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Mathematical knot with crossing number 6
In knot theory, the 62 knot is one of three prime knots with crossing number six, the others being the stevedore knot and the 63 knot. This knot is sometimes
62_knot
Mathematical knot with crossing number 6
In knot theory, the stevedore knot is one of three prime knots with crossing number six, the others being the 62 knot and the 63 knot. The stevedore knot
Stevedore_knot_(mathematics)
Type of stopper knot used in sailing and climbing
The figure-eight knot or figure-of-eight knot is a type of stopper knot. It is very important in sailing, rock climbing and caving as a method of stopping
Figure-eight_knot
Unique knot with a crossing number of four
In knot theory, a figure-eight knot (also called Listing's knot) is the unique knot with a crossing number of four. This makes it the knot with the third-smallest
Figure-eight knot (mathematics)
Figure-eight_knot_(mathematics)
Simplest non-trivial closed knot with three crossings
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
Trefoil_knot
Mathematical knot with crossing number 6
In knot theory, the 63 knot is one of three prime knots with crossing number six, the others being the stevedore knot and the 62 knot. It is alternating
63_knot
twist knot with four twists 62 knot - a prime knot with crossing number six 63 knot - a prime knot with crossing number six 71 knot, septafoil knot, (7
List of mathematical knots and links
List_of_mathematical_knots_and_links
Prime knot named for John Horton Conway
In mathematics, specifically in knot theory, the Conway knot (or Conway's knot) is a particular knot with 11 crossings, named after John Horton Conway
Conway_knot
Study of mathematical knots
In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope,
Knot_theory
Knot which lies on the surface of a torus in 3-dimensional space
In knot theory, a torus knot is a special kind of knot that lies on the surface of an unknotted torus in R3. Similarly, a torus link is a link which lies
Torus_knot
Minimum number of times a specific knot must be passed through itself to become untied
unknotting number 1 Stevedore knot unknotting number 1 62 knot unknotting number 1 63 knot unknotting number 1 71 knot unknotting number 3 In general
Unknotting_number
Mathematical knot with crossing number 5
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
Cinquefoil_knot
Embedding of the circle in three dimensional Euclidean space
mathematics, a knot is an embedding of the circle (S1) into three-dimensional Euclidean space, R3 (also known as E3). Often two knots are considered equivalent
Knot_(mathematics)
Motif with two doubly-interlinked loops
classified as a link, and is not a true knot according to the definitions of mathematical knot theory. The Solomon's knot consists of two closed loops, which
Solomon's_knot
In knot theory, prime knots are those knots that are indecomposable under the operation of knot sum. The prime knots with ten or fewer crossings are listed
List_of_prime_knots
Type of mathematical knot
pretzel knot, sometimes called the Fintushel–Stern knot (after Ron Fintushel and Ronald J. Stern), is an important example of a pretzel knot which exhibits
(−2,3,7)_pretzel_knot
Binding hitch knot
The constrictor knot is one of the most effective binding knots. Simple and secure, it is a harsh knot that can be difficult or impossible to untie once
Constrictor_knot
Non-trivial knot which cannot be written as the knot sum of two non-trivial knots
In knot theory, a prime knot or prime link is a knot that is, in a certain sense, indecomposable. Specifically, it is a non-trivial knot which cannot
Prime_knot
Type of mathematical link
knot (the figure-eight knot) 52 knot (the three-twist knot) 61 knot (the stevedore knot) 62 knot 63 knot 74 knot 10 161 knot (the "Perko pair" knot)
Hyperbolic_link
Mathematical knot with crossing number 5
In knot theory, the three-twist knot is the twist knot with three-half twists. It is listed as the 52 knot in the Alexander-Briggs notation, and is one
Three-twist_knot
Mathematical knot with crossing number 7
In knot theory, the Pentatwist knot, also known as the five-twist knot, or the 72, is one of seven prime knots with crossing number seven. It is the fifth
7_2_knot
Loop seen as a trivial knot
of knots, the unknot, not knot, or trivial knot, is the least knotted of all knots. Intuitively, the unknot is a closed loop of rope without a knot tied
Unknot
Three linked but pairwise separated rings
the "Ballantine rings". The first work of knot theory to include the Borromean rings was a catalog of knots and links compiled in 1876 by Peter Tait.
