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Simplest non-trivial closed knot with three crossings
knot (mathematics) Gordian Knot Pretzel link Trefoil knot metathesis Triquetra symbol Shaw, George Russell (MCMXXXIII). Knots: Useful & Ornamental, p.11
Trefoil_knot
Topics referred to by the same term
A Pretzel knot may refer to: Pretzel link: a concept in mathematics Soft pretzel with garlic Stafford knot: a rope knot used in sailing and heraldry This
Pretzel_knot
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
Type of mathematical knot
7) pretzel knot, sometimes called the Fintushel–Stern knot (after Ron Fintushel and Ronald J. Stern), is an important example of a pretzel knot which
(−2,3,7)_pretzel_knot
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
Baked pastry shaped into a knot
baked pastry made from dough that is commonly shaped into a knot. The traditional pretzel shape is a distinctive symmetrical form, with the ends of a
Pretzel
Liseberg. A pretzel knot is an element similar to the batwing, except the entrance and exit of the inversion is formed differently. In a pretzel knot, the twisted
List of roller coaster elements
List_of_roller_coaster_elements
Unique knot with a crossing number of four
hyperbolic 3-manifolds. The figure-eight knot and the (−2,3,7) pretzel knot are the only two hyperbolic knots known to have more than 6 exceptional surgeries
Figure-eight knot (mathematics)
Figure-eight_knot_(mathematics)
non-invertible knots exist until Hale Trotter discovered an infinite family of pretzel knots that were non-invertible in 1963. It is now known almost all knots are
Invertible_knot
Mathematical knot with crossing number 6
half twists, or as the (5,−1,−1) pretzel knot. The mathematical stevedore knot is named after the common stevedore knot, which is often used as a stopper
Stevedore_knot_(mathematics)
Type of mathematical knot
two. Greene & Jabuka (2011) showed it to be true for three-stranded pretzel knots with odd parameters. However, Gompf, Scharlemann & Thompson (2010) suggested
Ribbon_knot
single knot listed twice in Dale Rolfsen's knot table; the duplication was discovered by Kenneth Perko 12n242/(−2,3,7) pretzel knot (p, q)-torus knot - a
List of mathematical knots and links
List_of_mathematical_knots_and_links
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)
Inverted roller coaster at Kings Island
roller coaster. Banshee would feature seven inversions, including a pretzel knot inversion and a vertical loop around the lift hill. Banshee would be
Banshee_(roller_coaster)
schemes. Conway knot 11n34 Kinoshita–Terasaka knot 11n42 List of knots List of mathematical knots and links Knot tabulation (−2,3,7) pretzel knot Originally
List_of_prime_knots
Defunct shuttle roller coaster
Looping Coaster). The pretzel knot element (comprising two inversions) that produced these high g-forces was the only such pretzel knot inversion ever implemented
Moonsault_Scramble
American soft pretzel manufacturer
Pretzel Baking Company of South Philadelphia was the first large-scale mass production soft pretzel manufacturer in Philadelphia. The Federal Pretzel
Federal Pretzel Baking Company
Federal_Pretzel_Baking_Company
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)
Mathematical knot
singularity. A knot is fibered if and only if it is the binding of some open book decomposition of S 3 {\displaystyle S^{3}} . (−2,3,7) pretzel knot Fintushel
Fibered_knot
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
Cultural region of the United States
The Pretzel Belt, Pennsylvania Snack Belt or Pretzelvania, is a concentration of pretzel and snack food makers in the central southeastern region of Pennsylvania
Pretzel_Belt
Steel roller coaster at Liseberg
track design. The elements during the ride include two corkscrews, a pretzel knot, a top hat, a zero-g roll, and a rare Norwegian loop. The estimated cost
Helix_(roller_coaster)
Type of knot
The Carrick bend, also known as the Sailor's breastplate, is a knot used for joining two lines. It is particularly appropriate for very heavy rope or cable
Carrick_bend
Men's skirt from the Indian subcontinent
for wearers to simply tie a double "pretzel knot" from 2 points on the upper border, which produces a more secure knot. The lungi's length can also be adjusted
Lungi
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
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
Approach to knot theory by John Conway
knot diagrams. Tangles often show up as tangle diagrams in knot or link diagrams and can be used as building blocks for link diagrams, e.g. pretzel links
Tangle_(mathematics)
Way to join two given mathematical manifolds together
(nonoriented) knots. To see this, consider two noninvertible knots K, L which are not equivalent (as unoriented knots); for example take the two pretzel knots K =
Connected_sum
collar Pretzel link knot – in knot theory, a branch of mathematics, a pretzel link is a special kind of link Prusik knot – friction hitch or knot used to
List_of_knots
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
concept of a knot. Two classes of knots: torus knots and pretzel knots Cinquefoil knot also known as a (5, 2) torus knot. Figure-eight knot (mathematics)
List_of_knot_theory_topics
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
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
Three-looped overhand knot that is the traditional symbol of Staffordshire
including the Stafford knot, all enclosed in a circle of Stafford knots. The design closely matches the early design of the pretzel, which was made to represent
Stafford_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
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
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
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
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
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)
Type of pretzel
[citation needed] In Denmark, kringle denotes the pretzel-like knotted shape rather than the pretzel pastry type. Kringler (the plural of kringle) may
Kringle
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)
