Editing Knot

{{Short description|Method of fastening or securing linear material}}
{{About||speeds|Knot (unit)|the mathematical object|Knot (mathematics)|other uses|Knot (disambiguation)}}
[[File:Nf knots.png|thumb|upright=2|{{lang|sv|[[Nordisk familjebok]]}} knots:
{{Ordered list|
|Yarn knot ([[The Ashley Book of Knots|ABoK]] #2688)
|[[Manrope knot]] ([[The Ashley Book of Knots|ABoK]] #847)
|[[Granny knot]] ([[The Ashley Book of Knots|ABoK]] #1206)
|[[Wall and crown knot]] ([[The Ashley Book of Knots|ABoK]] #670, #671)<!--formerly Rosebud stopper knot followed by (?)-->
|[[Matthew Walker knot|Matthew Walker's knot]] ([[The Ashley Book of Knots|ABoK]] #681)
|[[Shroud knot]] ([[The Ashley Book of Knots|ABoK]] #1580)
|[[Turk's head knot]] ([[The Ashley Book of Knots|ABoK]] #1278-#1397)
|[[Overhand knot]], [[Figure-eight knot|Figure-of-eight knot]] ([[The Ashley Book of Knots|ABoK]] #514, #520)
|[[Reef knot]], [[Reef knot|Square knot]] ([[The Ashley Book of Knots|ABoK]] #1402)
|[[Two half-hitches]] ([[The Ashley Book of Knots|ABoK]] #54)
}}]]
[[File:Knopar - 2017.jpg|thumb|{{ill|Knot board|es|Cuadro de nudos}} on [[:de:Elbe 1 (Schiff, 1965)|Elbe 1 (ship, 1965)]]]]

A '''knot''' is an intentional complication in [[Rope|cordage]]<ref>{{citation |last=Ashley |first=Clifford W. |title=The Ashley Book of Knots |year= 1944 |publisher=Doubleday |location=New York |page=12 |quote="The word knot has three distinct meanings in common use. In the broadest sense it applies to all complications in cordage, except accidental ones, such as snarls and kinks, and complications adapted for storage, such as coils, hanks, skeins, balls, etc." }}</ref> which may be practical or decorative, or both. Practical knots are classified by function, including [[List of hitch knots|hitch]]es, [[List of bend knots|bend]]s, [[List of loop knots|loop knot]]s, and [[Rope splicing|splice]]s: a ''hitch'' fastens a rope to another object; a ''bend'' fastens two ends of a rope to each another; a ''loop knot'' is any knot creating a loop; and ''splice'' denotes any multi-strand knot, including bends and loops.<ref>{{citation|last=Ashley|first=Clifford W.|title=The Ashley Book of Knots|page=12|year=1944|location=New York|publisher=Doubleday}}</ref> A knot may also refer, in the strictest sense, to a stopper or knob at the end of a rope to keep that end from slipping through a grommet or eye.<ref>{{citation |last=Ashley |first=Clifford W. |title=The Ashley Book of Knots |year= 1944 |publisher=Doubleday |location=New York |page=12 |quote="In its second sense it does not include bends, hitches, splices, and sinnets, and in its third and narrowest sense the term applies only to a knob tied in a rope to prevent unreeving, to provide a handhold, or (in small material only) to prevent fraying." }}</ref> Knots have excited interest since ancient times for their practical uses, as well as their [[Topology|topological]] intricacy, studied in the area of mathematics known as [[knot theory]].

[[Image:Inca Quipu.jpg|thumb|right|An example of a [[quipu]] from the Inca Empire, currently in the [[Larco Museum|Larco Museum Collection]].]]
<!--[[File:Jean-François Godefroy Alexandre et le noeud gordien.JPG|110px|thumb|[[Alexander the Great]] cuts the [[Gordian Knot]] (1767)]]-->
[[File:Alexander cuts the Gordian Knot.jpg|thumb|''[[Alexander the Great|Alexander]] cuts the [[Gordian Knot]]'', by [[Jean-Simon Berthélemy]] (1743–1812)]]
[[File:Gordischer Knoten Frechen Kirilowitsch.jpg|thumb|110px|Gordian Knot statue (1990)]]
[[File:Magimagi - Mainbeam.jpg|thumb|right|[[Magimagi]] [[sennit]] of [[Fiji]] around wooden ceiling posts.]]
[[File:Teton tipi tie.jpg|thumb|110px|[[Blackfoot people|Blackfoot]] "Teton" tipi tie<ref>Anthropological Papers of the American Museum of Natural History. Material culture of the Blackfoot Indians. 1910.</ref>]]

