In knot theory, a branch of mathematics, the trefoil knot is the simplest example of a nontrivial knot. The trefoil can be obtained by joining the two loose ends of a common overhand knot, resulting in a knotted loop. As the simplest knot, the trefoil is fundamental to the study of mathematical knot theory.

Mar 28, 2025 · The trefoil knot 3_1, also called the threefoil knot or overhand knot, is the unique prime knot with three crossings. It is a (3, 2)-torus knot and has braid word sigma_1^3. The trefoil and its mirror image are not equivalent, as first proved by Dehn (1914).

Knot Theory for Everybody! This one is all about the Trefoil, or the 3_1 knot. This is part of a "how to tie" series, although tying the overhand is a pretty...

Another example is the trefoil knot, which has three crossings and is a very popular knot. The trefoil knot can be found in gure 2. Knot theory was rst developed in 1771 by Alexandre-Theophile Vandermonde, while the true mathematical studies of knots began in the 19th century with Carl Friedrich Gauss.

In knot theory, the trefoil knot is the simplest nontrivial knot. It can be obtained by joining the loose ends of an overhand knot. A trefoil knot is the unique prime knot with three crossings. Mathematically, it can be described in many variants. The symbol of the trefoil knot has known from ancient times as triquetra.

The Trefoil knot, Figure 8 Knot, Granny Knot, Square Knot, displayed by 3D-XplorMath are all harmonic or Fou-rier knots. That is they are parametrized using nite Fourier series for all three coordinates. The particular parametrizations are taken from the 1995 PhD thesis of Aaron Trautwein at The University of Iowa.

May 1, 2023 · The unknot or trivial knot is a knot that has a projection with 0 crossings. Example (Trefoil Knot) The trefoil knot is represented as below. It is a nontrivial knot with the least number of crossings. Isha Agarwal and Victoria Li Mentor: Julius BaldaufKnot Theory May 13th, 20236 / …

The next simplest knot is a trefoil. There are two varieties of trefoils which are mirror images of each other: the left-handed trefoil knot and the right-handed trefoil knot: Two knots are considered to be equivalent if they can be moved around in space so that they look alike. The following are also diagrams of the trefoil knot. Questions

The trefoil knot is the only knot for which the crossing number is minimal, namely 3; there are in fact two of them, they are enantiomorphic (images of one another by reflection). It is an overhand knot: the ends of which were connected.

In this study, the tools of mathematics, from algebra to geometry, are applied to answer basic questions about knots. For instance: Given a knot, can it be deformed into a trivial loop? The trefoil knot arises in an especially simple way. Consider the equation: where x …