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66-902: 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 , 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

132-463: 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

198-530: 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

264-472: 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

330-423: 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

396-460: A carcass. Chinese knotting 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 made from a single length of cord that is woven into different shapes, with each shape having a symbolic meaning. The most common color used in Chinese knotting is red,

462-464: 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

528-610: A color associated with luck in Chinese culture , although any color can be used. Charms, beads, and jade are sometimes incorporated into a Chinese knot. It is believed that Chinese knotting originated for recording information and exchanging messages before writing was commonplace. Traditionally, Chinese knots acted as good-luck charms to ward off evil spirits. Chinese knots are used today to decorate homes during festivities and are also commonly seen in traditional jade jewellery and traditional Chinese clothing . Chinese knots come in

594-476: 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

660-467: 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

726-405: 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

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792-467: 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

858-559: 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

924-720: 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

990-558: 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

1056-424: A variety of shapes and sizes. They are made from a single cord and are often double-layered and symmetrical in all directions. Satin cording is the most widely used material, especially when the knotting is done for clothing and jewellery; however, cotton, parachute cord , and other materials are frequently used as well. Knots are often paired with tassels , which are created separately and then incorporated into

1122-462: 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

1188-410: 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

1254-444: 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

1320-443: 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

1386-605: Is believed to originate from China, from which Korean knots evolved into its own culture in terms of design, color, and incorporation of local characteristics. The origins of maedeup date back to the Three Kingdoms of Korea in the first century CE. Maedeup articles were first used at religious ceremonies. A wall painting from 357 CE found in Anak , Hwanghae Province , now in North Korea , indicates that silk

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1452-736: 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

1518-425: Is called the dorae (or the double connection knot ). The dorae knot is used at the start and end of most knot projects. There are approximately 33 basic Korean knots which vary according to the region they come from. The bongsul tassel is noteworthy as the most representative work familiar to Westerners, and often purchased as souvenirs for macramé -style wall-hangings. Lanyard A lanyard

1584-487: 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

1650-421: 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

1716-615: Is on a small high-stemmed square pot from the Spring and Autumn period (770–476 BCE), which is now displayed in the Shanxi Museum . However, archaeology research has found that the earliest decorative knot artifact in China can be traced back to 4000 years ago, when a three-row rattan knotting of a double coin knot was excavated from Liangzhu ruins. Knots gradually evolved into a distinct decorative art in China , beginning with

1782-450: 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,

1848-695: 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

1914-618: The Northern dynasties period (317–581), and on silk paintings from the Western Han period (206 BCE – 9 CE). Archaeological and literary evidence indicate that knots were used in China as a method of keeping records, especially to assist in governance . The practice had some similarities to the Incan practice of quipu . Several works of classical Chinese literature make reference to it. The Tao Te Ching (ca. 400 BCE) alludes to

1980-529: The Qing dynasty (1644–1911), Chinese knotting evolved from folklore to an acceptable art form in Chinese society. The Lào zi culture again became popular during the Qing dynasty. During that time, basic knots were widely used to embellish everyday objects such as ruyi , sachets , purses, fan tassels, spectacle cases, and rosaries, and the single knot technique was extended into complicated knots. According to

2046-556: The 1970s, when Lydia Chen helped bring about a renewal of interest in the art form through the Chinese Knotting Promotion Center. Chinese knotting has since become a popular symbol and souvenir in festivals and commodity markets . The use of pan kou on clothing and knots as a folk craft remains alive in China. The knot-tying tradition in Japan is called hanamusubi , a term composed of

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2112-597: 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

2178-634: The Chinese classical novel Dream of the Red Chamber , the Lào zi was developed and spread between the middle and upper nobility, who used Lào zi as a way to express love and luck between family members, lovers, and friends. It was also a form of honorable craftsmanship studied and created by maids in the Imperial Palace. As written in the Gongnü Tan Wang lu ( 宫女谈往录 ), when knotting,

2244-461: The Chinese knots. In function, Japanese knots are more decorative than functional. With a greater emphasis on the braids that are used to create the knots, Japanese knotting tends to focus on individual knots. In Korea , decorative knot work is known as maedeup ( Korean :  매듭 ), often referred as Korean knotwork or Korean knots in English. The Korean knotting techniques

2310-516: The Tang and Song dynasty (960–1279 CE), the love-based knot became an important symbol, as evidenced in many of the poems, novels, and paintings of the era. In the memoir Dongjing Meng Hua Lu ( 東京夢華錄 ) written by Meng Yuanlao , it is observed that in the traditional wedding custom , a Concentric knot needed to be held by the bride and groom. Other ancient poems used the Concentric knot to portray love, such as Luo Binwang 's poem: "Knot

2376-544: 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

2442-463: The agreement by tie cords due to lack of characters." [其吏治，无文字，结绳齿木为约]. In addition to their use in recording, knots became a totem and belief motif. A double coin knot pattern painting on a silk banner was discovered by archaeologists in the Mawangdui tombs (206 BCE – CE 9). The pattern is of intertwined dragons forming a double coin knot in the middle of the fabric painting. The upper part of

