Knots: Difference between revisions

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Knots are useful for [[rigging]] for one thing.
Knots are useful for [[rigging]] for one thing. <br>
For why rigging may be relevant in the context of this wiki see page: [[Rigging]] <br>


'''Problem:''' Practical knots are not documented very systematically. <br>
<hr>
This makes learning them much faster via systematical understanding impossible and thus much slower. <br>
'''A problem the author spotted:''' <br>
'''Solution attempt here:''' Find better ways to systematically cover them to make it easier to learn them.
Practical knots are not documented very systematically. <br>
 
A lack of such educational material that is systematic in its own understanding and presentation …  <br>
★ … leaves untapped the potential of learning knots much faster <br>
★ … makes learning knots much harder and slower … <br>
especially for people with systematic mindsets that are challenged with <br>
remembering things out of context or with random ad-hoc mnenonic devices <br>
that just shift the problem of lack of context. <br>
 
'''The solution attempt here:''' <br>
Find better ways to systematically cover practical knots to make it easier to learn them given systematically building contexts. <br>
Treat all the knots as a by symmetries interwovenly connected body of knowledge.
 
<hr>
Note that this page is NOT about mathematical knots and links which need to be one or more closed loops. <br>
There exists some interesting work on a "periodic table of mathematical knots and links" but for <br>
the aim here to make learning easier by organizing practical knots more systematically <br>
this would not fit the purpose and miss the point. <br>
 
Still there is huge room for more systematic organization and didactic presentation.


== Interlocking overhand knots ==
== Interlocking overhand knots ==
[[File:Interlocking-overhand-bends 2025 english.svg|1024px|thumb|center|All basic interlocking overhand knots. Systematic coverage of all combinatorically possibilities. Featuring all to the six possible transformations.]]
{{wikitodo|Add the "periodic table of interlinking overhand knots" graphic. And link to knot forum post.}}


* https://en.wikipedia.org/wiki/Zeppelin_bend 🤝 ( https://en.wikipedia.org/wiki/Zeppelin_loop 🤠 & in-line 🛑)
* https://en.wikipedia.org/wiki/Zeppelin_bend 🤝 ( https://en.wikipedia.org/wiki/Zeppelin_loop 🤠 & in-line 🛑)
Line 21: Line 45:


== Interlocking unknots ==
== Interlocking unknots ==
{{wikitodo|Add illustrations.}}


* https://en.wikipedia.org/wiki/Carrick_bend 🤝 ( https://en.wikipedia.org/wiki/Carrick_bend_loop 🤠)
* https://en.wikipedia.org/wiki/Carrick_bend 🤝 ( https://en.wikipedia.org/wiki/Carrick_bend_loop 🤠)
* https://en.wikipedia.org/wiki/Reef_knot 🎁
* https://en.wikipedia.org/wiki/Reef_knot 🎁 (⚠️ do not use it for 🤝  as that is 💩 ☠️)
* https://en.wikipedia.org/wiki/Thief_knot 😈
* https://en.wikipedia.org/wiki/Thief_knot 😈
* https://en.wikipedia.org/wiki/Granny_knot 💩  
* https://en.wikipedia.org/wiki/Granny_knot 💩 (even for 🎁)
* https://en.wikipedia.org/wiki/Grief_knot (granny + thief) 🤦  
* https://en.wikipedia.org/wiki/Grief_knot (granny + thief) 🤦  
* https://en.wikipedia.org/wiki/Sheet_bend (two variants – same sides 🤝 opposite sides 💩)
* https://en.wikipedia.org/wiki/Sheet_bend (two variants – loose ends on same sides 🤝 loose ends on opposite sides 💩)
----
----
* https://en.wikipedia.org/wiki/Bowline 🤠
* https://en.wikipedia.org/wiki/Bowline 🤠
Line 44: Line 70:
* https://en.wikipedia.org/wiki/Reever_Knot 🌸
* https://en.wikipedia.org/wiki/Reever_Knot 🌸
* https://en.wikipedia.org/wiki/Harness_bend 🌸
* https://en.wikipedia.org/wiki/Harness_bend 🌸
* https://en.wikipedia.org/wiki/Friendship_knot 🌸 ( https://en.wikipedia.org/wiki/Friendship_knot_loop 🌸)  
* https://en.wikipedia.org/wiki/Friendship_knot 🌸 ( https://en.wikipedia.org/wiki/Friendship_knot_loop 🌸)
* https://en.wikipedia.org/wiki/Diamond_knot 🌸 (still unknots?, carrick bend derived)


