Blog

Improved clinch knot
Names	Improved clinch knot, fisherman’s knot, salmon knot
Category	Hitch
Efficiency	98%
Origin	Unknown
Typical use	fishing, angling, trapping
ABoK	#313

The improved clinch knot, also known as the fisherman’s knot^[1] or the salmon knot,^[2] is a knot that is used for securing a fishing line to the fishing lure, but can also affix fishing line to a swivel, clip, or artificial fly. This is a common knot used by anglers because of its simple tie and strong hold. The more tension is applied, the tighter the knot becomes, increasing the strength of the connection. It can be used with many kinds of line including mono-filament, fluorocarbon, and braided fishing line. The difference from the basic clinch knot is that the working end is passed through the loop that is created in the second-last step.^[3]

• List of knots

• Grog. “Improved clinch knot”. Animated Knots. Retrieved 25 April 2013.

Icicle hitch
Category	Hitch
Origin	John Smith, 1990
Related	Prusik, Klemheist knot, tautline hitch, gripping sailor’s hitch
Releasing	Unload the working end
Typical use	Tying to a post when weight is applied parallel to the post Tying to a rope when load is applied parallel to that rope
Caveat	The Klemheist knot will look almost identical, but the load with the klemheist should be applied with the bight lying across the turns on the post/rope the knot is tied to

An icicle hitch^[1] is a knot that is used for connecting to a post when weight is applied to an end running parallel to the post in a specific direction. This type of hitch will hold its place even when holding a substantial load on a smooth surface. One can even suspend from a tapered post (such as a marlinspike) with this knot (hence the name “icicle hitch”).^[2][3]

To tie an icicle hitch, bring the working end over the post, front to back, four or five times, working away from the end of the post (and the direction of expected pull). Bring the working end, back to front, alongside the standing end, leaving a substantial bight hanging behind the post. Bring this bight over both ends and over the end of the post. Tighten by pulling both ends perpendicular to the post. The pull on the standing end (running the direction of the post) will tighten the knot as more pull is given.

This knot is in the class of knots as the Prusik, klemheist, & Hedden knots –the “slip-and-grip” friction type, which pull tight when the load is applied (in the correct direction) and slide easily for re-placement with no load. The Prusik knot can withstand load in both directions, making it ideal for climbing situations. The icicle, like the klemheist, attaches to the hitched object and coils away from its pulling end, and relies on a constriction like the Chinese finger trap –under pull, the coil is drawn longer and thus tighter; whereas in the Hedden (& rolling hitch) the loading tightens the coil at its far end.

The icicle hitch was developed by John Smith of the International Guild of Knot Tyers, and demonstrated by him at the Guild’s eighth annual general meeting in 1990. It was published in the IGKT’s quarterly newsletter, Knotting Matters, in issue #32 (Summer 1990), pp.6,7.

• 
  Pull direction is LEFT, so make 5 turns to the RIGHT…
• 
  Drape working end over rod so it hangs beside standing part…
• 
  Loop the bight created around working and standing parts and over end of rod.
• 
  Set up tight…
• 
  Knot is now secure when pulled toward the left.

• List of knots
• List of friction hitch knots

• Watch how-to-tie video:
• Testing Sailing Knots that Really Grip

In mathematics, an I-bundle is a fiber bundle whose fiber is an interval and whose base is a manifold. Any kind of interval, open, closed, semi-open, semi-closed, open-bounded, compact, even rays, can be the fiber. An I-bundle is said to be twisted if it is not trivial.

Two simple examples of I-bundles are the annulus and the Möbius band, the only two possible I-bundles over the circle ${\displaystyle S^{1}}$. The annulus is a trivial or untwisted bundle because it corresponds to the Cartesian product ${\displaystyle S^{1}\times I}$, and the Möbius band is a non-trivial or twisted bundle. Both bundles are 2-manifolds, but the annulus is an orientable manifold while the Möbius band is a non-orientable manifold.

There are only two kinds of I-bundles when the base manifold is any surface but the Klein bottle ${\displaystyle K}$. That surface has three I-bundles: the trivial bundle ${\displaystyle K\times I}$ and two twisted bundles.

