Search for a tool
Knots Notation

Tool to identify a node and convert it to different notations (Alexander – Briggs – Rolfsen, Dowker – Thistlethwaite, Conway)

Results

Knots Notation -

Tag(s) : Notation System, Symbol Substitution

Share
Share
dCode and more

dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!
A suggestion ? a feedback ? a bug ? an idea ? Write to dCode!


Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!


Feedback and suggestions are welcome so that dCode offers the best 'Knots Notation' tool for free! Thank you!

Knots Notation

Knots Identifier/Decoder




See also: Conway Sequence

Answers to Questions (FAQ)

What is the knot notation? (Definition)

In node theory, in order to distinguish the different types of nodes and to characterize them in a unique way, several notations have been proposed.

What is the Alexander–Briggs–Rolfsen notation?

The Alexander – Briggs – Rolfsen notation is one of the oldest, presented in 1927, this notation of nodes allows an organization according to the number of crossings.

The notation is presented with 2 numbers, the first is the number of crossings, the second is the order among all the nodes having the same number of crossings (sometimes indicated as a subscript). This second number is arbitrary but tends to represent the complexity of the node, the simpler nodes have small indices.

Example: The trefoil knot char(02) is represented 31 ou 31

What is the Dowker–Thistlethwaite notation?

The Dowker – Thistlethwaite notation is named after Clifford Hugh Dowker and Morwen Thistlethwaite. The notation is generated by traversing the node from any point and any direction, noting each of the n crossings from 1 to 2n in order (the crossings are visited 2 times, so they are noted 2 times) with an additional rule : if the crossing is done from above, note -n instead of n. Then remove all odd numbers from the list obtained. The final Dowker – Thistlethwaite notation is the remaining even number list.

Example: The trefoil knot char(02) is represented 4,6,2 (or -4,-6,-2)

What is the Conway notation?

Conway's notation was proposed in his theory of entanglements in 1970. This notation describes the node according to its properties.

Source code

dCode retains ownership of the "Knots Notation" source code. Except explicit open source licence (indicated Creative Commons / free), the "Knots Notation" algorithm, the applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, breaker, translator), or the "Knots Notation" functions (calculate, convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (Python, Java, PHP, C#, Javascript, Matlab, etc.) and all data download, script, or API access for "Knots Notation" are not public, same for offline use on PC, mobile, tablet, iPhone or Android app!
Reminder : dCode is free to use.

Cite dCode

The copy-paste of the page "Knots Notation" or any of its results, is allowed (even for commercial purposes) as long as you credit dCode!
Exporting results as a .csv or .txt file is free by clicking on the export icon
Cite as source (bibliography):
Knots Notation on dCode.fr [online website], retrieved on 2024-12-02, https://www.dcode.fr/knot-notation

Need Help ?

Please, check our dCode Discord community for help requests!
NB: for encrypted messages, test our automatic cipher identifier!

Questions / Comments

Feedback and suggestions are welcome so that dCode offers the best 'Knots Notation' tool for free! Thank you!


https://www.dcode.fr/knot-notation
© 2024 dCode — The ultimate 'toolkit' to solve every games / riddles / geocaching / CTF.
 
Feedback