==History==
{{more citations needed|section|date=December 2020}}

Knots and '''knotting''' have been used and studied throughout history. For example, [[Chinese knotting]] is a decorative handicraft art that began as a form of Chinese folk art in the Tang and Song Dynasty (960–1279 AD) in China, later popularized in the Ming. [[Knot theory]] is the recent mathematical study of knots.

Knots of ancient origin include the [[bottle sling]], [[bowline]], [[cat's paw (knot)|cat's paw]], [[clove hitch]], [[cow hitch]], [[double fisherman's knot]], [[eskimo bowline]], [[figure-eight knot]], [[fisherman's knot]], [[half hitch]], [[kalmyk loop]], [[one-sided overhand bend]], [[overhand knot]], [[overhand loop]], [[reef knot]], [[running bowline]], [[single hitch]], [[thief knot]], [[Turk's head knot]], and [[two half-hitches]].

The eleven main knots of Chinese knotting are the four-flower knot, six-flower knot, [[Chinese button knot]], [[Matthew Walker knot|double connection knot]], [[carrick bend|double coin knot]], agemaki, [[friendship knot|cross knot]], square knot, [[Plafond knot]], [[Pan Chang knot]], and the [[good luck knot]].

Knots of more recent origin include the [[friendship knot]] of Chinese knotting.{{cn|date=August 2023}} The [[sheepshank|sheepshank knot]] originates from 1627{{cn|date=August 2023}} while the [[Western Union splice]] originates from the beginning of [[telegraphy]].<ref>{{cite book |last=Sharp |first=John MacLaren |year=1915 |title=Practical Electric Wiring |publisher=D. Appleton and Company |location=New York and London |url=https://babel.hathitrust.org/cgi/pt?id=wu.89089723613&view=1up&seq=27 |pages=12–14}}</ref>

==Use==
{{More citations needed section|date=July 2011}}

There is a large variety of knots, each with properties that make it suitable for a range of tasks. Some knots are used to attach the rope (or other knotting material) to other objects such as another rope, [[cleat (nautical)|cleat]], ring, or stake. Some knots are used to bind or constrict objects. Decorative knots usually bind to themselves to produce attractive patterns.

===Teaching===
[[File:School for Sailors NGM-v31-p351.jpg|thumb|right|Sailors learning knots and [[ropework]] in the early 20th century]]
[[File:Sjömanssäck - 1991.jpg|thumb|Sailor bag with different knots]]
While some people can look at diagrams or photos and tie the illustrated knots, others learn best by watching how a knot is tied. Knot tying skills are often transmitted by [[sailors]], [[Scouting|scouts]], [[climbing|climbers]], [[canyoning|canyoners]], [[caving|cavers]], [[arborist]]s, [[Firefighter#Rescue|rescue professionals]], [[stagehand]]s, [[fishermen]], [[lineman (technician)|linemen]] and [[surgeons]]. [[International Guild of Knot Tyers|The International Guild of Knot Tyers]] is an organization dedicated to the promotion of knot tying.

===Applications===

Truckers in need of securing a load may use a [[trucker's hitch]], gaining [[mechanical advantage]]. Knots can save [[spelunking|spelunkers]] from being buried under rock. Many knots can also be used as makeshift tools, for example, the [[bowline]] can be used as a rescue loop, and the [[munter hitch]] can be used for [[belaying]]. The [[diamond hitch]] was widely used to tie packages on to [[donkey]]s and [[mule]]s.

In hazardous environments such as mountains, knots are very important. In the event of someone falling into a ravine or a similar terrain feature, with the correct equipment and knowledge of knots a rappel system can be set up to lower a rescuer down to a casualty and set up a hauling system to allow a third individual to pull both the rescuer and the casualty out of the ravine. Further application of knots includes developing a high line, which is similar to a zip line, and which can be used to move supplies, injured people, or the untrained across rivers, crevices, or ravines. Note the systems mentioned typically require carabiners and the use of multiple appropriate knots. These knots include the bowline, double figure eight, munter hitch, munter mule, prusik, autoblock, and clove hitch. Thus any individual who goes into a mountainous environment should have basic knowledge of knots and knot systems to increase safety and the ability to undertake activities such as rappelling.

