## Table of Contents

59 relations: Alexander polynomial, Algebraic geometry, Alternating knot, Ambient isotopy, ATV Home, Braid group, Carolingian cross, Celtic cross, Chirality (mathematics), Cinquefoil knot, Circle, Clockwise, Clover, Complex number, Conway notation (knot theory), Crossing number (knot theory), Curve, Dowker–Thistlethwaite notation, Fiber bundle, Fibered knot, Figure-eight knot (mathematics), Gordian Knot, HOMFLY polynomial, Iconography, Jones polynomial, Kauffman polynomial, Knot (mathematics), Knot complement, Knot group, Knot invariant, Knot polynomial, Knot theory, Loop (topology), M. C. Escher, Mathematics, Milnor map, Mirror image, Mjölnir, Motif (visual arts), Overhand knot, Parametric equation, Plane curve, Polynomial, Pretzel link, Prime knot, Puncture (topology), Reidemeister move, Seifert fiber space, Semicubical parabola, Signature of a knot, ... Expand index (9 more) »

- Alternating knots and links
- Fibered knots and links
- Pretzel knots and links (mathematics)
- Prime knots and links
- Reversible knots and links
- Slice knots and links
- Torus knots and links
- Tricolorable knots and links
- Twist knots

## Alexander polynomial

In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type. Trefoil knot and Alexander polynomial are knot theory.

See Trefoil knot and Alexander polynomial

## Algebraic geometry

Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.

See Trefoil knot and Algebraic geometry

## Alternating knot

In knot theory, a knot or link diagram is alternating if the crossings alternate under, over, under, over, as one travels along each component of the link. Trefoil knot and alternating knot are alternating knots and links.

See Trefoil knot and Alternating knot

## Ambient isotopy

In the mathematical subject of topology, an ambient isotopy, also called an h-isotopy, is a kind of continuous distortion of an ambient space, for example a manifold, taking a submanifold to another submanifold.

See Trefoil knot and Ambient isotopy

## ATV Home

ATV Home was a free-to-air Cantonese television channel in Hong Kong, owned and operated by Asia Television.

## Braid group

In mathematics, the braid group on strands (denoted B_n), also known as the Artin braid group, is the group whose elements are equivalence classes of n-braids (e.g. under ambient isotopy), and whose group operation is composition of braids (see). Example applications of braid groups include knot theory, where any knot may be represented as the closure of certain braids (a result known as Alexander's theorem); in mathematical physics where Artin's canonical presentation of the braid group corresponds to the Yang–Baxter equation (see); and in monodromy invariants of algebraic geometry. Trefoil knot and braid group are knot theory.

See Trefoil knot and Braid group

## Carolingian cross

The Carolingian Cross is but one variation in the vast historical imagery of Christian symbolic representations of the Crucifixion of Jesus, going back to at least the ninth century.

See Trefoil knot and Carolingian cross

## Celtic cross

A Celtic cross symbol The Celtic cross is a form of Christian cross featuring a nimbus or ring that emerged in Ireland, France and Great Britain in the Early Middle Ages.

See Trefoil knot and Celtic cross

## Chirality (mathematics)

In geometry, a figure is chiral (and said to have chirality) if it is not identical to its mirror image, or, more precisely, if it cannot be mapped to its mirror image by rotations and translations alone. Trefoil knot and chirality (mathematics) are knot theory.

See Trefoil knot and Chirality (mathematics)

## Cinquefoil knot

In knot theory, the cinquefoil knot, also known as Solomon's seal knot or the pentafoil knot, is one of two knots with crossing number five, the other being the three-twist knot. Trefoil knot and cinquefoil knot are alternating knots and links, fibered knots and links, knot theory, prime knots and links, Reversible knots and links and torus knots and links.

See Trefoil knot and Cinquefoil knot

## Circle

A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.

## Clockwise

Two-dimensional rotation can occur in two possible directions or senses of rotation.

See Trefoil knot and Clockwise

## Clover

Clover, also called trefoil, are plants of the genus Trifolium (from Latin tres 'three' + folium 'leaf'), consisting of about 300 species of flowering plants in the legume family Fabaceae originating in Europe.

