Knot

# Knot

Overview
A knot is a method of fastening or securing linear material such as rope
Rope
A rope is a length of fibres, twisted or braided together to improve strength for pulling and connecting. It has tensile strength but is too flexible to provide compressive strength...

by tying or interweaving. It may consist of a length of one or several segments of rope, string, webbing
Webbing
Webbing is a strong fabric woven as a flat strip or tube of varying width and fibres often used in place of rope. The name webbing comes from the meshed material frequently used in its construction, which resembles a web...

, twine
Twine
Twine is a light string or strong thread composed of two or more smaller strands or yarns twisted together. More generally, the term can be applied to any thin cord....

, strap
Strap
A strap, sometimes also called strop, is an elongated flap or ribbon, usually of fabric or leather.Thin straps are used as part of clothing or baggage, or bedding such as a sleeping bag. See for example spaghetti strap, shoulder strap...

, or even chain
Chain
A chain is a sequence of connected links.Chain may also refer to:Chain may refer to:* Necklace - a jewelry which is worn around the neck* Mail , a type of armor made of interlocking chain links...

interwoven such that the line can bind to itself or to some other object—the "load". Knots have been the subject of interest for their ancient origins, their common uses, and the area of mathematics known as knot theory
Knot theory
In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone. In precise mathematical language, a knot is an embedding of a...

.
Discussion

Encyclopedia
A knot is a method of fastening or securing linear material such as rope
Rope
A rope is a length of fibres, twisted or braided together to improve strength for pulling and connecting. It has tensile strength but is too flexible to provide compressive strength...

by tying or interweaving. It may consist of a length of one or several segments of rope, string, webbing
Webbing
Webbing is a strong fabric woven as a flat strip or tube of varying width and fibres often used in place of rope. The name webbing comes from the meshed material frequently used in its construction, which resembles a web...

, twine
Twine
Twine is a light string or strong thread composed of two or more smaller strands or yarns twisted together. More generally, the term can be applied to any thin cord....

, strap
Strap
A strap, sometimes also called strop, is an elongated flap or ribbon, usually of fabric or leather.Thin straps are used as part of clothing or baggage, or bedding such as a sleeping bag. See for example spaghetti strap, shoulder strap...

, or even chain
Chain
A chain is a sequence of connected links.Chain may also refer to:Chain may refer to:* Necklace - a jewelry which is worn around the neck* Mail , a type of armor made of interlocking chain links...

interwoven such that the line can bind to itself or to some other object—the "load". Knots have been the subject of interest for their ancient origins, their common uses, and the area of mathematics known as knot theory
Knot theory
In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematician's knot differs in that the ends are joined together so that it cannot be undone. In precise mathematical language, a knot is an embedding of a...

.

## Use

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
Cleat (nautical)
In nautical contexts, a cleat is a device for securing a rope. The traditional design is attached to a flat surface or a spar and features two “horns” extending parallel to the deck or the axis of the spar, resembling an anvil....

, ring, or stake. Some knots are used to bind or constrict objects. Decorative knots usually bind to themselves to produce attractive patterns.

### Teaching

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 sailor
Sailor
A sailor, mariner, or seaman is a person who navigates water-borne vessels or assists in their operation, maintenance, or service. The term can apply to professional mariners, military personnel, and recreational sailors as well as a plethora of other uses...

s, scout
Scouting
Scouting, also known as the Scout Movement, is a worldwide youth movement with the stated aim of supporting young people in their physical, mental and spiritual development, that they may play constructive roles in society....

s, climber
Climbing
Climbing is the activity of using one's hands and feet to ascend a steep object. It is done both for recreation and professionally, as part of activities such as maintenance of a structure, or military operations.Climbing activities include:* Bouldering: Ascending boulders or small...

s, caver
Caving
Caving—also occasionally known as spelunking in the United States and potholing in the United Kingdom—is the recreational pastime of exploring wild cave systems...

s, arborist
Arborist
An arborist, or arboriculturist, is a professional in the practice of arboriculture, which is the cultivation, management, and study of individual trees, shrubs, vines, and other perennial woody plants...

s, rescue professionals, fishermen, linemen and surgeons
Surgeon
In medicine, a surgeon is a specialist in surgery. Surgery is a broad category of invasive medical treatment that involves the cutting of a body, whether human or animal, for a specific reason such as the removal of diseased tissue or to repair a tear or breakage...