2508-483: The art of tying knots dates back to prehistoric times. Discoveries include 100,000-year-old bone needles used for sewing and bodkins used to untie knots . Due to the delicate nature of the medium, little evidence of prehistoric Chinese knotting exists today. Some of the earliest evidence of knotting has been preserved on bronze vessels from the Warring States period (481–221 BCE), Buddhist carvings from

2574-482: 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

2640-623: The development of more sophisticated techniques and increasingly intricate woven patterns. During the Song and Yuan dynasties (960–1368), the Pan Chang knot , today's most recognizable Chinese knot, became popular. Much artwork evidence has also shown the knots as clothing decoration during the Ming dynasty (1368–1644); for instance, in Tang Yin 's artwork, a knotting ribbon is clearly shown. During

2706-460: 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

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2772-417: The fabric painting depicts the ancient deities Fuxi and Nüwa , the initiators of marriage in China, from whom many ancient poems derive "love" as a meaning of the double coin knot. There is evidence from the 3,000-year-old Yinxu oracle bone script that knots were recognized as symbols rather than for functional use. According to Lydia Chen, the earliest tangible evidence of knots as a decorative motif

2838-407: 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

2904-477: 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

2970-408: 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

3036-585: 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

3102-421: 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

3168-404: 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

3234-481: The maids of Ci Xi were able to quickly produce many different knots. There was little development of knotting during the Republic of China (1912–1949). Simpler knots were popular, for example the pan kou , which had been developed before the Qing dynasty, used knot button ornaments designed particularly for the cheongsam in this period. Knowledge and interest in Chinese knotting had declined considerably by

3300-587: The main work. Chinese knots are created in a variety of colors such as gold, green, blue, or black, though the most commonly used color is red, which symbolizes good luck and prosperity. Chinese knot scholar Lydia Chen lists eleven basic types of Chinese decorative knotwork. Complex knots are constructed from repeating or combining basic knots. 中国纽扣结(simplified) 三叶草结 (simplified) 十字结 (simplified) 双结 (simplified) 双钱结 (simplified) 好运结 (simplified) 盘长结 (simplified) 平结 (simplified) 圆锦结(simplified) 万字结 (simplified) Archaeological studies indicate that

3366-452: 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

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3432-510: The officers could be regulated, and (the affairs of) all the people accurately examined." The Eastern Han (25–220 CE) scholar Zheng Xuan , who annotated the Yi Jing , wrote that: "Big events were recorded with complicated knots, and small events were recorded with simple knots." [事大，大结其绳；事小，小结其绳]. The chapter of Tubo (Tibet) in the New Book of Tang says: "The government makes

3498-469: 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

3564-468: The practice in chapter 80. As translated by Wing-tsit Chan : "Let the people again knot cords and use them (in place of writing)" [使民復結繩而用之] The Yi Jing , Xi Ci II (ca. 168 BCE ), describes the practice: "In the highest antiquity, government was carried on successfully by the use of knotted cords (to preserve the memory of things). In subsequent ages the sages substituted for these written characters and bonds. By means of these (the doings of) all

3630-459: 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

3696-546: The ribbon as the Concentric knot, interlock the love as the clothes." [同心结缕带，连理织成衣]. It was also mentioned in a poem written by Huang Tingjian : "We had a time knotting together, loving as the ribbon tied." [曾共结，合欢罗带]. The most famous poem about the Love knot was written by Meng Jiao in Jie Ai ( 结爱 – lit.   ' Bond of Love ' ). The phenomenon of knot-tying continued to steadily evolve over thousands of years with

3762-408: 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

3828-413: 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

3894-425: 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

3960-403: 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

4026-559: The use of ribbon knotting and decorative knots on clothing during the Spring and Autumn period. This is attested in the Zuo Zhuan , where it is written that: "The collar has an intersection, and the belt is tied as knots." [衣有襘．帶有結] Chinese knotting was thus derived from the Lào zi culture. The Chinese word Lào is an ancient Chinese term for knots, and it was customary to tie a knot at

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4092-471: 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

4158-492: The waist with silk or cotton ribbon. The Sui and Tang dynasties (581–906 CE) saw the first peak of the Lào zi culture when basic knots, such as the Swastika knot and the round brocade knot, became popular adornments on garments, both among the nobility and the commoners. Knots were cherished not only as symbols and tools, but also as an essential part of everyday life to decorate and express thoughts and feelings. In

4224-406: 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

4290-414: The words hana , meaning "flower", and musubi , meaning "knot". The hanamusubi is a legacy of the Tang dynasty of China, when a Japanese Emperor in the 7th century was so impressed by Chinese knots which were used to tie a gift from the Chinese that he started to encourage Japanese people to adopt the practice. Japanese knots are more austere, formal, simple, and structurally looser than

4356-426: Was the primary medium at the time. Decorative cording was used on silk dresses, to ornament swords, to hang personal items from belts for the aristocracy, and in rituals, where it continues now in contemporary wedding ceremonies. Korean knotwork is differentiated from Korean embroidery . Maedeup is still a commonly practiced traditional art, especially among the older generations. The most basic knot in maedeup

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