== Overhand knot variants ==
== Overhand knot variants ==
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* https://en.wikipedia.org/wiki/Triple_fisherman%27s_knot 🤝
* https://en.wikipedia.org/wiki/Triple_fisherman%27s_knot 🤝


== Parallel threaded knots ==
== Parallel threaded knots (or parallel threadable knots) ==


* https://en.wikipedia.org/wiki/Water_knot (overhand) 🤝?  
* https://en.wikipedia.org/wiki/Water_knot (overhand) 🤝?  
Line 67: Line 94:
* ( https://en.wikipedia.org/wiki/Figure-eight_loop  🤠 )
* ( https://en.wikipedia.org/wiki/Figure-eight_loop  🤠 )
* ( https://en.wikipedia.org/wiki/Figure-eight_knot 🪢 )
* ( https://en.wikipedia.org/wiki/Figure-eight_knot 🪢 )
* ( https://en.wikipedia.org/wiki/Overhand_knot 🪢 )


== Friction knots ==
== Friction knots ==


* https://en.wikipedia.org/wiki/Magnus_hitch (slower to tie but better & neater) 💪
* https://en.wikipedia.org/wiki/Magnus_hitch (neater looking as line comes out parallel to incoming line) 💪
* https://en.wikipedia.org/wiki/Rolling_hitch ( https://en.wikipedia.org/wiki/Taut-line_hitch ) 💪
* https://en.wikipedia.org/wiki/Rolling_hitch ( https://en.wikipedia.org/wiki/Taut-line_hitch ) 💪 <br> Midshipmans hitch has same base topology as the taut-line hitch merely a slightly different knot dressing
* https://en.wikipedia.org/wiki/Jamming_knot 💪🤠🎁
* https://en.wikipedia.org/wiki/Jamming_knot 💪🤠🎁
* https://en.wikipedia.org/wiki/Farrimond_friction_hitch – more difficult to tie and dress but excellent slipped quick release