.

### Applications

Truckers in need of securing a load may use a trucker's hitch
Trucker's hitch
The trucker's hitch is a compound knot commonly used for securing loads on trucks or trailers. This general arrangement, using loops and turns in the rope itself to form a crude block and tackle, has long been used to tension lines and is known by multiple names...

Mechanical advantage is a measure of the force amplification achieved by using a tool, mechanical device or machine system. Ideally, the device preserves the input power and simply trades off forces against movement to obtain a desired amplification in the output force...

. Knots can save a spelunker from finding himself buried under rock. Many knots can also be used as makeshift tools, for example, the Bowline
Bowline
The bowline 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 untie. The bowline is sometimes referred as King of the knots because of its importance...

can be used as a rescue loop, and the Munter hitch
Munter hitch
The Munter hitch, also known as the Italian hitch, is a simple knot, commonly used by climbers and cavers as part of a life-lining or belay system. To climbers, this knot is also known as HMS, the abbreviation for the German term Halbmastwurfsicherung, meaning half clove hitch belay...

can be used as a belay. The Diamond hitch was widely used to tie packages on to donkey
Donkey
The donkey or ass, Equus africanus asinus, is a domesticated member of the Equidae or horse family. The wild ancestor of the donkey is the African Wild Ass, E...

s and mule
Mule
A mule is the offspring of a male donkey and a female horse. Horses and donkeys are different species, with different numbers of chromosomes. Of the two F1 hybrids between these two species, a mule is easier to obtain than a hinny...

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 a rope or two, some carabineers, and knowledge of knots you can set up a rappel system to lower yourself down to the individual and set up a hauling system to allow another individual to pull you and the injured person out of the ravine. Further application of knots includes developing a high line, which is basically equivalent to a zip line. Using the high line you can move supplies, injured people, or those lacking training in rappelling and rock climbing across a river or a large crevice or ravine. Note the systems mentioned typically require carabineers and the use of multiple useful 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 do interesting activities such as rappelling.

Knots can be applied in combination to produce complex objects such as lanyard
Lanyard
A lanyard is a rope or cord exclusively worn around the neck or wrist to carry something. Usually it is used where there is a risk of losing the object or to ensure it is visible at all times. Aboard a ship, it may refer to a piece of rigging used to secure objects...

s and netting
Net (textile)
Net or netting is any textile in which the warp and weft yarns are looped or knotted at their intersections, resulting in a fabric with large open spaces between the yarns....

. In ropework
Ropework
Ropework or Marlinespike Seamanship is the set of processes and skills used to make, repair, and use rope. This includes tying knots, splicing, making lashings, and proper use and storage of rope...

, the frayed end of a rope is held together by a type of knot called a whipping knot
Whipping knot
A whipping knot or whipping is a binding of twine around the end of a rope to prevent the fibres of the rope from unravelling.When a rope is cut, there is a natural tendency for the cut end to fray. A whipping is one way to try to prevent this, by applying multiple turns of twine tightly around...

. Many types of textile
Textile
A textile or cloth is a flexible woven material consisting of a network of natural or artificial fibres often referred to as thread or yarn. Yarn is produced by spinning raw fibres of wool, flax, cotton, or other material to produce long strands...

s use knots to repair damage. Macrame
Macramé
Macramé or macrame is a form of textile-making using knotting rather than weaving or knitting. Its primary knots are the square knot and forms of "hitching": full hitch and double half hitches...

, one kind of textile, is generated exclusively through the use of knotting, instead of knits
Knitting
Knitting is a method by which thread or yarn may be turned into cloth or other fine crafts. Knitted fabric consists of consecutive rows of loops, called stitches. As each row progresses, a new loop is pulled through an existing loop. The active stitches are held on a needle until another loop can...

, 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.

### Strength

Knots weaken the rope in which they are made. 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.

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
Fiber
Fiber is a class of materials that are continuous filaments or are in discrete elongated pieces, similar to lengths of thread.They are very important in the biology of both plants and animals, for holding tissues together....

