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Bimini twist

The Bimini twist ^[1] is a fishing knot used for offshore trolling and sportsfishing and the creation of double-line leaders.

A Bimini twist creates a loop at the end of the line in which it is tied. The loop is secured at the top with a long barrel of coiled line created by the tying process. A Bimini twist loop is stronger than the line itself. It is one of the rare knots that does not weaken the line in which it is tied. It is a simple method of doubling your fishing line in order to prevent chafing or to create the necessary loop in order to attach a wind-on leader without using strength in the mainline. For use in fishing applications, the old standby is 20-30 initial twists in nylon monofilament and 60 or more initial-twists in Spectra-type braided line.

An article in Sportfishing Magazine in February 2007 made the claim that fewer twists created greater strength. However, the holding mechanism in a Bimini Twist is the friction created by the twists. It was quickly and has since been often demonstrated that the 12-twist knot (proposed in the article) in Spectra-braid slipped before breaking. It is not known what testing errors led to the erroneous conclusion that fewer twists made a stronger knot.

• 
  How to tie a Bimini twist
• 
  How to tie a Bimini twist
• 
  Tie with help

• Video instructions on how to tie a Bimini twist
• fisha.com

In knot tying, a bight is a curved section or slack part between the two ends of a rope, string, or yarn.^[1] A knot that can be tied using only the bight of a rope, without access to the ends, is described as in the bight. The term “bight” 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.^[2]

Sources differ on whether an open loop or U-shaped curve in a rope qualifies as a bight. Ashley (1944) treats bights and loops as distinct, stating that a curve “no narrower than a semicircle” is a bight,^[3] while an open loop is a curve “narrower than a bight but with separated ends”.^[4] However, The Illustrated Encyclopedia of Knots (2002) states: “Any section of line that is bent into a U-shape is a bight.”^[5]

In order to make a slipped knot (also slipped loop and quick release knot), a bight must be passed, rather than the end. This slipped form of the knot is more easily untied. The traditional bow knot used for tying shoelaces is simply a reef knot with the final overhand knot made with two bights instead of the ends. Similarly, a slippery hitch is a slipped variation of the single hitch that spills instantly
when the end of the rope is pulled.^[6]

The phrase in the bight (or on a bight) means a bight of line is itself being used to make a knot. Specifically this means that the knot can be formed without access to the ends of the rope.^[7] This can be an important property for knots to be used in situations where the ends of the rope are inaccessible, such as forming a fixed loop in the middle of a long climbing rope.^[8]

Many knots normally tied with an end also have a form which is tied in the bight (for example, the bowline and the bowline on a bight). In other cases, a knot being tied in the bight is a matter of the method of tying rather than a difference in the completed form of the knot. For example, the clove hitch can be made “in the bight” if it is being slipped over the end of a post or into an open carabiner but not if being cast onto a closed ring, which requires access to an end of the rope.

• Ashley, Clifford W. (1944). The Ashley Book of Knots. New York: Doubleday. ISBN 9780385040259. {{cite book}}: ISBN / Date incompatibility (help)
• Budworth, Geoffrey (2002). The Illustrated Encyclopedia of Knots. ISBN 9781585746262.

Pipe hitch
A pipe hitch, finished with a cow hitch
Names	Pipe hitch, Well-pipe hitch [1]
Category	Hitch
Related	rolling hitch, klemheist knot, Tensionless hitch, Taut-line hitch
Releasing	Non-jamming
Typical use	securing a pipe or pole
Caveat	The direction of the pulling force should be away from the wrapped coils.
ABoK	504, 2047

A pipe hitch is a hitch-type knot used to secure smooth cylindrical objects,^[2] such as pipes, poles, beams, or spars. According to The Ashley Book of Knots, a pipe hitch is “used to lower a pipe or hoist one”^[1] and as “another method of tying to a rectangular timber.”^[3]

The pipe hitch will not slip when tied correctly to a pipe or pole. This knot is a variation of the Round turn and two half-hitches.^[4][5] This knot can be used with a rope to pull a pipe or spar out of the ground,^[6] or to hoist a pipe or beam.

