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An error does not become truth by reason of multiplied propagation, nor does truth become error because nobody sees it.
Mahatma Gandhi

To kill an error is as good a service as, and sometimes even better than, the establishing of a new truth or fact.
Charles Darwin



Added 2012 November 18th


OFFSET, SCHAAKE'S DELTA and cordage route of FIRST RETURN in RNBCK (Regular Nested-Bight Cylindrical Knots)

This topic consider that you have a very good working knowledge of the topics dating from 2012 Sept 23rd          2012 Oct  15th            2012 Oct 19th             2012 Oct 20th and
a lot of notions exposed in the Turkshead pages series.  Having read ARIANE user's manual can only help

English language pdf

Pour les franšais j'en ai fait une adaptation et mis une entrÚe dans Page-des-franšais_12
Avoir lu le manuel d'ARIANE ne peut qu'aider



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Added 2012 October 20th

This pdf on PLY and PASS completes ( and needs the knowledge given in)  the two topics just under this one : Oct 15th : Three concepts            Oct 19th: TYPE and PASS


download PDF in English


For those having problem understanding English I made an adaptation in Page-Franšais_12

direct download in French



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Added 2012 October 19th

A 10 pages PDF ( again more images than words ) on the relations between
TYPE and PASS
in Standard Herringbone-Pineapple Knots

download in English

pour les franšais qui "ont du mal" avec la langue Anglaise il y a une adaptation franšaise dans la Page-des-franšais_12

download en franšais ici directement


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Added 2012 October 15th

A 12 pages ( more images than words ! ) on THREE ESSENTIAL CONCEPTS FOR Nested-Bight Cylindrical Knots : CORDAGE ROUTE, CODING PATTERN, COLOUR PATTERN

download


pour ceux qui seraient plus Ó l'aise avec la langue franšaise qu'avec la langue anglaise une adaptation a ÚtÚ faite.



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Added 2012 Septembre 23rd


SHPCK == Standard Herringbone-Pineapple Cylindrical Knot
SIMPLE WORDED SMALL SUMMARY on SHPCK and their TYPES or how to get them ( see a full developement in Turkshead_16)


In summary:

visualise the diagram of a SHPCK cordage route with the BIGHT-BORDERS or BIGHTS-RIMS on the LEFT and on the RIGHT ( Horizontal mandrel frame of reference so the HALF-PERIOD N░ 1 of what will be considered to be the first THK component starts on LEFT BIGHT-RIM N░1 . The  first laid THK is also called the BASE THK  or FOUNDATION THK of the SHPCK.

Now look at the THK COMPONENT which has its PINS on the LEFT  BIGHT RIM N░1 ( the outermost BIGHT-RIM -- on each bight border the BIGHT-RIM are numbered from 1 to N ( N being the Number of PASS - strict notation is not N but A ) from the outside  toward the middle of the knot ( see appropriate topic in another Turkshead page ) ; say N = 5 then 1   2  3  4  5 -------5  4  3  2  1   the distance between  the two innermost BIGHT-RIM , here 5-------5 is the SPACING  in ARIANE and ' Distance x ' in Schaake)

Having identified that foundation knot you look on which RIGHT BIGHT RIM the 
Half-Period N░1 has its   PINS : this gives the "TYPE".
If it is on BIGHT RIM N░ 5 then it is a TYPE V, if it is on BIGHT RIM N░ 1 then it is a TYPE I


Hope that help

Vous avez une version en  Franšais sur Page-des-Franšais_12


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Added 2012 August 12th

The lost source of an illustration found by Jon MAGILL.

In one of my "paper" dating from end 2007(  PART_TWO_THK-OR-NOT.pdf  ) I used an image found on the Net of which I had lost the source.

Today ( 2012, August 12th ) I received a mail from an uncommmonly civil person : Jon Magill gave some of his time in order to help me. 

Here is the text from Jon MAGILL
[open quote]

Dear Charles,

After reading one of your documents about THK's, and seeing a diagram of a cycloid on a sphere, for which you had no recollection of the source, I have found it...

The figure was created by software called "Cinderella", which appears to be able to do
many interesting things. The figure in question was a demo of an "Elliptic Cycloid".

Best regards,

--Jon Magill
[end quote][


An heartfelt thank you Jon Magill from me



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Added 2012 May 25th

FACES ( FACETS , PANELS )

FOR THE VAST  HERD  UNABLE TO UNDERSTAND THE CONCEPT
OF FACES (FACETS , PANELS)  VERSUS CROSSINGS  as explained in the topic immediately under this one here is Nautile's VISUAL HELP FOR THE DUMB !



I am using two of Schaake's knots  that are absolutely perfect examples to help even the most slow on the uptake to get those notions about right ;-) :

- 750 Crossings and 360 Faces   my knot   the compared grids made with ARIANE

- 210 Crossings and 150 Faces   my knot   the compared grids made with ARIANE


Crossings = Faces ONLY for O1-U1 all over.