, the 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—80% of the rope's original strength.

In most situations forming loops and bends with conventional knots is far more practical than using rope splices
Rope splicing
Rope splicing in ropework is the forming of a semi-permanent joint between two ropes or two parts of the same rope by partly untwisting and then interweaving their strands. Splices can be used to form a stopper at the end of a line, to form a loop or an eye in a rope, or for joining two ropes...

, even though the latter can nearly maintain the rope's full strength. Prudent users allow for a large safety margin
Factor of safety
Factor of safety , also known as safety factor , is a term describing the structural capacity of a system beyond the expected loads or actual loads. Essentially, how much stronger the system is than it usually needs to be for an intended load...

in the strength of rope chosen for a task due to the weakening effects of knots, aging, damage, shock loading, etc. The working load limit
Safe working load is the load that a lifting device such as a crane, a cherry picker, or a lifting arrangement can safely lift, suspend or lower. Other synonyms include working load limit , which is the maximum working load designed by the manufacturer. The load represents a mass or force that...

of a rope is generally specified with a significant safety factor, up to 15:1 for critical applications. For life-threatening applications, other factors come into play.

### 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 main ways knots fail to hold are:

#### 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 a masts
Mast (sailing)
The mast of a sailing vessel is a tall, vertical, or near vertical, spar, or arrangement of spars, which supports the sails. Large ships have several masts, with the size and configuration depending on the style of ship...

and flagpoles.

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
Stopper (knot)
The term stopper knot has three distinct meanings in the context of knotting and cordage.-At the end of a line:A stopper knot is tied at the end of a rope to prevent the end from unraveling, slipping through another knot, or passing back through a hole, block, or belay/rappel device...

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

Capsizing (or spilling) a knot refers to changing a knot's form and rearranging its parts, usually by pulling on specific ends in certain ways. 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 "lightning method" of tying a Bowline. Some knots, such as the Carrick Bend
Carrick bend
The Carrick bend is a knot used for joining two lines. It is particularly appropriate for very heavy rope or cable that is too large and stiff to easily be formed into other common bends. It will not jam even after carrying a significant load or being soaked with water...

, 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 does not fail, it ceases to perform the desired function. For instance, a simple Rolling Hitch
Rolling hitch
The rolling hitch is a knot used to attach a rope to a rod, pole, or other rope. A simple friction hitch, it is used for lengthwise pull along an object rather than at right angles...

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
Water knot
The water knot is a knot frequently used in climbing for joining two ends of webbing together, for instance when making a sling.-Tying the water knot:...

, are said to "jam". Knots that come untied with less difficulty, such as the Zeppelin bend
Zeppelin bend
A Zeppelin bend is a general purpose bend knot. It is a secure, easily tied, and jam-resistant way to connect two ropes...

, are referred to as "non-jamming".

## Components

### BightBight (knot)In knot tying, a bight is a curved section, slack part, or loop between the two ends of a rope, string, or yarn. The term is also used in a more specific way when describing Turk's head knots, indicating how many repetitions of braiding are made in the circuit of a given knot.-Slipped knot:In order...

Any curved section, slack part, or loop between the ends of a rope, string, or yarn

### Bitter end

More a ropeworker's term than a knot term, it refers to the end of a rope that is tied off, hence the expression "hanging on to the bitter end". A bitt is a metal block with a crosspin used for tying lines to, found on piers. In fact the bitter end is the end of the anchor "cable" that connects to the anchor bitts in the cable locker under the forecastle or poop using the bitter pin. (British nautical usage). Other uses may be borrowed from this derivation.

### Standing end

The standing end is the 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.

### TurnTurn (knot)A turn is one round of rope on a pin or cleat, or one round of a coil. Turns can be made around various objects, through rings, or around the standing part of the rope itself or another rope. A turn also denotes a component of a knot....

A turn or single turn is a single pass behind or through an object.
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'.

## Categories

The list of knots is extensive, but common properties allow for a useful system of categorization. For example, loop
Loop (knot)
In reference to knots, loop may refer to:* One of the fundamental structures used to tie knots. Specifically, it is a full circle formed by passing the working end over itself.* A type of knot used to create a closed circle in a line....

