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# Trefoil knot

In topology, a branch of mathematics, the trefoil knot is the simplest example of a nontrivial knot. [1]

60 relations: Alexander polynomial, Algebraic geometry, Alternating knot, ATV Home, Braid group, Chemistry, Chirality (mathematics), Cinquefoil knot, Circle, Clover, Complex number, Conway notation (knot theory), Crossing number (knot theory), Curve, Dowker notation, Fiber bundle, Fibered knot, Fibration, Figure-eight knot (mathematics), Geometry, Gordian Knot, Iconography, Inverse element, Jones polynomial, Kauffman polynomial, Knot (mathematics), Knot complement, Knot group, Knot invariant, Knot polynomial, Knot theory, Loop (topology), M. C. Escher, Magic (illusion), Mathematics, Milnor map, Mirror image, Mjölnir, Motif (visual arts), Overhand knot, Parametric equation, Physics, Plane curve, Polynomial, Pretzel link, Prime knot, Reidemeister move, Seifert fiber space, Semicubical parabola, Signature of a knot, ... Expand index (10 more) »

## Alexander polynomial

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

## Algebraic geometry

Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.

## 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.

## ATV Home

ATV Home, also call aTV1, is one of the free-to-air Hong Kong Cantonese television channels in Hong Kong, the other being its arch-rival TVB Jade.

## Braid group

In mathematics, the braid group on strands, denoted by, is a group which has an intuitive geometrical representation, and in a sense generalizes the symmetric group.

## Chemistry

Chemistry is a branch of physical science that studies the composition, structure, properties and change of matter.

## 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.

## 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.

## Circle

A circle is a simple shape in Euclidean geometry.

## Clover

Clover or trefoil are common names for plants of the genus (Trifolium, Latin, tres "three"+folium "leaf"), consisting of about 300 species of plants in the leguminous pea family Fabaceae.

## Complex number

A complex number is a number that can be expressed in the form, where and are real numbers and is the imaginary unit, that satisfies the equation.

## 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.

## 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.

## Curve

In mathematics, a curve (also called a curved line in older texts) is, generally speaking, an object similar to a line but which is not required to be straight.

## Dowker notation

In the mathematical field of knot theory, the Dowker notation, also called the Dowker&ndash;Thistlethwaite notation or code, for a knot is a sequence of even integers.

## Fiber bundle

In mathematics, and particularly topology, a fiber bundle (or, in British English, fibre bundle) is a space that is locally a product space, but globally may have a different topological structure.

## 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. For example.

## Fibration

In topology, a branch of mathematics, a fibration is a generalization of the notion of a fiber bundle.

## 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.

## Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

## Gordian Knot

The Gordian Knot is a legend of Phrygian Gordium associated with Alexander the Great.

## Iconography

Iconography, as a branch of art history, studies the identification, description, and the 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.

## Inverse element

In abstract algebra, the idea of an inverse element generalises concepts of a negation (sign reversal) in relation to addition, and a reciprocal in relation to multiplication.

## Jones polynomial

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

## Kauffman polynomial

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

## Knot (mathematics)

In mathematics, a knot is an embedding of a circle in 3-dimensional Euclidean space, R3 (also known as E3), considered up to continuous deformations (isotopies).

## Knot complement

In mathematics, the knot complement of a tame knot K is the three-dimensional space surrounding the knot.

## Knot group

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

## 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.

## 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.

## Knot theory

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

## Loop (topology)

A loop in mathematics, in a topological space X is a continuous function f from the unit interval I.

## M. C. Escher

Maurits Cornelis Escher (17 June 1898 – 27 March 1972) was a Dutch graphic artist.

## Magic (illusion)

Magic (sometimes referred to as stage magic to distinguish it from paranormal or ritual magic) is a performing art that entertains audiences by staging tricks or creating illusions of seemingly impossible or supernatural feats using natural means.

## Mathematics

Mathematics (from Greek μάθημα máthēma, “knowledge, study, learning”) is the study of topics such as quantity (numbers), structure, space, and change.