The pipe hitch is started by wrapping four or more coils around a pipe or pole. It is finished by tying the working end around the standing part with a clove hitch,^[1] and less commonly with a cow hitch or a buntline hitch.

• List of knots

In the mathematical theory of knots, a Berge knot (named after mathematician John Berge) or doubly primitive knot is any member of a particular family of knots in the 3-sphere. A Berge knot K is defined by the conditions:

1. K lies on a genus two Heegaard surface S
2. in each handlebody bound by S, K meets some meridian disc exactly once.

John Berge constructed these knots as a way of creating knots with lens space surgeries and classified all the Berge knots. Cameron Gordon conjectured these were the only knots admitting lens space surgeries. This is now known as the Berge conjecture.

The Berge conjecture states that the only knots in the 3-sphere which admit lens space surgeries are Berge knots. The conjecture (and family of Berge knots) is named after John Berge.

Progress on the conjecture has been slow. Recently Yi Ni proved that if a knot admits a lens space surgery, then it is fibered. Subsequently, Joshua Greene showed that the lens spaces which are realized by surgery on a knot in the 3-sphere are precisely the lens spaces arising from surgery along the Berge knots.

Two blog posts in the weblog “Low Dimensional Topology – Recent Progress and Open Problems”
related to the Berge conjecture:

The Berge conjecture, by Jesse Johnson

Knot complements covering knot complements by Ken Baker

Pile Hitch
Category	Hitch
Related	Marlinspike Hitch, Icicle Hitch
Releasing	Non jamming
Typical use	Used as a mooring hitch to attach a line to a dock or post.
ABoK	#1815

The pile hitch is a kind of hitch, which is a knot used for attaching rope to a pole or other structure. The pile hitch is very easy to tie and can be tied in the bight, without access to either end of the rope, making it a valuable tool.

A pile hitch may be easily and quickly tied either in the end or bight of a heavy line. It is remarkably secure and is easy to cast off when the left bight has been loosened by a single well-aimed kick. Recommended for medium and heavy lines.

To tie, form a loop in the bight, and wrap both strands of this loop around the pole near the pole’s end. Pull the loop around and under the rope, then finish by putting the loop itself around the end of the pole.

• 
  Form a bight and
• 
  wrap the bight around the pole and under the rope.
• 
  Put the bight itself around the end of the pole.
• 
  Tighten the hitch and ready.

• List of knots

• http://notableknotindex.webs.com/pilehitch.html

A bend is a type of knot used to unite two lengths of rope, or two parts of the same rope. Bends are used in a variety of situations, including climbing, sailing, and securing loads. They are classified based on their ability to be tightened or released, their resistance to slipping, and their strength. Some common types include the sheet bend, the double fisherman’s knot, and the double figure-eight bend. Bends allow the combined ropes to support weight or transmit force.^[1]

The common reef knot (square knot) is sometimes mistakenly tied as a bend. When used as a bend rather than a binding knot, the reef knot will capsize under sufficient tension.^[2] For this reason, the reef knot is insecure as a bend and as such is not listed as one.

Employed as a binding knot, to reef and furl sails or to tie up parcels, [the reef knot] is invaluable. But employed as a bend […], the reef knot is probably responsible for more deaths and injuries than have been caused by the failure of all other knots combined.

• List of knot terminology
• Binding knot
• Rope splicing
• Whipping knot

• Verrill, A. Hyatt (2004). Knots, Splices and Rope Work : A Practical Treatise. Project Gutenberg. (also available in Gutenberg Project website)

Pigtails (or twin tail or twintail) are a hairstyle of twin ponytails or braids on opposite sides of the head. Sometimes unbraided pigtails are called doggie ears or bunches, and usage of the term “pigtails” varies.^[1]

The term pigtail appears in English in the American colonies in the 17th century to describe a twist of chewing tobacco. One of the steps in processing the tobacco was to twist a handful of leaves together to form a compact bunch that would then be cured (dried, either with or without smoking). The term “pigtail” was applied to the bunch based on its resemblance to a twisted pig’s tail.