Borromean_rings
Family of mathematical knots
In knot theory, a branch of mathematics, a twist knot is a knot obtained by repeatedly twisting a closed loop and then linking the ends together. (That
Twist_knot
Mathematical knot with crossing number 7
In knot theory, the 71 knot, also known as the septoil knot, the septafoil knot, or the (7, 2)-torus knot, is one of seven prime knots with crossing number
71_knot
Connected sum of two trefoil knots with opposite chirality
In knot theory, the square knot is a composite knot obtained by taking the connected sum of a trefoil knot with its reflection. It is closely related
Square_knot_(mathematics)
Type of knot
The half hitch is a simple hitch knot, where the working end of a line is brought over and under the standing part. Insecure on its own, it is a valuable
Half_hitch
Knot that bounds an embedded disk in 4-space
A slice knot is a mathematical knot in 3-dimensional space that bounds an embedded disk in 4-dimensional space. A knot K ⊂ S 3 {\displaystyle K\subset
Slice_knot
Connected sum of two trefoil knots with same chirality
In knot theory, the granny knot is a composite knot obtained by taking the connected sum of two identical trefoil knots. It is closely related to the square
Granny_knot_(mathematics)
Normalized hyperbolic volume of the complement of a hyperbolic knot
In the mathematical field of knot theory, the hyperbolic volume of a hyperbolic link is the volume of the link's complement with respect to its complete
Hyperbolic_volume
Knot that is not equivalent to its mirror image
field of knot theory, a chiral knot is a knot that is not equivalent to its mirror image (when identical while reversed). An oriented knot that is equivalent
Chiral_knot
Knots Landing is an American prime time television soap opera that originally aired on CBS from December 27, 1979, to May 13, 1993. A spin-off of Dallas
List of Knots Landing episodes
List_of_Knots_Landing_episodes
Flat woven decorative knot
The carrick mat is a flat woven decorative knot which can be used as a mat or pad. Its name is based on the mat's decorative-type carrick bend with the
Carrick_mat
Type of knot in knot theory
Bridge number 2 In the mathematical field of knot theory, a 2-bridge knot is a knot which can be regular isotoped so that the natural height function given
2-bridge_knot
Mathematical knot with crossing number 7
In mathematical knot theory, 74 is the name of a 7-crossing knot which can be visually depicted in a highly-symmetric form, and so appears in the symbolism
74_knot
Polynomials arising in knot theory
field of knot theory, the HOMFLY polynomial or HOMFLYPT polynomial, sometimes called the generalized Jones polynomial, is a 2-variable knot polynomial
HOMFLY_polynomial
Integer-valued knot invariant; least number of crossings in a knot diagram
mathematical area of knot theory, the crossing number of a knot is the smallest number of crossings of any diagram of the knot. It is a knot invariant. By way
Crossing_number_(knot_theory)
Andean record-keeping system using knotted cords
Cusco Quechua: khipu, [kʰipu]), are record-keeping devices fashioned from knotted cords. They were historically used by various cultures in the central Andes
Quipu
Knot that can't be tied in a string of constant diameter
In the mathematical theory of knots, a knot is tame if it can be "thickened", that is, if there exists an extension to an embedding of the solid torus
Wild_knot
Mathematical invariant of a knot or link
of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in 1984. Specifically, it is an invariant of an oriented knot or
Jones_polynomial
Type of mathematical knot
In the mathematical area of knot theory, a ribbon knot is a knot that bounds a self-intersecting disk with only ribbon singularities. Intuitively, this
Ribbon_knot
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. The
Knot_polynomial
Simplest nontrivial knot link
In mathematical knot theory, the Hopf link is the simplest nontrivial link with more than one component. It consists of two circles linked together exactly
Hopf_link
Two interlinked loops with five structural crossings
In knot theory, the Whitehead link, named for J. H. C. Whitehead, is one of the most basic links. It can be drawn as an alternating link with five crossings
Whitehead_link
2002 Iranian naval patrol craft ship class
98 MW), the boats move through a piercing propeller and reach a maximum of 62 knots (115 km/h). These are monohull boats made of Kevlar. The class design is
MIL_40-class_speedboat
as knot theory, an invertible knot is a knot that can be continuously deformed to itself, but with its orientation reversed. A non-invertible knot is
Invertible_knot
Prime knot with crossing number 10
theory of knots, the Perko pair, named after Kenneth Perko, is a pair of entries in classical knot tables that actually represent the same knot. In Dale
Perko_pair
Generalization of knots in 3-dimensional Euclidean space
problems in mathematics In knot theory, a virtual knot is a generalization of knots in 3-dimensional Euclidean space, R3, to knots in thickened surfaces Σ
Virtual_knot
Function of a knot that takes the same value for equivalent knots
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. The equivalence
