famous example of a knot. In the list of knots, ordered by crossing number, it is the first ‘real’ knot one meets, being the simplest non-trivial knot. (The first knot listed is usually the ‘unknot’, i.e. the unknotted circle.) The trefoil has crossing number 3.
Here is the traditional knot diagram for the trefoil knot:
Here is an alternative depiction with bridge number 2:
To include one of the above svg
pictures on a page, write
[[!include trefoil knot - SVG]]
or
[[!include trefoil knot (2 bridge) - SVG]]
.
The knot group of the trefoil knot (calculated either by the Dehn or Wirtinger presentations) has two very useful presentations:
, which is the braid group, Br 3;
, in which the pair of numbers, , is apparent. These reflect the fact that the trefoil is a -torus knot. (Of course, it is also a (3,2)-torus knot.)
category : knot theory
Last revised on July 18, 2024 at 18:30:24. See the history of this page for a list of all contributions to it.