Knots can be applied in combination to produce complex objects such as [[lanyard]]s and [[net (textile)|netting]]. In [[ropework]], the frayed end of a rope is held together by a type of knot called a [[whipping knot]]. Many types of [[textile]]s use knots to repair damage. [[Macramé]], one kind of textile, is generated exclusively through the use of knotting, instead of [[knitting|knits]], crochets, weaves or felting.  Macramé can produce self-supporting three-dimensional textile structures, as well as flat work, and is often used ornamentally or decoratively.

==Properties==

===Strength===
<!--[[Knot strength]] and [[Knot efficiency]] redirect directly here.-->
Knots weaken the rope in which they are made.<ref name="Richards2005">{{Cite journal|title=Knot Break Strength vs Rope Break Strength|last=Richards|first=Dave|journal=Nylon Highway|number=50|publisher=Vertical Section of the [[National Speleological Society]]|year=2005|url=http://www.caves.org/section/vertical/nh/50/knotrope.html|access-date=2010-10-11}}</ref> When knotted rope is strained to its breaking point, it almost always fails at the knot or close to it, unless it is defective or damaged elsewhere. The bending, crushing, and chafing forces that hold a knot in place also unevenly stress rope fibers and ultimately lead to a reduction in strength. The exact mechanisms that cause the weakening and failure are complex and are the subject of continued study. Special fibers that show differences in color in response to strain are being developed and used to study stress as it relates to types of knots.<ref name="Greenfieldboyce">{{cite news |last1=Greenfieldboyce |first1=Nell |title=A Knotty Problem Solved |url=https://www.npr.org/2020/01/02/793050811/a-knotty-problem-solved |access-date=3 January 2020 |work=All Things Considered |date=January 2, 2020}}</ref><ref name="Patil">{{Cite journal |last1=Patil |first1=Vishal P. |last2=Sandt |first2=Joseph D. |last3=Kolle |first3=Mathias |last4=Dunkel |first4=Jörn |date=3 January 2020 |title=Topological Mechanics of Knots and Tangles |journal=[[Science (journal)|Science]] |volume=367 |issue=6473 |pages=71–75 |doi=10.1126/science.aaz0135 |pmid=31896713 |bibcode=2020Sci...367...71P |s2cid=209677605 |doi-access=free }}</ref>

Relative '''knot strength''', also called '''knot efficiency''', is the breaking strength of a knotted rope in proportion to the breaking strength of the rope without the knot. Determining a precise value for a particular knot is difficult because many factors can affect a knot efficiency test: the type of [[fiber]], the [[Rope#Styles of rope construction|style of rope]], the size of rope, whether it is wet or dry, how the knot is dressed before loading, how rapidly it is loaded, whether the knot is repeatedly loaded, and so on. The efficiency of common knots ranges between 40 and 80% of the rope's original strength.<ref name="hsok-ch10">{{Citation| last=Warner| first=Charles| year=1996| contribution=Studies on the Behaviour of Knots| editor-last=Turner| editor-first=J.C.| editor2-last=van de Griend| editor2-first=P.| title=History and Science of Knots| series=K&E Series on Knots and Everything| location=Singapore| publisher=World Scientific Publishing| volume=11| pages=181–203| isbn=978-981-02-2469-1}}</ref><ref>{{Cite journal |first1=J.|last1=Šimon |first2=V. |last2=Dekýš |first3=P. |last3=Palček |title=Revision of Commonly Used Loop Knots Efficiencies |journal=Acta Physica Polonica A |volume=138 |issue=3 |pages=404–420 |doi=10.12693/APhysPolA.138.404|year=2020 |bibcode=2020AcPPA.138..404S |doi-access=free }}</ref>