this set was done by Gromov. The figure-eight knot and the (-2, 3, 7) pretzel knot are the only two knots whose complements are known to have more than
Hyperbolic_Dehn_surgery
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
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
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
Minimum number of times a specific knot must be passed through itself to become untied
In the mathematical area of knot theory, the unknotting number of a knot is the minimum number of times the knot must be passed through itself (crossing
Unknotting_number
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
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 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
695th Lord Mayor of London (born 1958)
mantled party Vert and Purpure lined Argent Escutcheon Argent within a Pretzel Knot of five loops Sable interlaced with another Gules the outer part of each
Michael_Mainelli
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
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
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 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
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
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
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
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
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
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
topology topics. Knot (mathematics) Link (knot theory) Wild knots Examples of knots (and links) Unknot Trefoil knot Figure-eight knot (mathematics) Borromean
List of geometric topology topics
List_of_geometric_topology_topics
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
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)
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
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
Invariant of mathematical knots
abutting to their instanton knot Floer homology group and used this to show that Khovanov Homology (like the instanton knot Floer homology) detects the
Khovanov_homology
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
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
Polynomial invariant of framed links
In the mathematical field of knot theory, the bracket polynomial (also known as the Kauffman bracket) is a polynomial invariant of framed links. Although
Bracket_polynomial
Determining whether a knot is the unknot
algorithmically recognizing the unknot, given some representation of a knot, e.g., a knot diagram. There are several types of unknotting algorithms. A major
Unknotting_problem
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
Interlinked multi-loop construction where cutting one loop frees all the others
In knot theory, a branch of topology, a Brunnian link is a nontrivial link that becomes a set of trivial unlinked circles if any one component is removed
Brunnian_link
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)
Two-variable polynomial knot invariant
In knot theory, the Kauffman polynomial is a 2-variable knot polynomial due to Louis Kauffman. It is initially defined on a link diagram as F ( K ) (
Kauffman_polynomial
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
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
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
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
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
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
One of three types of isotopy-preserving local changes to a knot diagram
In the mathematical area of knot theory, a Reidemeister move is any of three local moves on a link diagram. Kurt Reidemeister (1927) and, independently
Reidemeister_move
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
Invariant of a knot diagram
In knot theory, there are several competing notions of the quantity writhe, or Wr {\displaystyle \operatorname {Wr} } . In one sense, it is purely a property
Writhe
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
Flag of English county
including the Stafford knot, all enclosed in a circle of Stafford knots. The design closely matches the early design of the pretzel, which was made to represent
Flag_of_Staffordshire
Bar and restaurant in Portland, Oregon, U.S.
"meatball" sub, an "Eastern" bowl, grilled cheese, spaghetti, chili pie, pretzel knots, and chips and salsa. Bye and Bye serves beer, cider, cocktails, and
Bye_and_Bye_(bar)
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
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 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
Number of "holes" of a surface
graph: genus 0 Toroidal graph: genus 1 Double Toroidal graph: genus 2 Pretzel graph: genus 3 The non-orientable genus, demigenus, or Euler genus of a
Genus_(mathematics)
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
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
Game of physical skill
embraced the idea for the Pretzel game but when Mel Taft found that Transogram had the trademark to a toy dog named Pretzel, the team at Milton Bradley
Twister_(game)
Dark ride at Kings Island
Opening Nightmare. Sir Pretzel – A newly-introduced contortionist billed as "the Human Knot". The character references the Pretzel Amusement Ride Company
Phantom Theater: Opening Nightmare
Phantom_Theater:_Opening_Nightmare
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
Techniques for consensually restraining people for sexual pleasure
column tie which could be used to bind two limbs. They all start with a basic knot, and finish with securing the loose ends. There is basic advice on precautions
Bondage_positions_and_methods
Link of three loops with ten crossings
In the mathematical theory of knots, L10a140 is the name in the Thistlethwaite link table of a link of three loops, which has ten crossings between the
L10a140_link
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
PRETZEL KNOT
PRETZEL KNOT
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PRETZEL KNOT
PRETZEL KNOT
PRETZEL KNOT
PRETZEL KNOT
PRETZEL KNOT
PRETZEL KNOT