= Legend =
= Legend =
Line 86: Line 115:
* 💪🤠🎁 strangling loop
* 💪🤠🎁 strangling loop
* 😈 secret tampering surveilance
* 😈 secret tampering surveilance
* 🛑 stopper knot
* 🌸 ornamental
= Misc tips and notes =
'''If you memorize just one thing/knot from here go for the butterfly loop.''' <br>
Beside loops, use it to '''abandon the offset-overhand-bend and the reef-knot for extending rope length'''. <br>
''These two unfortunately are the worst possible choices that are thought and known the most.'' <br>
Learn at least one mid rope tying technique for the butterfly loop. There are two common ones.<br>
For end-to-end of rope joining (butterfly bend) without any extra memorization, <br>
you can treat the open ends as if it were a connected loop. <br>
Use any random temporary junk-knot if it helps. <br>
Untie the junk knot after the butterfly is formed. <br>
Thereby converting the loop into a bend. <br>
Direct tying of the rope-joining butterfly-bend is optional, if you wanna try that then <br>
check out the diagram on interlocking overhand bends on this page.
Beyond that memorize basic '''friction knots'''. <br>
These are least integratable in the systematic schemes here but highly practical. <br>
Rolling hitch (and optionally magnus hitch as neat variant) <br>
Inward oriented for packing and outward oriented for tensioning. <br>
The '''double overhand noose is nice for a self-tightening loop''' that <br>
can self-dissolve when it can be pulled from a carabiner or stick. <br>
Also the double overhand knot is good for the fishermans knot/bend. <br>
It's the same tying technique so not much additional memorization effort. <br>
Just switching the handedness correctly can require a bit of practice. <br>
'''Mid rope tieable knots without access to the ends are nice.''' <br>
Beside the butterfly loop there is also the constrictor knot which has this property too. <br>
The constrictor is a (hard to untie) hitch though with very different application cases. <br>
There is also the very trivial most basic slip knot that can be handy in cases. <br>
== Practizing tricks ==
Here is a '''practicing trick''' that … <br>
– allows one to re-derive some knots via their interrelations. <br>
– allows for refreshing memory by tinkering a bit. <br>
Try to intentionally manually capsize some named interlocking unknots to arrive at named hitches (and vice-versa). <br>
This works in many cases. Not for the carrick bend. For this one one gets a bad hitch that would be quite a mess. <br>
Thus it does not capsize and is safe and good. <br>
The carrick bend is similar to the zeppelin bend in safety and easy untiability after loading <br>
but the former is interlocking unknots the latter is interlocking overhand knots. <br>
== Advanced ==
'''Tricky:''' <br>
★ Many knots can be made into loops including e.g. the zeppelin bend. <br>
★ With access to an end the interlocking overhand knots can be tied mid rope <br>
– as stopper knots for the ones that would come out at opposing ends (i.e. normally loose ends fused and minimal length) <br>
– as loops for the ones that come out at same side (i.e. normally loose ends make a loop) <br>
For '''some of the most practical ornamental knots''' (so far practical applies here) <br>
where two strings go in parallel and come out parallel there are useful: <br>
★ the shakehands knot but with one end threaded in the opposite direction (tricky) <br>
★ two-strand diamond knot (a variant of the carrick bend with additional threading that needs quite a bit of working) <br>
★ the snake knot: [https://commons.wikimedia.org/wiki/File:Schlangenknoten.png (snake knot graphic)] <br>
= Relation to mathematical knots =
There has been indeed discovered something like a periodic table of knots. <br>
Giving a systemic scheme to programmatically generate all possible knots and links. <br>
Minimum Braids: A Complete Invariant of Knots and Links
https://arxiv.org/abs/math/0401051
There are several issues for bridging from this to practical knots. <br>
* For every knot thee often are multiple way to dress it which is information that goes beyond the mere topology of the knot.
* Mathematical knots are always based on closed loop strings
= Relation to nanoscale =
Nanotubes are likely not very suitable to tie knots into them <br>
as smaller bending radii will make them collapse king and cause breakage of covalent bonds.


= Related =
= Related =


* [[Rigging]]
* '''[[Rigging]]'''


= External links =
= External links =
Line 105: Line 208:
* https://en.wikipedia.org/wiki/Category:Knot_stubs
* https://en.wikipedia.org/wiki/Category:Knot_stubs
* https://en.wikipedia.org/wiki/Category:Double_knots
* https://en.wikipedia.org/wiki/Category:Double_knots
* https://en.wikipedia.org/wiki/Category:Hitch_knots
* https://en.wikipedia.org/wiki/Hitch_(knot)
----
----
== Knot forum discussions ==
* [https://forum.igkt.net/index.php?topic=6989.msg46738 2021 – Topic: novel table for interllocking overhands bends ]

Latest revision as of 19:50, 27 December 2025

This article is a stub. It needs to be expanded.

Knots are useful for rigging for one thing.
For why rigging may be relevant in the context of this wiki see page: Rigging

A problem the author spotted:
Practical knots are not documented very systematically.

A lack of such educational material that is systematic in its own understanding and presentation …
★ … leaves untapped the potential of learning knots much faster
★ … makes learning knots much harder and slower …
especially for people with systematic mindsets that are challenged with
remembering things out of context or with random ad-hoc mnenonic devices
that just shift the problem of lack of context.

The solution attempt here:
Find better ways to systematically cover practical knots to make it easier to learn them given systematically building contexts.
Treat all the knots as a by symmetries interwovenly connected body of knowledge.

Note that this page is NOT about mathematical knots and links which need to be one or more closed loops.
There exists some interesting work on a "periodic table of mathematical knots and links" but for
the aim here to make learning easier by organizing practical knots more systematically
this would not fit the purpose and miss the point.

Still there is huge room for more systematic organization and didactic presentation.