In most situations forming loops and bends with conventional knots is far more practical than using [[Rope splicing|rope splices]], even though the latter can maintain nearly the rope's full strength. Prudent users allow for a large [[factor of safety|safety margin]] in the strength of rope chosen for a task due to the weakening effects of knots, aging, damage, shock loading, etc.  The [[safe working load|working load limit]] of a rope is generally specified with a significant safety factor, up to 15:1 for critical applications.<ref name="grog-reliability">{{Cite web|url=http://www.animatedknots.com/reliability.php? |title=Knot & Rope Safety |publisher=Animated Knots by Grog |year=2010 |access-date=2010-09-14 |url-status=dead |archive-url=https://web.archive.org/web/20150407023208/http://www.animatedknots.com/reliability.php |archive-date=April 7, 2015 }}. "[http://www.animatedknots.com/safety.php?Categ=ropecare&LogoImage=LogoGrog.png&Website=www.animatedknots.com#ScrollPoint Knot & Rope Safety]", ''AnimatedKnots.com''. Accessed April 2016.</ref> For life-threatening applications, other factors come into play.{{Citation needed|date=October 2012}}

===Security===
Even if the rope does not break, a knot may still fail to hold. Knots that hold firm under a variety of adverse conditions are said to be more secure than those that do not.

The following sections describe the main ways that knots fail to hold.

====Slipping====
The load creates tension that pulls the rope back through the knot in the direction of the load. If this continues far enough, the working end passes into the knot and the knot unravels and fails. This behavior can worsen when the knot is repeatedly strained and let slack, dragged over rough terrain, or repeatedly struck against hard objects such as [[mast (sailing)|masts]] and [[flagpole]]s.

Even with secure knots, slippage may occur when the knot is first put under real tension. This can be mitigated by leaving plenty of rope at the working end outside of the knot, and by dressing the knot cleanly and tightening it as much as possible before loading. Sometimes, the use of a [[stopper knot]] or, even better, a [[backup knot]] can prevent the working end from passing through the knot; but if a knot is observed to slip, it is generally preferable to use a more secure knot. Life-critical applications often require backup knots to maximize safety.

====Capsizing====
[[File:Bowline (PSF).jpg|right|thumb|[[Bowline]]]]
To capsize (or spill) a knot is to change its form and rearrange its parts, usually by pulling on specific ends in certain ways.<ref name="hsok-ch10"/> When used inappropriately, some knots tend to capsize easily or even spontaneously. Often the capsized form of the knot offers little resistance to slipping or unraveling. A [[reef knot]], when misused as a bend, can capsize dangerously.

Sometimes a knot is intentionally capsized as a method of tying another knot, as with the [[Bowline#Tying|"lightning method"]] of tying a [[bowline]]. Some knots, such as the [[carrick bend]], are generally tied in one form then capsized to obtain a stronger or more stable form.

====Sliding====
In knots that are meant to grip other objects, failure can be defined as the knot moving relative to the gripped object.  While the knot itself is not untied, it ceases to perform the desired function. For instance, a simple [[rolling hitch]] tied around a railing and pulled parallel to the railing might hold up to a certain tension, then start sliding. Sometimes this problem can be corrected by working-up the knot tighter before subjecting it to load, but usually the problem requires either a knot with more wraps or a rope of different diameter or material.

===Releasability===
Knots differ in the effort required to untie them after loading.  Knots that are very difficult to untie, such as the [[water knot]], are said to "jam" or be '''jamming knots'''.  Knots that come untied with less difficulty, such as the [[Zeppelin bend]], are referred to as "'''non-jamming'''".

==Components==
[[File:Eyes and turns.jpg|right|thumb|A: open loop, B: closed loop, C: turn, D: round turn, E: two round turns.]]
[[File:Cross knots ABOK 34.jpg|right|thumb|#34 Cross #35 Elbow #36 Round turn]]
[[File:Ansted Sea Terms 1898 - Names of the parts of a rope.jpg|right|thumb|#27 End #29 Bight #28 Standing]]

:{{Further|List of knot terminology}}

=== Bight ===
:A [[bight (knot)|bight]] is any curved section, slack part, or loop between the ends of a rope, string, or yarn.

