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42-561: In general, a node is a localized swelling (a " knot ") or a point of intersection (a vertex ). Node may refer to: Knot 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

84-463: A 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

126-531: 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 . Other noted trick knots include: 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

168-472: 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. 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

210-423: A trucker's hitch , gaining mechanical advantage . Knots can save 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 donkeys and mules . In hazardous environments such as mountains, knots are very important. In

252-490: A carcass. Lanyard A lanyard is a length of cord , webbing , or strap that may serve any of various functions, which include a means of attachment, restraint, retrieval, activation, and deactivation. A lanyard is also a piece of rigging used to secure or lower objects aboard a ship. The earliest references to lanyards date from 15th century France: "lanière" was a thong or strap-on apparatus. Bosun's pipe , marlinspike , and small knives typically had

294-464: A clip attached to the end. A plastic pouch or badge holder with at least one clear side is attached to the lanyard with the person's name badge or ID card. Occasionally, small items like business cards, pens or tools can be placed behind the badge for easy access. Lanyards can also be used as keychains , particularly in situations where keys can easily be lost, such as gyms, public pools and communal showers. In these cases, lanyards may be customised with

336-476: A knot with more wraps or a rope of different diameter or material. 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 ". The list of knots is extensive, but common properties allow for

378-467: A lanyard consisting of a string loop tied together with a diamond knot . It helped secure the item and gave an extended grip over a small handle. In the French military, lanyards were used to connect a pistol , sword , or whistle (for signaling) to a uniform semi-permanently. Lanyards were used by mounted cavalry on land and naval officers at sea. A pistol lanyard can be easily removed and reattached by

420-405: A lanyard usually have a small through-hole built into a corner or edge of the case or anchored to the frame of the device; the corresponding lanyard generally has a loop of thread on the end that is attached to that hole with a simple knot, usually a cow hitch . Some earphones incorporate the audio signal into the lanyard, meaning it doubles up as headphone cords as well. The Wii Remote wrist strap

462-469: A precise value for a particular knot is difficult because many factors can affect a knot efficiency test: the type of fiber , 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 and 80% of the rope's original strength. In most situations forming loops and bends with conventional knots

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504-559: A section of heavy-duty nylon strapping attached to a metal ring or carabiner which tightens around an attachment point. The strap may be a fixed length or adjustable, and will attach to the wearer to support them against a fixed object or pole. Certain lanyards are still worn on uniforms as decorations similar to an aiguillette or fourragère . Among these are the Orange Lanyard in the Military William Order of

546-720: 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. 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, 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. The form of

588-558: A useful system of categorization. For example, 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. Trick knots are knots that are used as part of

630-462: Is a form of lanyard, keeping the device attached to a player's arm during the often vigorous movements involved in its use. Lanyards are commonly used to display badges, tickets or ID cards for identification where security is required, such as businesses , corporations , hospitals , prisons , conventions , trade fairs , and backstage passes used in the entertainment industry . Such lanyards are often made of braided or woven fabric or split with

672-410: 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 , ring, or stake. Some knots are used to bind or constrict objects. Decorative knots usually bind to themselves to produce attractive patterns. While some people can look at diagrams or photos and tie

714-443: Is applied. This prevents choking or hanging. Lanyards with a breakaway feature are most often used in hospitals and healthcare clinics , schools , nursing homes , child care facilities, or factories that require employees to operate machinery. Lineman lanyards are used by lineworker utility and other workers to prevent falls, although similar straps are also used recreationally by mountain climbers. This type of lanyard will have

756-740: 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 , and the unknot (a simple loop), showing that one cannot be moved into the other (without strands passing through each other). A simple mathematical theory of hitches has been proposed by Bayman and extended by Maddocks and Keller. It makes predictions that are approximately correct when tested empirically. No similarly successful theory has been developed for knots in general. Knot tying consists of

798-489: Is far more practical than using rope splices , even though the latter can maintain nearly the rope's full strength. Prudent users allow for a large safety margin 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 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. Even if