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 to using a round turn. An example of this is the bowline
Bowline
The bowline 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 untie. The bowline is sometimes referred as King of the knots because of its importance...

. Constricting knots often rely on friction to cinch down tight on loose bundles; an example is the Miller's knot
Miller's knot
A miller's knot is a binding knot used to secure the opening of a sack or bag. Historically, large sacks often contained grains; thus the association of these knots with the miller's trade...

. Knots may belong to more than one category.

Bend :A knot uniting two lines (for knots joining two ends of the same line, see binding knots or loops
Loop (knot)
In reference to knots, loop may refer to:* One of the fundamental structures used to tie knots. Specifically, it is a full circle formed by passing the working end over itself.* A type of knot used to create a closed circle in a line....

). List of bends.
Binding :A knot that restricts object(s) by making multiple winds. List of binding knots.
Coil
Coil knot
Coil knot may refer to:*Alpine coil*Butterfly coil...

:Knots used to tie up lines for storage. List of coil knots. Another handy coil is here.
Decorative knot :A complex knot exhibiting repeating patterns often constructed around and enhancing an object. List of decorative knots.
Hitch :A knot tied to a post, cable, ring, or spar. List of hitch knots.
Lashing
Lashing knot
A lashing is an arrangement of rope used to secure two or more items together in a somewhat rigid manner. Lashings are most commonly applied to timber poles, and are commonly associated with the scouting movement and with sailors....

:A knot used to hold (usually) poles together. List of lashing knots.
Loop
Loop (knot)
In reference to knots, loop may refer to:* One of the fundamental structures used to tie knots. Specifically, it is a full circle formed by passing the working end over itself.* A type of knot used to create a closed circle in a line....

:A knot used to create a closed circle in a line. List of loop knots.
Plait
Braid
A braid is a complex structure or pattern formed by intertwining three or more strands of flexible material such as textile fibres, wire, or human hair...

(or braid):A number of lines interwoven in a simple regular pattern. List of plait knots.
Slip
Slip knot
A slip knot is one of two different classes of knot. The most common are knots which attach a line to an object and tighten when tension is applied to the free end of the line...

(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. List of slip knots.
Slipped :Some knots may be finished by passing a bight
Bight (knot)
In knot tying, a bight is a curved section, slack part, or loop between the two ends of a rope, string, or yarn. The term is also used in a more specific way when describing Turk's head knots, indicating how many repetitions of braiding are made in the circuit of a given knot.-Slipped knot:In order...

rather than the end, for ease of untying. The common shoelace knot is an example, being a reef knot
Reef knot
The reef knot or square knot is an ancient and simple binding knot used to secure a rope or line around an object. Although the reef knot is often seen used for tying two ropes together, it is not recommended for this purpose due to potential instability of the knot.A reef knot is formed by tying...

with both ends slipped.
Seizing
Seizing
Seizings are a class of knots used to semi-permanently bind together two ropes, two parts of the same rope, or rope and another object. Akin to lashings, they use string or small-stuff to produce friction and leverage to immobilize larger ropes. Seizings are not recommended for heavy loads....

:A knot used to hold two lines or two parts of the same line together. List of seizing knots.
Sennit
Sennit
Sennit is a type of cordage made by plaiting strands of dried fibre or grass. It can be used ornamentally in crafts, like a kind of macrame, or to make straw hats...

:A number of lines interwoven in a complex pattern. See also Chain sinnet
Chain sinnet
A chain sinnet is a method of shortening a rope or other cable while in use or for storage. It is formed by making a series of simple crochet-like stitches in the line.-Tying:To tie:#Create a loop in the rope...

.
Splice
Rope splicing
Rope splicing in ropework is the forming of a semi-permanent joint between two ropes or two parts of the same rope by partly untwisting and then interweaving their strands. Splices can be used to form a stopper at the end of a line, to form a loop or an eye in a rope, or for joining two ropes...

:A knot formed by interweaving strands of rope rather than whole lines. More time-consuming but usually stronger than simple knots. List of splices.
Stopper
Stopper (knot)
The term stopper knot has three distinct meanings in the context of knotting and cordage.-At the end of a line:A stopper knot is tied at the end of a rope to prevent the end from unraveling, slipping through another knot, or passing back through a hole, block, or belay/rappel device...