=== Bitter end ===
:As a ropeworker's term, "bitter end" refers to the end of a rope that is tied off. In British nautical usage, the bitter end is the ship end of the anchor cable, secured by the anchor bitts and the bitter pin in the cable locker under the [[forecastle]]. At anchor, the more anchor line that is payed out, the better the anchor's hold. In a storm, if the anchor drags, ships will pay out more and more anchor line until they reach the "bitter end." At this point, they can only hope the anchor holds, hence the expression "hanging on to the bitter end". (A ''[[bitts|bitt]]'' is a metal block with a crosspin for tying lines to, also found on piers.)  Also, the working end.

=== Loop ===
:A curve narrower than a bight but with separate ends.

=== Elbow ===
:Two crossing points created by an extra twist in a loop or a circle.

=== Standing end ===
:The standing end is the longer end of the rope not involved in the knot, often shown as unfinished.  It is often (but not always) the end of the rope under load after the knot is complete. For example, when a clove hitch ties a boat to a pier, the end going to the boat is the ''standing end''.

=== Standing part ===
:Section of line between knot and the standing end (seen above).

=== Turn ===
:A '''[[Turn (knot)|turn]]''' or '''single turn''' is a curve with crossed legs.
:A '''round turn''' is the complete encirclement of an object; requires two passes.
:'''Two round turns''' circles the object twice; requires three passes.

=== Working end ===
:The active end of a line used in making the knot. May also be called the "running end", "live end", or "tag end".

=== Working part ===
:Section of line between knot and the working end.

==Knot categories==
{{Further|List of knots}}
{{More citations needed section|date=July 2011}}
The [[list of knots]] is extensive, but common properties allow for a useful system of categorization. For example, ''[[loop (knot)|loop]]'' knots share the attribute of having some kind of an anchor point constructed on the [[standing end]] (such as a loop or overhand knot) into which the working end is easily hitched, using a [[round turn]]. An example of this is the [[bowline]]. ''Constricting'' knots often rely on friction to cinch down tight on loose bundles; an example is the [[Miller's knot]]. Knots may belong to more than one category.

;[[Bend knot|Bend]] :A knot uniting two lines<ref name=EB1911>{{cite EB1911 |wstitle=Knot |volume=15 |page=871}}</ref> (for knots joining two ends of the same line, see [[binding (knot)|binding knots]] or [[loop (knot)|loops]]).
;[[binding (knot)|Binding]] :A knot that restricts object(s) by making multiple winds.
;[[Coiling|Coil knot]] :Knots used to tie up lines for storage.
;[[Decorative knot]] :A complex knot exhibiting repeating patterns often constructed around and enhancing an object.
;[[Hitch knot|Hitch]] :A knot tied to a post, cable, ring, or spar.
;[[Lashing knot|Lashing]] :A knot used to hold (usually) poles together.
;[[loop (knot)|Loop]] :A knot used to create a closed circle in a line.
;[[Braid|Plait]] (or braid):A number of lines interwoven in a simple regular pattern.
;[[slip knot|Slip]] (or running) :A knot tied with a hitch around one of its parts. In contrast, a loop is closed with a bend. While a slip knot can be closed, a loop remains the same size.
;[[Bight (knot)#Slipped knot|Slipped]] :Some knots may be finished by passing a [[Bight (knot)|bight]] rather than the end, for ease of untying. The common shoelace knot is an example, being a [[reef knot]] with both ends slipped.
;[[Seizing]] :A knot used to hold two lines or two parts of the same line together.<ref name=EB1911/>
;[[Sennit]] :A number of lines interwoven in a complex pattern. See also [[Chain sinnet]].
;[[Rope splicing|Splice]] :A knot formed by interweaving strands of rope rather than whole lines. More time-consuming but usually stronger than simple knots.
;[[Stopper knot|Stopper]] :A knot tied to hold a line through a hole.
;[[whipping knot|Whipping]] :A binding knot used to prevent another line from fraying.

