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Type of knot
The stevedore knot is a stopper knot, often tied near the end of a rope. It is more bulky and less prone to jamming than the closely related figure-eight
Stevedore_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)
Occupation of loading and unloading ships
type of stopper knot is called the stevedore knot. Securely tying up parcels of goods is called stevedore lashing or stevedore knotting. While loading
Dockworker
Family of mathematical knots
twist knots: One half-twist (trefoil knot, 31) Two half-twists (figure-eight knot, 41) Three half-twists (52 knot) Four half-twists (stevedore knot, 61)
Twist_knot
Type of stopper knot used in sailing and climbing
and equally secure. — The Ashley Book of Knots The stevedore knot is an extension of simple figure-eight knot with an additional turn before the end is
Figure-eight_knot
Knot that forms a fixed thicker point to prevent unreeving
handle. Knots commonly used for this purpose are: Overhand knot Double overhand knot Figure-eight knot Stevedore knot Ashley's stopper knot The Chinese
Stopper_knot
eight (stevedore knot) – bulky stopper knot often tied near the end of a rope that is secure-when-slack Double fisherman's knot (grapevine knot) – joins
List_of_knots
Knot that bounds an embedded disk in 4-space
except for the trivial knot and the Stevedore knot 6 1 {\displaystyle 6_{1}} , not slice. All topologically and smoothly slice knots with crossing number
Slice_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
where q is the number of half-twists. In particular the stevedore knot is not fibered. Fibered knots and links arise naturally, but not exclusively, in complex
Fibered_knot
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 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
Type of knot
figure-of-eight loop but with an extra half-turn before finishing the knot. Also similar to the stevedore loop, the figure-nine loop is generally shown as being based
Figure-of-nine_loop
polygon (pentagram) 52 knot/Three-twist knot - the twist knot with three-half twists 61 knot/Stevedore knot (mathematics) - a prime knot with crossing number
List of mathematical knots and links
List_of_mathematical_knots_and_links
There are many types of knots that are commonly used in the pursuit of rock climbing, ice climbing, and general mountaineering, the most popular of which
List_of_climbing_knots
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 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
Minimum number of times a specific knot must be passed through itself to become untied
knot 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
Class of knot used to add weight to the end of a rope to make it easier to throw
A heaving line knot is a family of knots which are used for adding weight to the end of a rope, to make the rope easier to throw. In nautical use, a heaving
Heaving_line_knot
Type of knot
The fisherman's knot is a knot—specifically a bend—that joins two lines. The double fisherman's knot and triple fisherman's knot are variations used in
Fisherman's_knot
Method of fastening or securing linear material
button knot, double connection knot, double coin knot, agemaki, cross knot, square knot, Plafond knot, Pan Chang knot, and the good luck knot. Knots of more
Knot
Proteins with backbone entangled in a knot
the knots discovered in proteins are deep trefoil (31) knots. Figure eight knots (41), three-twist knots (52), Stevedore knots (61) and Septoil knot (71)
Knotted_protein
Type of knot
The slip knot is a stopper knot which is easily undone by pulling the tail (working end). The slip knot is related to the running knot, which will release
Slip_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
commonly used terms related to knots. Contents: A B C D E F G H I J K L M N O P Q R S T U V W X Y Z A bend is a knot used to join two lengths of rope
List_of_knot_terminology
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
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
Type of knot
The hangman's knot or hangman's noose (also known as a collar during the Elizabethan era) is a knot most often associated with its use in hanging a person
Hangman's_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
later shown to be identical. Stevedore knot (mathematics), a prime knot with crossing number 6 Three-twist knot is the twist knot with three-half twists, also
List_of_knot_theory_topics
Knot defined by parametric equations defining Lissajous curves
y ) = ( 0.7 , 0.2 ) {\displaystyle (\phi _{x},\phi _{y})=(0.7,0.2)} Stevedore knot ( n x , n y , n z ) = ( 3 , 2 , 5 ) {\displaystyle (n_{x},n_{y},n_{z})=(3
Lissajous_knot
Decorative handicraft art
Chinese knotting, also known as zhongguo jie (Chinese: 中國結; pinyin: Zhōngguó jié), is a Chinese folk art with ties to Buddhism and Taoism. A Chinese knot is
Chinese_knotting
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
Simple knot used to form a fixed loop at the end of a rope
The bowline (/ˈboʊlɪn/) is an ancient and simple knot used to form a fixed loop at the end of a rope. It has the virtues of being both easy to tie and
Bowline
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
Link formed from a finite number of twisted sections
pretzel knot is the (right-handed) trefoil; the (−1, −1, −1) pretzel knot is its mirror image. The (5, −1, −1) pretzel knot is the stevedore knot (61).