Knot_invariant
Type of mathematical knot
mathematical theory of knots, a satellite knot is a knot that contains an incompressible, non boundary-parallel torus in its complement. Every knot is either hyperbolic
Satellite_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
Alternating_knot
Type of knot
A miller's knot (also sack knot or bag knot) is a binding knot used to secure the opening of a sack or bag. Historically, large sacks often contained
Miller's_knot
Attempt to classify and tabulate all possible knots
tabulate all possible knots. By 1998, all 1.7 million prime knots up to 16 crossings had been tabulated, and by 2020 all 350 million knots up to 19 crossings
Knot_tabulation
Proposed unmanned aerial vehicle
Edwards Air Force Base. It reached an altitude of 4,000 ft and a speed of 62 knots (71 mph; 115 km/h) for 28 minutes. Its landing gear dug into the dry lakebed
Boeing_Phantom_Eye
Group whose operation is a composition of braids
§ Introduction). Example applications of braid groups include knot theory, where any knot may be represented as the closure of certain braids (a result
Braid_group
Type of knot
gillnet). List of binding knots List of knots Clifford W. Ashley, The Ashley Book of Knots (New York: Doubleday, 1944), 62. Ashley, 291. An Introduction
Ground-line_hitch
Encyclopedic website dedicated to knot theory
The Knot Atlas is a website, an encyclopedia rather than atlas, dedicated to knot theory. It and its predecessor were created by mathematician Dror Bar-Natan
The_Knot_Atlas
Doppler weather radar system
250 metres (820 ft) in horizontal. The non-ambiguous radial velocity is 62 knots (71 mph; 115 km/h) up to 230 kilometres (140 mi) from the radar. The range
Terminal Doppler Weather Radar
Terminal_Doppler_Weather_Radar
Property in knot theory
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
Tricolorability
Heavyweight torpedo
has a pump jet propulsion system giving it a maximum speed of over 45+ knots. It can also track several targets and classify them at the same. In 2020
Torped_62
Utility helicopter family by Bell
returned 24 days, 4 hours, 36 minutes and 24 seconds later, averaging 35.62 knots (40.99 mph; 65.97 km/h). Bower had added a 91-US-gallon (340 L) auxiliary
Bell_206
Fundamental group of a knot complement
a knot is an embedding of a circle into 3-dimensional Euclidean space. The knot group of a knot K is defined as the fundamental group of the knot complement
Knot_group
Fibrous material from trees or other plants
surface of a knot for months or even years after manufacture and show as a yellow or brownish stain. A knot primer paint or solution (knotting), correctly
Wood
Peter Guthrie Tait in his study of knots. The Tait conjectures involve concepts in knot theory such as alternating knots, chirality, and writhe. All of the
Tait_conjectures
Knot invariant
a knot invariant which assigns a polynomial with integer coefficients to each knot type. James Waddell Alexander II discovered this, the first knot polynomial
Alexander_polynomial
Link that consists of finitely many unlinked unknots
unlink in Wiktionary, the free dictionary. In the mathematical field of knot theory, an unlink is a link that is equivalent (under ambient isotopy) to
Unlink
Complement of a knot in three-sphere
In mathematics, the knot complement of a tame knot K is the space where the knot is not. If a knot is embedded in the 3-sphere, then the complement is
Knot_complement
Thoroughbred racehorse
Tie The Knot (foaled 1994 - Died October 2012) was an Australian-bred Thoroughbred racehorse who won 13 Group One races. In 1999-2000, he was voted Australian
Tie_the_Knot
Man-made canal
Outright record fell to the Australian sail craft Yellow Pages at * 46.62 knots sailing in the sheltered waters of sandy point, Australia ending the 7-year
The_Canal
Analog of the knot group
In knot theory, an area of mathematics, the link group of a link is an analog of the knot group of a knot. They were described by John Milnor in his Ph
Link_group
Knot invariant named after Cahit Arf
In the mathematical field of knot theory, the Arf invariant of a knot, named after Cahit Arf, is a knot invariant obtained from a quadratic form associated
Arf_invariant_of_a_knot
NCAA Division I men's basketball team representing Le Moyne College
Freshman Dwayne Pean converted a three-point play with 32 seconds left that knotted the score and forced the extra session. The Dolphins dominated play after
Le Moyne Dolphins men's basketball
Le_Moyne_Dolphins_men's_basketball
Collection of knots that do not intersect, but may be linked
mathematical knot theory, a link is a collection of knots that do not intersect, but which may be linked (or knotted) together. A knot can be described
Link_(knot_theory)
Adjustable hitch knot
The taut-line hitch is an adjustable loop knot for use on lines under tension. It is useful when the length of a line will need to be periodically adjusted
Taut-line_hitch
King George V-class battleship of the Royal Navy
000 shp (82,000 kW) at emergency overload. This gave Howe a top speed of 27.62 knots (51.15 km/h; 31.78 mph). The ship carried 4,210 long tons (4,300 t) of
HMS_Howe_(32)
Ritual haircare practice