===Basic useful knots===
* [[Alpine butterfly knot]] for a secure loop in the middle of a rope when the ends are not free
* [[Bowline]] for tying a loop in the end of a rope, as around one's waist or to secure a ring or grommet. The knot is also used as an anchor knot and is used in many knot systems that are used in mountainous terrain such as a highline or hauling system.
* [[Constrictor knot]] for making bundles or cinching the neck of a sack, though this knot jams and may need to be cut
* [[Figure-eight knot]] as a stopper
* [[Grass bend]] for tying belts together, though insecure with ropes
* [[Monkey's fist]] used to weight the end of a rope
* [[Prusik]] for ascending a rope
* [[Reef knot]] (square knot), a common but insecure [[binding knot]] for joining the ends of a piece of cordage wrapped around an object or objects
* [[Sheet bend]] for joining the ends of two ropes, which need not be the same diameter
** [[Sheet bend#Double sheet bend|Double sheet bend]] for tying the ends of two dissimilarly sized ropes together
* [[Spanish bowline]] used to hoist crewmen aloft or suspend them over the side
* [[Versatackle knot|Versatackle]] for hoisting heavy loads and tightening rigging
* [[Water knot]] for tying a knot in flat material such as nylon webbing

====Hitches====
* [[Anchor bend]] (or anchor hitch) for tying a rope to a boat anchor
* [[Clove hitch]] for tying a rope to a pole – simple and will not jam, but not particularly secure and will not work on rectangular shapes
* [[Buntline hitch]] for tying a rope to a pole or other shape, but can jam
* [[Diamond hitch]] for packing trail animals
* [[Rolling hitch]] for securing a rope to a pole when the pull is lengthwise rather than outward, or to tie one rope to the middle of another
* [[Taut-line hitch]] (or Midshipman's hitch) for forming an adjustable (ratcheting) loop that does not slip smaller under tension
* [[Timber hitch]] for securing or hauling long narrow loads, with the pull in one direction
* [[Trucker's hitch]] for clinching down a load

===Trick knots===
[[Magic (illusion)|Trick]] knots are knots that are used as part of a [[magic trick]], a [[joke]], or a [[puzzle]]. They are useful for these purposes because they have a deceptive appearance, being easier or more difficult to tie or untie than their appearance would suggest. The easiest trick knot is the [[slip knot]].<ref>Karl Fulves, Joseph K. Schmidt, ''Self-Working Rope Magic: 70 Foolproof Tricks'' (1990), page 17.</ref> Other noted trick knots include:
* [[Grief knot]]. The starkly differing behavior of the knot, depending on how it is arranged, has been exploited as the basis of a [[parlor trick]].<ref name="ashley415">{{citation |last=Ashley |first=Clifford W. |title=The Ashley Book of Knots |year= 1944 |publisher=Doubleday |location=New York |page=415 }}</ref>  When pulling on the standing ends the knot starts slipping and the working ends become crossed. By twisting the working ends so that they uncross and then recross in reverse, the knot's structure capsizes so that it will no longer slip. The twisting motion resembles the turning of a key, "locking" and "unlocking" the knot.
* [[Tom fool's knot]], used as a trick knot due to the speed with which it can be made.

==Coxcombing==
<!--[[Coxcombing]] redirects directly here.-->
'''Coxcombing''' is a decorative knotwork performed by [[sailors]] during the [[Age of Sail]].

The general purpose was to dress-up, protect, or help identify specific items and parts of ships and boats.

It is still found today in some whippings and wrappings of small diameter line on boat tillers and ships' wheels to enhance the grip, or to identify rudder amidships.

Knots used in coxcombing include [[Turk's head knot]], [[Figure-eight knot|Flemish]], [[French whipping]], and others.

==Knot theory==
{{main|Knot theory}}
[[Image:TrefoilKnot 01.svg|thumb|right|150px|A [[trefoil knot]] is a mathematical version of an [[overhand knot]].]]

Knot theory is a branch of [[topology]]. It deals with the [[mathematics|mathematical]] analysis of knots, their structure and properties, and with the relationships between different knots. In topology, a [[knot (mathematics)|knot]] is a figure consisting of a single loop with any number of crossing or knotted elements: a closed curve in space which may be moved around so long as its strands never pass through each other. As a closed loop, a mathematical knot has no proper ends, and cannot be undone or untied; however, any physical knot in a piece of string can be thought of as a mathematical knot by fusing the two ends. A configuration of several knots winding around each other is called a ''link''. Various mathematical techniques are used to classify and distinguish knots and links. For instance, the [[Alexander polynomial]] associates certain numbers with any given knot; these numbers are different for the [[trefoil knot]], the [[Figure-eight knot (mathematics)|figure-eight knot]], and the [[unknot]] (a simple loop), showing that one cannot be moved into the other (without strands passing through each other).<ref>{{Cite journal |last1=Nakanishi |first1=Yasutaka |last2=Okada |first2=Yuki |title=Differences of Alexander polynomials for knots caused by a single crossing change |journal=Topology and Its Applications |volume=159 |issue=4 |pages=1016–1025 |doi=10.1016/j.topol.2011.11.023|year=2012 |doi-access=free }}</ref>