Interlocking overhand knots

Error creating thumbnail: Unable to run external programs, proc_open() is disabled.
All basic interlocking overhand knots. Systematic coverage of all combinatorically possibilities. Featuring all to the six possible transformations.

(wiki-TODO: Add the "periodic table of interlinking overhand knots" graphic. And link to knot forum post.)

Interlocking unknots

(wiki-TODO: Add illustrations.)

Ornamental:

Overhand knot variants

Parallel threaded knots (or parallel threadable knots)

Friction knots

Legend

  • 🪢 basic knot
  • 🤝 bend - connecting end to end
  • 💪 friction knot
  • 💩 ☠️ bad and dangerous
  • ⭕ hitch knot
  • 🎁 packing knot
  • 🤠 fixed noose
  • 🤠⭕ sliding loop
  • 💪🤠🎁 strangling loop
  • 😈 secret tampering surveilance
  • 🛑 stopper knot
  • 🌸 ornamental

Misc tips and notes

If you memorize just one thing/knot from here go for the butterfly loop.
Beside loops, use it to abandon the offset-overhand-bend and the reef-knot for extending rope length.
These two unfortunately are the worst possible choices that are thought and known the most.
Learn at least one mid rope tying technique for the butterfly loop. There are two common ones.
For end-to-end of rope joining (butterfly bend) without any extra memorization,
you can treat the open ends as if it were a connected loop.
Use any random temporary junk-knot if it helps.
Untie the junk knot after the butterfly is formed.
Thereby converting the loop into a bend.
Direct tying of the rope-joining butterfly-bend is optional, if you wanna try that then
check out the diagram on interlocking overhand bends on this page.

Beyond that memorize basic friction knots.
These are least integratable in the systematic schemes here but highly practical.
Rolling hitch (and optionally magnus hitch as neat variant)
Inward oriented for packing and outward oriented for tensioning.

The double overhand noose is nice for a self-tightening loop that
can self-dissolve when it can be pulled from a carabiner or stick.
Also the double overhand knot is good for the fishermans knot/bend.
It's the same tying technique so not much additional memorization effort.
Just switching the handedness correctly can require a bit of practice.

Mid rope tieable knots without access to the ends are nice.
Beside the butterfly loop there is also the constrictor knot which has this property too.
The constrictor is a (hard to untie) hitch though with very different application cases.
There is also the very trivial most basic slip knot that can be handy in cases.

Practizing tricks

Here is a practicing trick that …
– allows one to re-derive some knots via their interrelations.
– allows for refreshing memory by tinkering a bit.
Try to intentionally manually capsize some named interlocking unknots to arrive at named hitches (and vice-versa).
This works in many cases. Not for the carrick bend. For this one one gets a bad hitch that would be quite a mess.
Thus it does not capsize and is safe and good.
The carrick bend is similar to the zeppelin bend in safety and easy untiability after loading
but the former is interlocking unknots the latter is interlocking overhand knots.

Advanced

Tricky:
★ Many knots can be made into loops including e.g. the zeppelin bend.
★ With access to an end the interlocking overhand knots can be tied mid rope
– as stopper knots for the ones that would come out at opposing ends (i.e. normally loose ends fused and minimal length)
– as loops for the ones that come out at same side (i.e. normally loose ends make a loop)

For some of the most practical ornamental knots (so far practical applies here)
where two strings go in parallel and come out parallel there are useful:
★ the shakehands knot but with one end threaded in the opposite direction (tricky)
★ two-strand diamond knot (a variant of the carrick bend with additional threading that needs quite a bit of working)
★ the snake knot: (snake knot graphic)

Relation to mathematical knots

There has been indeed discovered something like a periodic table of knots.
Giving a systemic scheme to programmatically generate all possible knots and links.

Minimum Braids: A Complete Invariant of Knots and Links https://arxiv.org/abs/math/0401051

There are several issues for bridging from this to practical knots.

  • For every knot thee often are multiple way to dress it which is information that goes beyond the mere topology of the knot.
  • Mathematical knots are always based on closed loop strings

Relation to nanoscale

Nanotubes are likely not very suitable to tie knots into them
as smaller bending radii will make them collapse king and cause breakage of covalent bonds.

Related

External links

Knot forum discussions

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