## Complex number

In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted, called the imaginary unit and satisfying the equation i^.

See Trefoil knot and Complex number

## Conway notation (knot theory)

In knot theory, Conway notation, invented by John Horton Conway, is a way of describing knots that makes many of their properties clear. Trefoil knot and Conway notation (knot theory) are knot theory.

See Trefoil knot and Conway notation (knot theory)

## Crossing number (knot theory)

In the mathematical area of knot theory, the crossing number of a knot is the smallest number of crossings of any diagram of the knot.

See Trefoil knot and Crossing number (knot theory)

## Curve

In mathematics, a curve (also called a curved line in older texts) is an object similar to a line, but that does not have to be straight.

## Dowker–Thistlethwaite notation

In the mathematical field of knot theory, the Dowker–Thistlethwaite (DT) notation or code, for a knot is a sequence of even integers. Trefoil knot and Dowker–Thistlethwaite notation are knot theory.

See Trefoil knot and Dowker–Thistlethwaite notation

## Fiber bundle

In mathematics, and particularly topology, a fiber bundle (''Commonwealth English'': fibre bundle) is a space that is a product space, but may have a different topological structure.

See Trefoil knot and Fiber bundle

## Fibered knot

In knot theory, a branch of mathematics, a knot or link K in the 3-dimensional sphere S^3 is called fibered or fibred (sometimes Neuwirth knot in older texts, after Lee Neuwirth) if there is a 1-parameter family F_t of Seifert surfaces for K, where the parameter t runs through the points of the unit circle S^1, such that if s is not equal to t then the intersection of F_s and F_t is exactly K. Trefoil knot and fibered knot are fibered knots and links.

See Trefoil knot and Fibered knot

## Figure-eight knot (mathematics)

In knot theory, a figure-eight knot (also called Listing's knot) is the unique knot with a crossing number of four. Trefoil knot and figure-eight knot (mathematics) are alternating knots and links, fibered knots and links, knot theory, prime knots and links and Twist knots.

See Trefoil knot and Figure-eight knot (mathematics)

## Gordian Knot

The cutting of the Gordian Knot is an Ancient Greek legend associated with Alexander the Great in Gordium in Phrygia, regarding a complex knot that tied an oxcart.

See Trefoil knot and Gordian Knot

## HOMFLY polynomial

In the mathematical field of knot theory, the HOMFLY polynomial or HOMFLYPT polynomial, sometimes called the generalized Jones polynomial, is a 2-variable knot polynomial, i.e. a knot invariant in the form of a polynomial of variables m and l. A central question in the mathematical theory of knots is whether two knot diagrams represent the same knot. Trefoil knot and HOMFLY polynomial are knot theory.

See Trefoil knot and HOMFLY polynomial

## Iconography

Iconography, as a branch of art history, studies the identification, description and interpretation of the content of images: the subjects depicted, the particular compositions and details used to do so, and other elements that are distinct from artistic style.

See Trefoil knot and Iconography

## Jones polynomial

In the mathematical field of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984. Trefoil knot and Jones polynomial are knot theory.

See Trefoil knot and Jones polynomial

## Kauffman polynomial

In knot theory, the Kauffman polynomial is a 2-variable knot polynomial due to Louis Kauffman. Trefoil knot and Kauffman polynomial are knot theory.

See Trefoil knot and Kauffman polynomial

## Knot (mathematics)

In mathematics, a knot is an embedding of the circle into three-dimensional Euclidean space, (also known as). Often two knots are considered equivalent if they are ambient isotopic, that is, if there exists a continuous deformation of which takes one knot to the other.

See Trefoil knot and Knot (mathematics)

## Knot complement

In mathematics, the knot complement of a tame knot K is the space where the knot is not. Trefoil knot and knot complement are knot theory.

See Trefoil knot and Knot complement

## Knot group

In mathematics, a knot is an embedding of a circle into 3-dimensional Euclidean space.

See Trefoil knot and Knot group

## Knot invariant

In the mathematical field of knot theory, a knot invariant is a quantity (in a broad sense) defined for each knot which is the same for equivalent knots.