Together with the Seifert fiber spaces, I-bundles are fundamental elementary building blocks for the description of three-dimensional spaces. These observations are simple well known facts on elementary 3-manifolds.

Line bundles are both I-bundles and vector bundles of rank one. When considering I-bundles, one is interested mostly in their topological properties and not their possible vector properties, as one might be for line bundles.

• Khovanov homology

• Scott, Peter (1983). “The geometries of 3-manifolds”. Bulletin of the London Mathematical Society. 15 (5): 401–487. doi:10.1112/blms/15.5.401. hdl:2027.42/135276. MR 0705527.
• Hempel, John (1976). 3-manifolds. Annals of Mathematics Studies. Vol. 86. Princeton University Press. ISBN 978-0-8218-6939-0.

• Example of use of I-bundles, nice pdf-slide presentation by Jeff Boerner at Dept. of Math, University of Iowa.

In mathematics, a hyperbolic link is a link in the 3-sphere with complement that has a complete Riemannian metric of constant negative curvature, i.e. has a hyperbolic geometry. A hyperbolic knot is a hyperbolic link with one component.

As a consequence of the work of William Thurston, it is known that every knot is precisely one of the following: hyperbolic, a torus knot, or a satellite knot. As a consequence, hyperbolic knots can be considered plentiful. A similar heuristic applies to hyperbolic links.

As a consequence of Thurston’s hyperbolic Dehn surgery theorem, performing Dehn surgeries on a hyperbolic link enables one to obtain many more hyperbolic 3-manifolds.

• Borromean rings are hyperbolic.
• Every non-split, prime, alternating link that is not a torus link is hyperbolic by a result of William Menasco.
• 4₁ knot (the figure-eight knot)
• 5₂ knot (the three-twist knot)
• 6₁ knot (the stevedore knot)
• 6₂ knot
• 6₃ knot
• 7₄ knot
• 10 161 knot (the “Perko pair” knot)
• 12n242 knot

• SnapPea
• Hyperbolic volume (knot)

• Colin Adams (1994, 2004) The Knot Book, American Mathematical Society, ISBN 0-8050-7380-9.
• William Menasco (1984) “Closed incompressible surfaces in alternating knot and link complements”, Topology 23(1):37–44.
• William Thurston (1978-1981) The geometry and topology of three-manifolds, Princeton lecture notes.

• Colin Adams, Handbook of Knot Theory

Braid length	2
Braid no.	2
Crossing no.	2
Hyperbolic volume	0
Linking no.	1
Stick no.	6
Unknotting no.	1
Conway notation	[2]
A–B notation	22 1
Thistlethwaite	L2a1
Last / Next	L0 / L4a1
Other
alternating, torus, fibered

In mathematical knot theory, the Hopf link is the simplest nontrivial link with more than one component.^[1] It consists of two circles linked together exactly once,^[2] and is named after Heinz Hopf.^[3]

A concrete model consists of two unit circles in perpendicular planes, each passing through the center of the other.^[2] This model minimizes the ropelength of the link and until 2002 the Hopf link was the only link whose ropelength was known.^[4] The convex hull of these two circles forms a shape called an oloid.^[5]

Depending on the relative orientations of the two components the linking number of the Hopf link is ±1.^[6]

The Hopf link is a (2,2)-torus link^[7] with the braid word ${\displaystyle \sigma _{1}^{2}}$.^[8]

The knot complement of the Hopf link is R × S¹ × S¹, the cylinder over a torus.^[9] This space has a locally Euclidean geometry, so the Hopf link is not a hyperbolic link. The knot group of the Hopf link (the fundamental group of its complement) is Z² (the free abelian group on two generators), distinguishing it from an unlinked pair of loops which has the free group on two generators as its group.^[10]

The Hopf-link is not tricolorable: it is not possible to color the strands of its diagram with three colors, so that at least two of the colors are used and so that every crossing has one or three colors present. Each link has only one strand, and if both strands are given the same color then only one color is used, while if they are given different colors then the crossings will have two colors present.