:A knot tied to hold a line through a hole. List of stopper knots.
Trick
Trick
Trick may refer to:* Trick , a 2009 album by Kumi Koda* Trick , a 1999 American film* Tricks , a 2007 Polish film by Andrzej Jakimowski* Trick , a comedic Japanese television drama...

:A knot that is used as part of a magic trick, a joke, or a puzzle. List of trick knots.
Whipping
Whipping knot
A whipping knot or whipping is a binding of twine around the end of a rope to prevent the fibres of the rope from unravelling.When a rope is cut, there is a natural tendency for the cut end to fray. A whipping is one way to try to prevent this, by applying multiple turns of twine tightly around...

:A binding knot used to prevent another line from fraying.

### Basic useful knots

• Bowline
Bowline
The bowline 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 untie. The bowline is sometimes referred as King of the knots because of its importance...

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.
• Square knot, a binding knot for joining the ends of a piece of cordage wrapped around an object or objects
• Sheet bend
Sheet bend
The sheet bend is a bend, that is, a knot that joins two ropes together. Doubled, it is effective in binding lines of different diameter or rigidity securely together, although it has a tendency to work loose when not under load.The sheet bend is related in structure to the bowline...

for joining the ends of two ropes, which need not be the same diameter
• Double sheet bend for tying the ends of two dissimilarly sized ropes together
• Water knot
Water knot
The water knot is a knot frequently used in climbing for joining two ends of webbing together, for instance when making a sling.-Tying the water knot:...

for tying a knot in flat material such as nylon webbing
• Buntline hitch
Buntline hitch
The buntline hitch is a knot used for attaching a rope to an object. It is formed by looping the rope around an object, then making a clove hitch around the rope's standing part, taking care to tie the two half-hitches that compose the clove hitch in the direction of the object, rather than away...

for tying a rope to a pole
• Timber hitch
Timber hitch
The timber hitch is a knot used to attach a single length of rope to a piece of wood. This knot is easily undone after use.To make the knot, pass the rope completely around the wood. Pass the running end around the standing part, then through the loop that you have just formed. Make three turns...

for securing or hauling long narrow loads
• Rolling hitch
Rolling hitch
The rolling hitch is a knot used to attach a rope to a rod, pole, or other rope. A simple friction hitch, it is used for lengthwise pull along an object rather than at right angles...

for securing a rope to a pole, or one rope to the middle of another
• Taut-line hitch
Taut-line hitch
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 in order to maintain tension. It is made by tying a rolling hitch around the standing part after passing around an anchor object...

for forming an adjustable loop that keeps its size under tension
• freedom knot
Freedom knot
The freedom knot is a knot which can be used for tying shoelaces. Also known as a bow or bunny ears. This knot is more resistant to coming untied than the standard shoelace knot....

for joining two pieces of rope such as tying shoelaces
• Trucker's hitch
Trucker's hitch
The trucker's hitch is a compound knot commonly used for securing loads on trucks or trailers. This general arrangement, using loops and turns in the rope itself to form a crude block and tackle, has long been used to tension lines and is known by multiple names...

• Constrictor knot
Constrictor 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 tightened. It is made similarly to a clove hitch but with one end passed under the other, forming an overhand knot under a riding turn...

for making bundles or cinching the neck of a sack
• Alpine butterfly knot
Alpine butterfly knot
The alpine butterfly knot is a knot used to form a fixed loop in the middle of a rope. Tied in the bight, it can be made in a rope without access to either of the ends; this is a distinct advantage when working with long climbing ropes. The butterfly loop is an excellent mid-line rigging knot, it...

for a secure loop in the middle of a rope when the ends aren't free
• Prusik for ascending a rope
• Diamond hitch for packing trail animals
• Figure-of-eight knot as a stopper
• Spanish bowline
Spanish Bowline
A double loop knot that can be used to lift a person. For a conscious person, each loop is placed around a leg and the person holds onto the standing part of the rope. This knot can serve as a makeshift Bosun's chair...