From the later 17th century through the 19th century, the term came to be applied to any braided (“plaited”, in British parlance) hairstyle. The British army also adopted a single pigtail or “queue” as its standard dress for long hair. British barristers continue to wear a wig with pigtails as a way to hide the hairline in an attempt to provide basic anonymity.

Robert Louis Stevenson mentions “pigtail” referring to hair and then to “pigtail tobacco” in the first and fourth chapters of Treasure Island, respectively.^[2]

Most modern dictionaries still define “pigtail” as a single tight braid. However, many speakers use the term to describe two symmetrical bunches of hair on either side of the head, braided or not.^[1]

There are numerous styles of pigtails in which a person may wear their hair. They may be braided, straightened, beaded, ribboned, in buns, fishtailed, and even French braided. Pigtails can be placed on different parts of a person’s head: high, low, or to the side.

In some regions of China, traditional culture related the wearing of pigtails to a girl’s marital status. A young, unmarried, Chinese girl would often wear two buns, or bundles of hair on either side of the head to display her availability to prospective husbands. This style of pigtails is sometimes referred to as “ox horns.” However, when this girl would marry, the two pigtails, or buns, would be replaced with just one, thus indicating her marriage.

The Manchu and later Qing dynasty men’s coiffe called the “queue” is sometimes described incorrectly as a pigtail.

Notable pigtails in pop culture include Baby Spice of the Spice Girls and Britney Spears in the … Baby One More Time music video. Fictional characters known for pigtails include Harley Quinn, Angelica Pickles in Rugrats, Sailor Moon, Louise Lasser as Mary Hartman in Mary Hartman, Mary Hartman, and Boo from Monsters Inc..^[3][4]

Bunches

Bunches (also called pigtails, bunchies, twintails or angel wings) are a hairstyle in which the hair is parted down the middle and gathered into two symmetrical bundles, like ponytails, secured near the scalp. Sometimes this hairstyle is referred to as “pigtails”, but in other cases the term “pigtails” applies only if the hair is braided.^[1]

In Japan

Unbraided pigtails are extremely popular in Japan, especially in anime and manga fandom and Japanese otaku culture.^[5] Traditionally a hairstyle worn by young girls, it has come to represent innocence, and is also known as the “twintail” or futatsu-yui (二つ結い). Anime and manga characters sporting twintails have been prevalent since the 1960s, and the hairstyle has since entered mainstream culture, in part due to Vocaloid Hatsune Miku embracing the look.^[5] This includes the creation of a “Japan Twintail Association” to promote and celebrate the hairstyle, as well as running photo spreads of models sporting the dual tails.^[5] “Twin Tail Day” is officially recognized by the Japan Anniversary Association and falls on February 2, when women post images of themselves with the hairstyle onto Twitter.^[6]

• In Japan, hair bunches are called ‘twin tails’ (ツインテール, tsuin teeru). A popular variation is the odango hairstyle, in which each ponytail is partially coiled around its base to form a small bun from which the remaining length hangs free.

• Pigtail Ordinance
• French braid
• List of hairstyles

• Media related to Pigtails at Wikimedia Commons
• The dictionary definition of pigtail at Wiktionary

Beer knot
Category	Bend
Efficiency	80%
Related	Water knot
Releasing	Jamming
Typical use	Making slings with tubular webbing
Caveat	Difficult to visually assess the length of the free end inside webbing

A beer knot is a bend used to join tubular webbing. Its most common application is in constructing slings used in rock climbing. Compared with the water knot, it has the advantages of a higher strength,^[1] smaller profile, and a cleaner appearance due to the lack of free-hanging tails. However, the beer knot can be more difficult to tie than the water knot, and one of the tails is hidden from view, making safety checks for adequate tail length more difficult.