==Physical theory of friction knots==
{{See also|Capstan equation}}

A simple mathematical theory of hitches has been proposed by Bayman<ref>Bayman, "Theory of hitches," Am J Phys, 45 (1977) 185</ref> and extended by Maddocks and Keller.<ref>Maddocks, J.H. and Keller, J. B., "Ropes in Equilibrium," SIAM J Appl. Math., 47 (1987), pp. 1185–1200.</ref> It makes predictions that are approximately correct when tested empirically.<ref>{{cite web|url=http://www.lightandmatter.com/article/knots.html|title=The physics of knots|website=www.lightandmatter.com}}</ref> No similarly successful theory has been developed for knots in general.

==Knot tying==
{{Unreferenced section|date=January 2011}}
[[image:AshleyBook.jpg|thumb|right|[[The Ashley Book of Knots]] is considered the definitive work on the topic]]

Knot tying consists of the techniques and skills employed in tying a knot in [[rope]], [[nylon webbing]], or other articles. The proper tying of a knot can be the difference between an attractive knot and a messy one, and occasionally life and death. It is important to understand the often subtle differences between what works, and what does not. For example, many knots "spill" or pull through, particularly if they are not "backed up," usually with a single or double overhand knot to make sure the end of the rope does not make its way through the main knot, causing all strength to be lost.

===Difficulty===
The tying of a knot may be very straightforward (such as with an [[overhand knot]]), or it may be more complicated, such as a [[monkey's fist]] knot. Tying knots correctly requires an understanding of the type of material being tied (string, [[Rope|cord]], [[monofilament line]], [[kernmantle rope]], or nylon webbing). For example, cotton string may be very small and easy to tie with much internal friction to keep it from falling apart once tied, while stiff 5/8" thick kernmantle rope will be very difficult to tie, and may be so slick as to tend to come apart once tied.

===Material===
The form of the material will influence the tying of a knot as well. Rope is round in cross-section, and has little dependence upon the manner in which the material is tied. Nylon webbing, on the other hand, is flat, and usually "tubular" in construction, meaning that it is spiral-woven, and has a hollow core. In order to retain as much of the strength as possible with webbing, the material must be tied "flat" such that parallel sections do not cross, and that the sections of webbing are not twisted when they cross each other within a knot.

The crossing of strands is important when dealing with round rope in other knots; for example, the [[figure-eight loop]] loses strength when strands are crossed while the knot is being "finished" and tightened. Moreover, the [[standing end]] or the end from which the hauling will be done must have the greater radius of curvature in the finished knot to maximize the strength of the knot.

===Tools===
Tools are sometimes employed in the finishing or untying of a knot, such as a [[fid]], a tapered piece of wood that is often used in splicing. With the advent of [[wire rope]], many other tools are used in the tying of "knots." However, for cordage and other non-metallic appliances, the tools used are generally limited to sharp edges or blades such as a [[sheepsfoot blade]], occasionally a fine needle for proper whipping of [[laid rope]], a hot cutter for nylon and other synthetic fibers, and (for larger ropes) a shoe for smoothing out large knots by rolling them on the ground.

==Use by animals==
The [[hagfish]] is known to strip slime from its skin by tying itself into a simple overhand knot, and moving its body to make the knot travel toward the tail. It also uses this action in reverse (tail to head) to pry out flesh after biting into a carcass.<ref>{{Cite web |last=Waters |first=Hannah |date=2012-10-17 |title=14 Fun Facts About Hagfish |url=https://www.smithsonianmag.com/science-nature/14-fun-facts-about-hagfish-77165589/ |access-date=2023-03-18 |website=Smithsonian Magazine |language=en}}</ref>

==See also==
* [[Circuit topology]]
* [[Chinese knot]]ting
* [[Gordian Knot]]
* [[International Guild of Knot Tyers]]
* [[List of knots]]
* [[Quipu]]