kanga, another of the five Ks, and tied into a simple knot known as a joora or rishi knot. This knot of hair is usually held in place with the kanga and
Kesh_(Sikhism)
Element of story structure
[denumɑ̃]) derived from Old French desnouer 'to untie' which is from Latin nodus 'knot'. In the terminology of classical drama the final resolution is traditionally
Denouement
Orientable surface whose boundary is a knot or link
boundary is a given knot or link. Such surfaces can be used to study the properties of the associated knot or link. For example, many knot invariants are most
Seifert_surface
Notation used to describe knots based on operations on tangles
In knot theory, Conway notation, invented by John Horton Conway, is a way of describing knots that makes many of their properties clear. It composes a
Conway_notation_(knot_theory)
Mathematical knot
In knot theory, a branch of mathematics, a knot or link K {\displaystyle K} in the 3-dimensional sphere S 3 {\displaystyle S^{3}} is called fibered or
Fibered_knot
Class of mathematical knot with special properties
theory of knots, a Berge knot (named after mathematician John Berge) or doubly primitive knot is any member of a particular family of knots in the 3-sphere
Berge_knot
Ticonderoga-class cruiser
USS Robert Smalls (CG-62) is a Ticonderoga-class guided-missile cruiser built during the Cold War for the United States Navy. Commissioned in 1989, the
USS_Robert_Smalls
United States battleship and now museum ship
USS New Jersey (BB-62) is an Iowa-class battleship and the second ship of the United States Navy to be named after the U.S. state of New Jersey. She was
USS_New_Jersey_(BB-62)
Simple lashing knot
knot, the underlying structure of the transom knot is the strangle knot. The introduction of a second, perpendicular spar into a loose strangle knot tied
Transom_knot
Austro-Hungarian Navy's Habsburg-class pre-dreadnought battleship
at 15,063 indicated horsepower (ihp), which produced a top speed of 19.62 knots (36.34 km/h; 22.58 mph). The ship's hull was constructed from longitudinal
SMS_Habsburg
Mathematical tool for studying knots
tool used to study knots. A central question in the mathematical theory of knots is whether two knot diagrams represent the same knot. One way to answer
Skein_relation
Country in South Asia
Wiley. ISBN 978-0-471-39340-5. Jones, G.; Ramdas, K. (2005). (Un)tying the Knot: Ideal and Reality in Asian Marriage. National University of Singapore Press
India
American heavy metal band
This is all I'll say. JUST YOU WAIT TIL THE TRUTH COMES OUT. Long Live The Knot". On March 18, 2019, the band officially announced via their website that
Slipknot_(band)
Mathematical notation for describing the structure of knots
In the mathematical field of knot theory, the Dowker–Thistlethwaite (DT) notation or code, for a knot diagram is a sequence of even integers. The notation
Dowker–Thistlethwaite notation
Dowker–Thistlethwaite_notation
Type of invariant in Knot theory
mathematical theory of knots, a finite type invariant, or Vassiliev invariant (so named after Victor Anatolyevich Vassiliev), is a knot invariant that can
Finite_type_invariant
Invariant of framed knots
In knot theory, the self-linking number is an invariant of framed knots. It is related to the linking number of curves. A framing of a knot is a choice
Self-linking_number
In the mathematical field of knot theory, the crosscap number of a knot K is the minimum of C ( K ) ≡ 1 − χ ( S ) , {\displaystyle C(K)\equiv 1-\chi (S)
Crosscap_number
Kind of operation in knot theory
field of knot theory, a mutation is an operation on a knot that can produce different knots. Suppose K is a knot given in the form of a knot diagram.
Mutation_(knot_theory)
United States Navy aircraft carrier (1959–1998)
97.1689342°W / 26.1034852; -97.1689342 The fifth USS Independence (CV/CVA-62) was an aircraft carrier of the United States Navy. She was the fourth and
USS_Independence_(CV-62)
Link formed from a finite number of twisted sections
In the mathematical theory of knots, a pretzel link is a special kind of link. It consists of a finite number of tangles made of two intertwined circular
Pretzel_link
King George V-class battleship of the Royal Navy
000 shp (82,000 kW) at emergency overload. This gave Anson a top speed of 27.62 knots (51.15 km/h; 31.78 mph). The ship carried 4,210 long tons (4,300 t) of
HMS_Anson_(79)
Clothing item worn around the neck
T T, Knot 62). A version knotted through only the outermost loop is known as the Victoria knot (Li Ro Li Ro Li Co T, Knot 6). Christensen knot (also
Necktie
Pre-dreadnought class in Austria-Hungary
063 indicated horsepower (11,232 kW), which produced a top speed of 19.62 knots (36.34 km/h; 22.58 mph). Árpád's system was slightly less efficient, at
Habsburg-class_battleship
Every knot or link can be represented as a closed braid
In mathematics Alexander's theorem states that every knot or link can be represented as a closed braid; that is, a braid in which the corresponding ends
Alexander's_theorem
Pharaoh of Egypt from 51 to 30 BC
Roller (2010), pp. 61–62. Hölbl (2001), p. 235. Fletcher (2008), pp. 112–113. Roller (2010), pp. 26, 62. Roller (2010), p. 62. Burstein (2004), pp. 18
Cleopatra
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