## 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.

## 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.

## Mjölnir

In Norse mythology, Mjölnir (Mjǫllnir) is the hammer of Thor, a major Norse god associated with thunder.

## Motif (visual arts)

In art, a motif is an element of a pattern, image or part of one.

## Overhand knot

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

## Parametric equation

In mathematics, parametric equations of a curve express the coordinates of the points of the curve as functions of a variable, called a parameter.

## Physics

Physics (from knowledge of nature, from φύσις phúsis "nature") is the natural science that involves the study of matterAt the start of The Feynman Lectures on Physics, Richard Feynman offers the atomic hypothesis as the single most prolific scientific concept: "If, in some cataclysm, all scientific knowledge were to be destroyed one sentence what statement would contain the most information in the fewest words? I believe it is that all things are made up of atoms – little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another..." and its motion through space and time, along with related concepts such as energy and force."Physical science is that department of knowledge which relates to the order of nature, or, in other words, to the regular succession of events." More broadly, it is the general analysis of nature, conducted in order to understand how the universe behaves."Physics is one of the most fundamental of the sciences. Scientists of all disciplines use the ideas of physics, including chemists who study the structure of molecules, paleontologists who try to reconstruct how dinosaurs walked, and climatologists who study how human activities affect the atmosphere and oceans. Physics is also the foundation of all engineering and technology. No engineer could design a flat-screen TV, an interplanetary spacecraft, or even a better mousetrap without first understanding the basic laws of physics. (...) You will come to see physics as a towering achievement of the human intellect in its quest to understand our world and ourselves."Physics is an experimental science. Physicists observe the phenomena of nature and try to find patterns that relate these phenomena.""Physics is the study of your world and the world and universe around you." Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy. Over the last two millennia, physics was a part of natural philosophy along with chemistry, certain branches of mathematics, and biology, but during the scientific revolution in the 17th century, the natural sciences emerged as unique research programs in their own right. Physics intersects with many interdisciplinary areas of research, such as biophysics and quantum chemistry, and the boundaries of physics are not rigidly defined. New ideas in physics often explain the fundamental mechanisms of other sciences while opening new avenues of research in areas such as mathematics and philosophy. Physics also makes significant contributions through advances in new technologies that arise from theoretical breakthroughs. For example, advances in the understanding of electromagnetism or nuclear physics led directly to the development of new products that have dramatically transformed modern-day society, such as television, computers, domestic appliances, and nuclear weapons; advances in thermodynamics led to the development of industrialization, and advances in mechanics inspired the development of calculus.

## Plane curve

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

## Polynomial

In mathematics, a polynomial is an expression consisting of variables (or indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents.

In knot theory, a branch of mathematics, a pretzel link is a special kind of link.

## Prime knot

In knot theory, a prime knot or prime link is a knot that is, in a certain sense, indecomposable.

## Reidemeister move

In the mathematical area of knot theory, a Reidemeister move refers to one of three local moves on a link diagram.

## Seifert fiber space

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

## Semicubical parabola

In mathematics, a cuspidal cubic or semicubical parabola is an algebraic plane curve defined parametrically as.

## Signature of a knot

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

## Slice knot

A slice knot is a type of mathematical knot.

## Topology

In mathematics, topology (from the Greek τόπος, place, and λόγος, study), is the study of topological spaces.

## Torus

In geometry, a torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis 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.

## 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.

## Triquetra

Triquetra (Latin tri- "three" and quetrus "cornered") originally meant "triangle" and was used to refer to various three-cornered shapes.

## Unknot

The unknot arises in the mathematical theory of knots.

## Valknut

The valknut (Old Norse valr, "slain warriors" + knut, "knot") is a symbol consisting of three interlocked triangles, and appears on various Germanic objects.

## Visual arts

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

## 3-sphere

In mathematics, a 3-sphere (also called a glome) is a higher-dimensional analogue of a sphere.

## References

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