==References==
=== Citations ===
{{Reflist}}

=== General sources ===
* [[Clifford Ashley|Clifford W. Ashley]]. ''[[The Ashley Book of Knots]]''. Doubleday, New York. {{ISBN|0-385-04025-3}}.
* Geoffrey Budworth (1999). ''The Ultimate Encyclopedia of Knots & Ropework''. Annes Publishing Limited. {{ISBN|1-55267-986-1}}.
* John Cassidy (1985). ''The Klutz Book of Knots''. Klutz Press, [[Palo Alto, California]]. {{ISBN|0-932592-10-4}}.
* Paul Hasluck with foreword by Des Pawson (2018) ''The Art of Tying Knots.'' Endless Mountains Publishing Company. {{ISBN|0-998852-73-2}}.
* Cyrus L. Day. ''Knots & Splices''. International Marine/McGraw-Hill Companies. {{ISBN|0-87742-252-4}}.
* Raoul Graumont. ''Handbook of Knots''. Cornell Maritime Press/Tidewater Publishers. {{ISBN|0-87033-030-6}}.
* R.S. Lee. ''All The Knots You Need''. Algrove Publishing. {{ISBN|0-921335-47-4}}.
* Allen Padgett and Bruce Smith. ''On Rope''. National Speleological Society. {{ISBN|0-9615093-2-5}}.
* Des Pawson (2001). ''Pocket Guide to Knots & Splices''. Produced for Propsero Books by RPC Publishing Ltd., London. {{ISBN|1-55267-218-2}}.
* Brion Toss. ''The Complete Rigger's Apprentice''. International Marine/McGraw-Hill Companies. {{ISBN|0-07-064840-9}}.
* J. C. Turner and P. van de Griend (ed.) (1996). ''History and Science of Knots''. World Scientific. {{ISBN|981-02-2469-9}}.
* {{cite journal |first1=J. |last1=Šimon |first2=V. |last2=Dekýš |first3=P. |last3=Palček |title=Revision of Commonly Used Loop Knots Efficiencies |journal=Acta Physica Polonica A |date=2020 |volume=138 |issue=3 |pages=404–420 |doi=10.12693/APhysPolA.138.404|bibcode=2020AcPPA.138..404S |doi-access=free }}
* {{cite book
 |last= Aldridge
 |first= Arthur F.
 |date= 1918
 |title= Knots, a study of marlinespike seamanship which embraces bends, hitches, ties, fastenings and splices and their practical application
 |url= https://archive.org/details/knotsstudyofmarl00aldr
 |location= New York City
 |publisher= Rudder
 | oclc = 1047502131
 | ol = 18970340M
}}
* {{cite book
 |last = Burgess
 |first = J. Tom
 |author-link = Joseph Tom Burgess
 |date = 1884
 |title = Knots, ties and splices; a handbook for seafarers, travellers, and all who use cordage; with historical, heraldic, and practical notes 
 |url = https://archive.org/details/cu31924014519940
 |location = London
 |publisher = George Routledge and sons
 |ol = 24176273M
}}
* {{cite book
 | last1 = Dana
 | first1 = Homer Jackson
 | last2 = Pearl
 | first2 = William Armour
 |date= 1922
 |title= The use of ropes and tackle
 |url= https://archive.org/details/useofropestackle00danarich
 |location= Pullman, WA
 |publisher= Washington State College
 | oclc = 1158196429
}}
* {{cite book
 |last= Hasluck
 |first= Paul Nooncree
 |author-link= Paul Nooncree Hasluck
 |date= 1907
 |title= Knotting and splicing ropes and cordage
 |url= https://archive.org/details/gri_33125000664421
 |location= Philadelphia
 |publisher= David McKay
 | ol = 6954703M
}}
* {{cite book
 |last= Verrill
 |first= Alpheus Hyatt
 |author-link = Alpheus Hyatt Verrill
 |date= 1917
 |title= Knots, Splices and Rope Work
 |url= https://www.gutenberg.org/ebooks/13510
 |publisher= Norman W. Henley Publishing
}}

== External links ==
{{Wikibooks|Simplified list of knots}}
{{Commons category|Knots}}

{{Knots}}
{{Mathematics and art}}
{{Seamanship}}
{{Authority control}}

[[Category:Knots| ]]