840-422: Is often used ornamentally or decoratively. 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

882-450: 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 , Flemish , French whipping , and others. Knot theory is a branch of topology . It deals with the mathematical analysis of knots, their structure and properties, and with the relationships between different knots. In topology,

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924-478: Is the recent mathematical study of knots. Knots of ancient origin include the bottle sling , bowline , 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

966-695: The Netherlands and the German Armed Forces Badge of Marksmanship . A white lanyard has formed part of the uniform of Britain's Royal Artillery (RA) since the end of the 19th century. Originally a simple cord carrying a fuse key, the braided and whitened lanyard became the recognised distinction of a Gunner. The distinction was extended to women of the Auxiliary Territorial Service attached to RA units during World War II . Certain battalions descended from

1008-597: The British Royal Artillery wear a lanyard which originally held a key for adjusting the fuzes of explosive shells . The style, design or material used will vary depending on end-purpose of the lanyard. Lanyard materials include polyester , nylon , satin , silk , polyethylene terephthalate (PET), braided leather or braided paracord . Lanyards are widely used with small electronic devices such as cameras , MP3 players and USB flash drives to prevent loss or dropping. Electronics designed to take

1050-544: The ability to undertake activities such as rappelling. Knots can be applied in combination to produce complex objects such as lanyards and netting . In ropework , the frayed end of a rope is held together by a type of knot called a whipping knot . Many types of textiles use knots to repair damage. Macramé , one kind of textile, is generated exclusively through the use of knotting, instead of knits , crochets, weaves or felting. Macramé can produce self-supporting three-dimensional textile structures, as well as flat work, and

1092-482: 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 , are generally tied in one form then capsized to obtain a stronger or more stable form. In knots that are meant to grip other objects, failure can be defined as

1134-460: 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

1176-407: The finished knot to maximize the strength of the knot. 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

1218-480: The four-flower knot, six-flower knot, Chinese 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 recent origin include the friendship knot of Chinese knotting. The sheepshank knot originates from 1627 while the Western Union splice originates from the beginning of telegraphy . There

1260-408: The illustrated knots, others learn best by watching how a knot is tied. Knot tying skills are often transmitted by sailors , scouts , climbers , canyoners , cavers , arborists , rescue professionals , stagehands , fishermen , linemen and surgeons . The International Guild of Knot Tyers is an organization dedicated to the promotion of knot tying. Truckers in need of securing a load may use

1302-586: 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. To capsize (or spill) a knot is to change its form and rearrange its parts, usually by pulling on specific ends in certain ways. When used inappropriately, some knots tend to capsize easily or even spontaneously. Often

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1344-421: 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

1386-404: 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 masts 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

1428-452: 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

1470-469: The operator suddenly becomes incapacitated, their fall will pull on the lanyard attached to their wrist, which will then pull the switch to immediately stop the machine or vehicle. Some law enforcement officers and members of the military utilise specialised lanyards to keep sidearms from falling to the ground during missions. Many ID card lanyards have a built-in feature known as a "breakaway" closure. Breakaway lanyards release when pulled or when pressure

1512-459: The related name and/or logo of the event, business, or organisation. Lanyards can feature a variety of customisation techniques including screen-printing , Jacquard loom weaving, heat transfer , and offset printing . Lanyards are also often attached to dead man's switches or "kill switches" on dangerous machinery, such as large industrial cutting or slicing machines; on vehicles, such as jet-skis or trains; and on exercise treadmills, so that if

1554-408: 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. 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

1596-413: 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

1638-425: 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

1680-403: 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

1722-471: The user, but will stay connected to the pistol whether it is drawn for use or it is placed into a holster for carrying. In the military, lanyards of various colour combinations and braid patterns are worn on the shoulders of uniforms to denote the wearer's qualification or regimental affiliation. In horse regiments, lanyards were worn on the left, enabling a rider to pull a whistle from the left tunic pocket and maintain communication with his troop. Members of

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1764-408: 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. 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

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