See Trefoil knot and Knot invariant

## Knot polynomial

In the mathematical field of knot theory, a knot polynomial is a knot invariant in the form of a polynomial whose coefficients encode some of the properties of a given knot.

See Trefoil knot and Knot polynomial

## Knot theory

In topology, knot theory is the study of mathematical knots.

See Trefoil knot and Knot theory

## Loop (topology)

In mathematics, a loop in a topological space is a continuous function from the unit interval to such that In other words, it is a path whose initial point is equal to its terminal point.

See Trefoil knot and Loop (topology)

## M. C. Escher

Maurits Cornelis Escher (17 June 1898 – 27 March 1972) was a Dutch graphic artist who made woodcuts, lithographs, and mezzotints, many of which were inspired by mathematics.

See Trefoil knot and M. C. Escher

## Mathematics

Mathematics is a field of study that discovers and organizes abstract objects, methods, theories and theorems that are developed and proved for the needs of empirical sciences and mathematics itself.

See Trefoil knot and Mathematics

## Milnor map

In mathematics, Milnor maps are named in honor of John Milnor, who introduced them to topology and algebraic geometry in his book Singular Points of Complex Hypersurfaces (Princeton University Press, 1968) and earlier lectures. Trefoil knot and Milnor map are knot theory.

See Trefoil knot and Milnor map

## Mirror image

A mirror image (in a plane mirror) is a reflected duplication of an object that appears almost identical, but is reversed in the direction perpendicular to the mirror surface.

See Trefoil knot and Mirror image

## Mjölnir

Mjölnir (from Old Norse Mjǫllnir) is the hammer of the thunder god Thor in Norse mythology, used both as a devastating weapon and as a divine instrument to provide blessings.

## Motif (visual arts)

In art and iconography, a motif is an element of an image.

See Trefoil knot and Motif (visual arts)

## Overhand knot

The overhand knot is one of the most fundamental knots, and it forms the basis of many others, including the simple noose, overhand loop, angler's loop, reef knot, fisherman's knot, half hitch, and water knot.

See Trefoil knot and Overhand knot

## Parametric equation

In mathematics, a parametric equation defines a group of quantities as functions of one or more independent variables called parameters.

See Trefoil knot and Parametric equation

## Plane curve

In mathematics, a plane curve is a curve in a plane that may be a Euclidean plane, an affine plane or a projective plane.

See Trefoil knot and Plane curve

## Polynomial

In mathematics, a polynomial is a mathematical expression consisting of indeterminates (also called variables) and coefficients, that involves only the operations of addition, subtraction, multiplication and exponentiation to nonnegative integer powers, and has a finite number of terms.

See Trefoil knot and Polynomial

## Pretzel link

In the mathematical theory of knots, a pretzel link is a special kind of link. Trefoil knot and pretzel link are pretzel knots and links (mathematics).

See Trefoil knot and Pretzel link

## Prime knot

In knot theory, a prime knot or prime link is a knot that is, in a certain sense, indecomposable. Trefoil knot and prime knot are prime knots and links.

See Trefoil knot and Prime knot

## Puncture (topology)

In topology, puncturing a manifold is removing a finite set of points from that manifold.

See Trefoil knot and Puncture (topology)

## Reidemeister move

In the mathematical area of knot theory, a Reidemeister move is any of three local moves on a link diagram.

See Trefoil knot and Reidemeister move

## Seifert fiber space

A Seifert fiber space is a 3-manifold together with a decomposition as a disjoint union of circles.

See Trefoil knot and Seifert fiber space

## Semicubical parabola

In mathematics, a cuspidal cubic or semicubical parabola is an algebraic plane curve that has an implicit equation of the form (with) in some Cartesian coordinate system.

See Trefoil knot and Semicubical parabola

## Signature of a knot

The signature of a knot is a topological invariant in knot theory.

See Trefoil knot and Signature of a knot

## Slice knot

A slice knot is a mathematical knot in 3-dimensional space that bounds an embedded disk in 4-dimensional space. Trefoil knot and slice knot are slice knots and links.