Pretzel_link
Type of knot
The cow hitch, also called the lark's head, is a hitch knot used to attach a rope to an object. The cow hitch comprises a pair of single hitches tied in
Cow_hitch
Type of knot
The clove hitch is an ancient type of knot, made of two successive single hitches tied around an object. It is most effectively used to secure a middle
Clove_hitch
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
Type of knot
The trucker's hitch is a compound knot commonly used for securing loads on trucks or trailers. The general arrangement, using loops and turns in the rope
Trucker's_hitch
Type of knot used to join two lengths of rope
of all other knots combined. — Clifford Ashley, Ashley Book of Knots List of knot terminology Binding knot Rope splicing Whipping knot Ashley, Clifford
Bend_(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)
Necktie knot
Windsor knot, sometimes referred to as a full Windsor (or misleadingly as a double Windsor) to distinguish it from the half-Windsor, is a knot used to
Windsor_knot
Type of knot
A Prusik (/ˈprʌsɪk/ PRUSS-ik) is a friction hitch or knot used to attach a loop of cord around a rope, applied in climbing, canyoneering, mountaineering
Prusik
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
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
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)
1944 encyclopedia of knots by Clifford W. Ashley
The Ashley Book of Knots (ABoK) is an encyclopedia of knots written and illustrated by the American sailor and artist Clifford W. Ashley. First published
The_Ashley_Book_of_Knots
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)
Type of knot
The surgeon's knot is a surgical knot and is a simple modification to the reef knot. It adds an extra twist when tying the first throw, forming a double
Surgeon's_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
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
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
Rope loop and knot
at the end of a rope in which the knot tightens under load and can be loosened without untying the knot. The knot can be used to secure a rope to a post
Noose
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
Type of knot
true lover's knot, also called true love knot or simply love-knot amongst others, is used for many distinct knots. The association of knots with the symbolism
True_lover's_knot
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
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
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
Knot that makes a pair of fixed-size loops in the middle of a rope
The bowline on a bight is a knot which makes a pair of fixed-size loops in the middle of a rope. Its advantage is that it is reasonably easy to untie after
Bowline_on_a_bight
Knot used in fishing
The Palomar knot (/ˈpæləmɑːr/ PAL-ə-mar) is a knot that is used for securing a fishing line to a fishing lure, hook, or swivel. It is strong and easy to
Palomar_knot
Knot used to form a fixed loop in the middle of a rope
loop, also known as lineman's loop, butterfly knot, alpine butterfly knot and lineman's rider, is a knot used to form a fixed loop in the middle of a rope
Butterfly_loop
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
Type of knot
an inferior knot to the alpine butterfly knot, possibly dangerously so, in that it can be yanked out of shape and turn into a running knot or noose. Budworth
Artillery_loop
Common binding knot
The reef knot, or square knot, is an ancient and simple binding knot used to secure a rope or line around an object. It is sometimes also referred to
Reef_knot
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
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)
Adjustable knot used to control friction in a belay system
also known as the Italian hitch, mezzo barcaiolo is a simple adjustable knot, commonly used by climbers, cavers, and rescuers to control friction in a
Munter_hitch
Type of bend knot
A blood knot (barrel knot) is a bend knot most usefully employed for joining sections of monofilament nylon line while maintaining a high portion of the
Blood_knot
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
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
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
Type of knot
first knot given in the Ashley Book of Knots. Additionally, it is one of the six knots given in the International Guild of Knot Tyers' Six Knot Challenge
Sheet_bend
Type of knot
The granny knot is a binding knot, used to secure a rope or line around an object. It is considered inferior to the reef knot (square knot), which it
Granny_knot
Type of knot
The diamond knot (or knife lanyard knot) is a knot for forming a decorative loop on the end of a cord such as on a lanyard. A similar knot, also called
Diamond_knot
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
Knot
The Lapp knot is a type of bend. It has the same structure as the sheet bend, but the opposite ends are loaded. The slipped Lapp bend (among arbourists
Lapp_knot
Type of knot used to join a rope to an object
A hitch is a type of knot used to secure a rope to an object or another rope. Hitches are used in a variety of situations, including climbing, sailing
Hitch_(knot)
Type of knot
farmer's loop is a knot which forms a fixed loop. As a midline loop knot made with a bight, it is related to several other similar knots, including the alpine
Farmer's_loop
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
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
Overhand_knot
Type of loop knot
A double bowline (or round turn bowline) is a type of loop knot. Instead of the single turn of the regular bowline, the double bowline uses a round turn
Double_bowline
Organization
The International Guild of Knot Tyers (or IGKT) is a worldwide association for people with an interest in knots and knot tying. Officially established
International Guild of Knot Tyers
International_Guild_of_Knot_Tyers
Type of elaborate design on dress uniforms
An Austrian knot (or Hungarian knot), alternatively warrior's knot or vitézkötés, is an elaborate design of twisted cord or lace worn as part of a dress
Austrian_knot
Type of knot
Chinese button knot is essentially a knife lanyard knot where the lanyard loop is shortened to a minimum, i.e. tightened to the knot itself. There emerges
Chinese_button_knot
Combined features of granny and thief
A grief knot (also what knot) is a knot which combines the features of a granny knot and a thief knot, producing a result which is not generally useful
Grief_knot
Knotted handicraft
(Craftlace, scoobies, lanyard, gimp, or boondoggle) is material used in knotting craft. It originated in France, where it became a fad in the late 1950s
Scoubidou
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
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
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
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
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
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
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)
Type of knot
perfection loop, is a type of knot which forms a fixed loop. Useful for fine or slippery line, it is one of the few loop knots which holds well in bungee
Angler's_loop
Type of knot
knot used for rappelling or rope rescue. Unlike most knots, the tensionless hitch retains a 100% efficiency rating, meaning the strength of the knot is
Tensionless_hitch
Type of knot
A shank is a type of knot that is used to shorten a rope or take up slack, such as the sheepshank. The sheepshank knot is not stable. It will fall apart
Sheepshank
Hand weaving technique
The Ghiordes/Turkish knot and the Senneh/Persian knot, typical of Anatolian carpets and Persian carpets, are the two primary knots. A flat or tapestry
Knotted-pile_carpet
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