Testing by PMI in 1995 showed that the beer knot preserves about 80% of the strength of the webbing.^[1]

The beer knot was introduced to the National Speleological Society in the 1980s by Peter Ludwig, from Austria.^[1]

• List of bend knots
• List of knots

• Video Instruction for Tying a Beer Knot

Physical knot theory is the study of mathematical models of knotting phenomena, often motivated by considerations from biology, chemistry, and physics (Kauffman 1991). Physical knot theory is used to study how geometric and topological characteristics of filamentary structures, such as magnetic flux tubes, vortex filaments, polymers, DNAs, influence their physical properties and functions. It has applications in various fields of science, including topological fluid dynamics, structural complexity analysis and DNA biology (Kauffman 1991, Ricca 1998).

Traditional knot theory models a knot as a simple closed loop in three-dimensional space. Such a knot has no thickness or physical properties such as tension or friction. Physical knot theory incorporates more realistic models. The traditional model is also studied but with an eye toward properties of specific embeddings (“conformations”) of the circle. Such properties include ropelength and various knot energies (O’Hara 2003).

Most of the work discussed in this article and in the references below is not concerned with knots tied in physical pieces of rope. For the more specific physics of such knots, see Knot: Physical theory of friction knots.

• Kauffman, L.H. (1991) Knots and Physics. Series on Knots and Everything 1, World Scientific.
• Kauffman, L.H., Editor (1991) Knots and Applications. Series on Knots and Everything 6, World Scientific.
• O’Hara, J. (2003) Energy of Knots and Conformal Geometry. Series on Knots and Everything 33, World Scientific.
• Ricca, R.L. (1998) Applications of knot theory in fluid mechanics. In Knot Theory (ed. V.F.R. Jones et al.), pp. 321–346. Banach Center Publs. 42, Polish Academy of Sciences, Warsaw.

In knot theory, a petal projection of a knot is a knot diagram with a single crossing, at which an odd number of non-nested arcs (“petals”) all meet. Because the above-below relation between the branches of a knot at this crossing point is not apparent from the appearance of the diagram, it must be specified separately, as a permutation describing the top-to-bottom ordering of the branches.

Every knot or link has a petal projection; the minimum number of petals in such a projection defines a knot invariant, the petal number of the knot. Petal projections can be used to define the Petaluma model, a family of probability distributions on knots with a given number of petals, defined by choosing a random permutation for the branches of a petal diagram.

A petal projection is a description of a knot as a special kind of knot diagram, a two-dimensional self-crossing curve formed by projecting the knot from three dimensions down to a plane. In a petal projection, this diagram has only one crossing point, forming a topological rose. Every two branches of the curve that pass through this point cross each other there; branches that meet tangentially without crossing are not allowed. The “petals” formed by arcs of the curve that leave and then return to this crossing point are all non-nested, bounding closed disks that are disjoint except for their common intersection at the crossing point.^[1]

Beyond this topological description, the precise shape of the curve is unimportant. For instance, curves of this type could be realized algebraically as certain rose curves. However, it is common instead to draw a petal projection using straight line segments across the crossing point, connected at their endpoints by smooth curves to form the petals.^[1]

In order to specify the above-below relation of the branches of the curve at the crossing point, each branch is labeled with an integer, from 1 to the number of branches, giving its position in the top-down ordering of the branches as would be seen from a three-dimensional viewpoint above the projected diagram. The cyclic permutation of these integers, in the radial ordering of the branches around the crossing point, can be used as a purely combinatorial description of the petal projection.^[1]

In order to form a single knot, rather than a link, a petal projection must have an odd number of branches at its crossing point. Every knot can be represented as a petal projection, for diagrams with a sufficiently large number of petals. The minimum possible number of petals in a petal projection of a given knot defines a knot invariant called its petal number.^[1][2]

The Petaluma model is a random distribution on knots, parameterized by an odd number ${\displaystyle 2n+1}$ of petals in a petal diagram, and defined by constructing a petal diagram with this number of petals using a uniformly random permutation on its branches.^[3]

Petal projections, and the petaluma model, can be generalized from knots to links. However, for this generalization, it is no longer possible to guarantee that all petals are non-nested. Instead, the generalized petal projections for links have a different type of standard diagram allowing some nesting of the petals.^[3]