The Hopf fibration is a continuous function from the 3-sphere (a three-dimensional surface in four-dimensional Euclidean space) into the more familiar 2-sphere, with the property that the inverse image of each point on the 2-sphere is a circle. Thus, these images decompose the 3-sphere into a continuous family of circles, and
each two distinct circles form a Hopf link. This was Hopf’s motivation for studying the Hopf link: because each two fibers are linked, the Hopf fibration is a nontrivial fibration. This example began the study of homotopy groups of spheres.^[11]

The Hopf link is also present in some proteins.^[12][13] It consists of two covalent loops, formed by pieces of protein backbone, closed with disulfide bonds. The Hopf link topology is highly conserved in proteins and adds to their stability.^[12]

The Hopf link is named after topologist Heinz Hopf, who considered it in 1931 as part of his research on the Hopf fibration.^[14] However, in mathematics, it was known to Carl Friedrich Gauss before the work of Hopf.^[3] It has also long been used outside mathematics, for instance as the crest of Buzan-ha, a Japanese Buddhist sect founded in the 16th century.

• Borromean rings, a link with three closed loops
• Catenane, a molecule with two linked loops
• Solomon’s knot, two loops which are doubly linked

• Weisstein, Eric W., “Hopf Link”, MathWorld
• “Hopf link“, The Knot Atlas.
• “LinkProt” – the database of known protein links.

Honda knot
Names	Honda knot, Lariat loop, Bowstring knot
Category	Loop
Releasing	Non-jamming
Typical use	Lassos, stringing bows
ABoK	#227, #1024, #1127, #151

A honda knot is the loop knot commonly used in a lasso.^[1] Its round shape, especially when tied in stiff rope, helps it slide freely along the rope it is tied around. To tie, first place an overhand knot in the end of the rope. Then tie a second overhand knot, pass the running end of the rope through it, and tighten.

A lariat loop is similarly constructed but will not slip from the running end. To tie a lariat loop: first tie an overhand knot, then pinch it so that the running end slides freely back and forth. Pass the rope end through just that “free-sliding” loop, and tighten. The photograph at right displays a lariat loop, with an additional overhand knot acting as a stopper knot because the lariat loop can slip by way of the rope’s end when tension is not applied to the running end. It can be quickly adjusted, but does not function exactly the same as a lasso knot, which makes it perhaps safer.

• List of knots

The hitching tie is a simple knot used to tie off stuff sacks that allows quick access as it unties quickly.^[1][2] To untie the knot, just pull hard on the free end of the rope and the knot will fall open. This is simply a noose or slip knot, with the loop tightened around an object. This is not a very strong knot for climbing or other extreme activities.

• 
  Marlinespike hitch
  
• 
  Noose

• List of knots

The clove hitch

A hitch is a type of knot used to secure a rope to an object or another rope. Hitches 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 of hitch knots include the clove hitch, the timber hitch, and the round turn and two half-hitches.

A simple mathematical theory of hitches has been proposed by Bayman.^[1] It predicts whether or not a hitch will hold, given the diameter of the post, the diameter of the rope, and the coefficient of friction between the post and the rope. The theory has been extended by Maddocks and Keller, including an approximate treatment of knots that are not hitches.^[2] For example, they predict that a square knot will hold when the coefficient of friction of the rope with itself is greater than 0.24. These predictions are approximately correct when tested empirically.^[3]

• List of knots
• Single hitch

Highwayman’s hitch
A Highwayman’s hitch tied around a wooden pole
Names	Highwayman’s hitch, Highwayman’s hitch, draw hitch, Highwayman’s cutaway, Bank Robbers Knot, Getaway hitch or Quick-release knot
Category	Hitch
Related	Tumble hitch, Mooring Hitch
Releasing	Non-jamming
Typical use	Quick-release, draw loop hitch
Caveat	Potentially unstable, especially when tied around large objects

The Highwayman’s hitch is a quick-release draw hitch used for temporarily securing a load that will need to be released easily and cleanly –i.e, that will come completely free of the hitched object.^[1] The hitch can be untied with a tug of the working end, even when under tension. The highwayman’s hitch can be tied in the middle of a rope, and so the working end does not need to be passed around the anchor when tying or releasing.^[2]