See Trefoil knot and Slice knot

## Torus

In geometry, a torus (tori or toruses) is a surface of revolution generated by revolving a circle in three-dimensional space one full revolution about an axis that is coplanar with the circle.

## Torus knot

In knot theory, a torus knot is a special kind of knot that lies on the surface of an unknotted torus in R3. Trefoil knot and torus knot are fibered knots and links, knot theory and torus knots and links.

See Trefoil knot and Torus knot

## Tricolorability

In the mathematical field of knot theory, the tricolorability of a knot is the ability of a knot to be colored with three colors subject to certain rules. Trefoil knot and tricolorability are Tricolorable knots and links.

See Trefoil knot and Tricolorability

## Triquetra

The triquetra (from the Latin adjective triquetrus "three-cornered") is a triangular figure composed of three interlaced arcs, or (equivalently) three overlapping vesicae piscis lens shapes.

See Trefoil knot and Triquetra

## Unknot

In the mathematical theory of knots, the unknot, not knot, or trivial knot, is the least knotted of all knots. Trefoil knot and unknot are fibered knots and links, knot theory, prime knots and links, slice knots and links and torus knots and links.

## Valknut

The valknut is a symbol consisting of three interlocked triangles.

## Visual arts

The visual arts are art forms such as painting, drawing, printmaking, sculpture, ceramics, photography, video, filmmaking, comics, design, crafts, and architecture.

See Trefoil knot and Visual arts

## 3-sphere

In mathematics, a 3-sphere, glome or hypersphere is a higher-dimensional analogue of a sphere.

## See also

### Alternating knots and links

- 62 knot
- 63 knot
- 71 knot
- 74 knot
- Alternating knot
- Borromean rings
- Carrick mat
- Cinquefoil knot
- Figure-eight knot (mathematics)
- Granny knot (mathematics)
- Hopf link
- L10a140 link
- Solomon's knot
- Square knot (mathematics)
- Stevedore knot (mathematics)
- Three-twist knot
- Trefoil knot
- Whitehead link

### Fibered knots and links

- (−2,3,7) pretzel knot
- 62 knot
- 63 knot
- 71 knot
- Carrick mat
- Cinquefoil knot
- Fibered knot
- Figure-eight knot (mathematics)
- Hopf link
- Perko pair
- Torus knot
- Trefoil knot
- Unknot

### Pretzel knots and links (mathematics)

- (−2,3,7) pretzel knot
- Pretzel link
- Square knot (mathematics)
- Stevedore knot (mathematics)
- Trefoil knot

### Prime knots and links

- 62 knot
- 63 knot
- 71 knot
- 74 knot
- Carrick mat
- Cinquefoil knot
- Conway knot
- Figure-eight knot (mathematics)
- Hopf link
- Kinoshita–Terasaka knot
- List of prime knots
- Perko pair
- Prime knot
- Stevedore knot (mathematics)
- Three-twist knot
- Trefoil knot
- Unknot
- Whitehead link

### Reversible knots and links

- (−2,3,7) pretzel knot
- 62 knot
- 71 knot
- 74 knot
- Cinquefoil knot
- Perko pair
- Stevedore knot (mathematics)
- Three-twist knot
- Trefoil knot

### Slice knots and links

- Conway knot
- Kinoshita–Terasaka knot
- Ribbon knot
- Slice knot
- Square knot (mathematics)
- Stevedore knot (mathematics)
- Trefoil knot
- Unknot

### Torus knots and links

- 71 knot
- Cinquefoil knot
- Hopf link
- Torus knot
- Trefoil knot
- Unknot

### Tricolorable knots and links

### Twist knots

- Figure-eight knot (mathematics)
- Stevedore knot (mathematics)
- Three-twist knot
- Trefoil knot
- Twist knot

## References

Also known as (2,3) torus knot, (2,3)-torus knot, (3,2)-torus knot, (−1, −1, −1) pretzel knot, 3 1 knot, 3₁ knot, Cloverleaf knot, Overhand knot (knot theory), Threefoil knot, Trefoil Curve, Trefoil knot (mathematics), Underhand knot.