Used to hoist crewmen aloft or suspend them over the side
• Midshipman's Hitch (also known as a Taut-line Hitch, above)
• Monkey's fist
Monkey's fist
A monkey's fist or monkey paw is a type of knot, so named because it looks somewhat like a small bunched fist/paw. It is tied at the end of a rope to serve as a weight, making it easier to throw, and also as an ornamental knot. This type of weighted rope can be used as an improvised weapon,...

used to haul a heavier rope
• Versatackle
Versatackle knot
A versatackle is a way of simulating a block and tackle without actual pulleys or deadeyes. It consists of two loops with the rope passed back and forth between them...

hoist heavy loads and tighten rigging

## Knot theory

Knot theory is a branch of topology
Topology
Topology is a major area of mathematics concerned with properties that are preserved under continuous deformations of objects, such as deformations that involve stretching, but no tearing or gluing...

. It deals with the mathematical
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...

analysis of knots, their structure and properties, and with the relationships between different knots. In topology, a knot
Knot (mathematics)
In mathematics, a knot is an embedding of a circle in 3-dimensional Euclidean space, R3, considered up to continuous deformations . A crucial difference between the standard mathematical and conventional notions of a knot is that mathematical knots are closed—there are no ends to tie or untie on a...

is a figure consisting of a single loop, abstracted from any physical rope or line, with any number of crossing or "knotted" elements. As such, it has no proper ends, and cannot be undone or untied. Various mathematical techniques are used to classify and distinguish knots. For instance, the Alexander polynomial
Alexander polynomial
In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type. James Waddell Alexander II discovered this, the first knot polynomial, in 1923...

can be used to distinguish the trefoil knot
Trefoil knot
In topology, a branch of mathematics, the trefoil knot is the simplest example of a nontrivial knot. The trefoil can be obtained by joining together the two loose ends of a common overhand knot, resulting in a knotted loop...

from the figure-of-eight knot
Figure-eight knot (mathematics)
In knot theory, a figure-eight knot is the unique knot with a crossing number of four. This is the smallest possible crossing number except for the unknot and trefoil knot...

and the unknot
Unknot
The unknot arises in the mathematical theory of knots. Intuitively, the unknot is a closed loop of rope without a knot in it. A knot theorist would describe the unknot as an image of any embedding that can be deformed, i.e. ambient-isotoped, to the standard unknot, i.e. the embedding of the...

(a simple loop).

• List of knots
• List of knot terminology
• Knot (mathematics)
Knot (mathematics)
In mathematics, a knot is an embedding of a circle in 3-dimensional Euclidean space, R3, considered up to continuous deformations . A crucial difference between the standard mathematical and conventional notions of a knot is that mathematical knots are closed—there are no ends to tie or untie on a...

• Quipu
Quipu
Quipus or khipus were recording devices used in the Inca Empire and its predecessor societies in the Andean region. A quipu usually consisted of colored, spun, and plied thread or strings from llama or alpaca hair. It could also be made of cotton cords...

• Chinese knotting
• List of decorative knots
• round turn and two half-hitches
Round turn and two half-hitches
The round turn and two half hitches is a hitch used to secure the end of a rope to a fixed object. The name refers to the components used to form the knot: a round turn wraps the rope around the object and the two half hitches secure the end around the standing part...

### Notations

• Clifford W. Ashley
Clifford Ashley
Clifford Warren Ashley was an American artist, author, sailor, and knot expert. He was born in New Bedford, Massachusetts, son of Abiel Davis Ashley and Caroline Morse. Ashley married Sarah Scudder Clark in 1932 and had two daughters, also adopting his wife's oldest daughter from a previous...

. The Ashley Book of Knots
The Ashley Book of Knots
The Ashley Book of Knots is an encyclopedia of knots first published in 1944 by Clifford Warren Ashley. The culmination of over 11 years of work, it contains some 7000 illustrations and more than 3854 entries covering over 2000 different knots. The entries include instructions, uses, and for some...

. 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
Palo Alto, California
Palo Alto is a California charter city located in the northwest corner of Santa Clara County, in the San Francisco Bay Area of California, United States. The city shares its borders with East Palo Alto, Mountain View, Los Altos, Los Altos Hills, Stanford, Portola Valley, and Menlo Park. It is...

. ISBN 0-932592-10-4
• 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