The hitch was called the highwayman’s cutaway in 1947 by Cyrus L. Day. He related that, according to Hal McKail, the knot was attributable to the notorious 18th-century English highwayman Dick Turpin. Day’s book, however, suggested it for use as a quick-release mooring hitch for solo sailing.^[2]

While the knot is alleged to have actually been used by highwaymen,^[3] this claim is rejected by knot expert Geoffrey Budworth, who stated, “there is no evidence to substantiate the reputation of the highwayman’s hitch as a quick-getaway-knot for robbers on horseback.”^[1]

The knot is three bights that each successively lock the previous one:

1. the first one, in the middle of the rope, wraps around the pole,
2. the second one (called the toggle bight) is a bight of the standing part locking the first one so the pole is held tight, and
3. the third one (called the slip-tuck) is a bight of the working part (slack end) locking the second bight.

The locking actions are achieved by reaching through each bight to pull the next one through.

The knot has to be finished by pulling the standing part tight to ensure that it holds.

Until the knot is tightened and properly dressed, the highwayman’s hitch has little holding power.
The highwayman’s hitch is susceptible to capsizing when the pole is substantially larger than the rope diameter. The failure occurs because the second bight sees the force of the standing part, but is held in place by the working part, which has no tension. When capsizing, tension on the standing part pulls the second bight through the first bight. This drags the slip-tuck through, and will release the hitch if the third bight isn’t long enough.

Alternatives to the highwayman’s hitch have been devised to mitigate collapse when tied around large objects.

One simple improvement is to repeat the second and third bights i.e. one more bight of the standing part and then one more bight of the working part, each successively locking the previous bight; this has the disadvantage of requiring longer rope from both parts.

Another technique is to twist each bight before reaching through it for the next locking bight; the disadvantage here is the difficulty of tightening afterwards.

In his book Outdoor Knots, Clyde Soles presents one of Dan Lehman’s revisions to the highwayman’s hitch that is simple and effective, naming it the “slip-free hitch” (actually, this name denotes all such hitches).^[4] One simply rearranges the trio of bights so that the heavily loaded bight in the standing part will surround, rather than go through, the next-made bight; the finishing slipped-tuck bight will thus go through the 2nd-made bight, and so be less severely loaded. As the frame against which this rope toggle is nipped is entirely parts of the knot (and not depending upon proximity to the hitched object), this revision avoids the capsizing vulnerability of the highwayman’s hitch.

The Notable Knot Index recommends the tumble hitch as a more stable hitch. It’s a similar hitch, but less prone to capsizing because the main part remains passive and the locking is done by two successive bights of the working part (no end needed) wrapping around both the standing part and the post/pole before locking the previous bight.^[5]

• List of knots

Highpoint hitch
Names	Highpoint hitch, High post hitch
Category	Hitch
Related	Buntline hitch
Releasing	Non-jamming
Typical use	Quick-release, draw loop hitch
ABoK	#398, #1809

The highpoint hitch (or high post hitch^[1]) is a type of knot used to attach a rope to an object. The main feature of the hitch is that it is very secure, yet if tied as a slipped knot it can be released quickly and easily with one pull, even after heavy loading. The highpoint hitch is tied in the same manner as a slipped buntline hitch until the final turn, where they diverge.^[2]

The highpoint hitch is very secure, since any load will tighten the turns against each other, at the same time tightening the grip on the working end.

To release the slipped version of this knot, pull the working end in the direction of the load. This action pulls the two turns apart at the same time as releasing the draw-loop, and the whole knot simply falls apart.

To tie the hitch around a pole, begin by passing the working end a half turn round the pole. Next, pass a half turn round the standing part. Then, pass a half turn round both the working end and the standing part, above the first turn (i.e. closer to the pole). Finally, push a bight of the working end through the middle of the hitch – between the two half turns, and between the standing part and the working end. Pull on the standing part to tighten, if necessary sliding the hitch snugly up against the pole.

Tying the highpoint hitch

Partially tied slipped highpoint hitch

Completed slipped highpoint hitch