Doubling and tripling augment the area of each Face but do not augment the number of
FACES as it it simple the SAME cordage route that is followed a second time ( a third time).


IMNSHO ( in my not so humble opinion) FACESare about meaningless ( except to
differentiate two knots with the equal numbers of crossings but different pattern of coding
leading to different numbers of Faces) if only because "the potential work load" is the result
of the number of crossings, the number of faces being only an index of the proportion by
which this work loadin the Over and Under sense is diminished.



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Added 2011 June 30th

ABOUT SOME WORDS THAT MAY SEEM OBSCURE TO SOME AND LEAD
TO CROSSED COMMUNICATION :

CROSSING         
                        FACE (facet)         
                                                     PASS              
                                                                    PLY



Here is my experience of those concepts.


FACE / FACEs this is used in the case of knots put to use with the FUNCTION of cover
for some volume, be it spherical or covering other shapes : cubes, anti-prisms, ovoids,
cylinders, pyramids, polyhedrons.....Imagination and geometry are the limiting factors.

Note :
If a ball core is used it CANNOT be said to be a globe knot but it is a spherical cover.
If the knot has no core, is in itself the full *volume* of the knotted structure and is not
just like a coat of paint applied on its surface then it can be said to be a globe knot.  (e.g : a
monkey-fist with no core, tightened on itself is a globe knot.

In mathematics SPHERE = AREA or SURFACE  
BALL or GLOBE == the VOLUME ( think "globe of a breast ).
Similar:  HELIX is 3-D curve  but SPIRAL is 2-D curve, do not use one when the other apply !

Spherical cover is NOT a special TYPE of knots but a "special FUNCTION" or "APPLICATION" given to SOME knots.



A FACE is *either*  ONE CROSSING as in the case of the O1-U1 coding
*or* a series of successive ADJACENT CROSSINGS of the SAME type ( e.g :O3 or
U2...). Of course adjacent along the cordage route !

A CROSSING is what we all know : the exact place where one piece of the cord is above
or under another piece of the cord in a knot and play a functional role of "locking".

A CROSSING is a wholesome entity not made of any separated "pieces" .

A FACE is to be considered as made of "pieces", those pieces being CROSSING(s)   
( at least one in the case O1-U1 where number of  FACEs= Number of CROSSINGs )


***** there can *NEVER* be MORE FACEs than there are CROSSINGs (that is obvious from the definitions : a crossing exist in itself as a 'whole' , a FACE is made of CROSSING(s)))

***** there can be AS MANY FACEs ( facets ) as there are CROSSINGs ( in the case O1-U1 or U1-O1).

***** there can be LESS FACEs than there are CROSSINGs

(see illustration ONE , illustration TWO and illustration THREE and ponder them )

In my experiences FACEs is mainly used for knots that do not have a *very particular
individuality
* well defined by mathematical criteria such as STANDARD and PERFECT HPAK (with nested bights)  or for STANDARD HERRINGBONE KNOT( no nested bight) have though of
course it is possible to count FACEs in PINEAPPLE KNOTS in particular when they are not HERRINGBONE-PINEAPPLE.
This use of "FACE" happens when those 'separate' knots are put to use with the *particular function,*  of being the covering put on the surface of a shape.

If FACE is difficult think TILE and TILING to cover the surface.

I hope this makes it clearer as far as the FACE versus CROSSING is concerned.

Now let us see some 'shade' of  usage.

In a STANDARD HERRINGBONE-PINEAPPLE KNOT (SHPAK)  FACEs are not counted but rather
it is the number of PASSes that is retained as characteristic nomenclature ; it says the length of the series of successive adjacent crossings of same type that form the herringbone pattern, it is the length "of the bone" and it is in direct correspondance with the number of BIGHTs in a BIGHT-NEST. ( We cannot say "with the number of THK components" as in a PERFECT  HPAK there is a single strand that make all the BIGHTs and BIGHT-NESTs. and there no THK component individualised by one or several strands)

PASSes as you can see pertain to INDIVIDUAL segments of  CORDAGE ROUTE.

We also  find this usage and meaning of PASSes in some Regular Knot ( single strand following a THK cordage route ) with particular pattern and  COLUMN-CODING such as  HEADHUNTER KNOTS, FAN KNOTS, GAUCHO

Some persons use, ambiguously if not outright mistakenly, PASS when they want to state that they FOLLOWED AGAIN AN ALREADY EXISTING CORDAGE ROUTE.
Essentially it is just making it "thicker".
When there is no new cordage route created by the piece of cordage that just follows ( on  the side,  as "follow the leader" ) an already laid cordage route as when one make a "doubled" THK or "double doubled" (that is tripled)  PASS is better left alone.

In such a case either use the "old expressions" (doubled, doubly doubled or triple...) or better, because less subjected to misunderstanding use PLY as 2-PLY for a doubled cordage route, 3-PLY for a tripled cordage route.



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Added 2011 July 4th

ABOUT  CASA and SOBRE by Schaake

I have always been hostile to this Casa concept but here I find ( reviewed ALL the
issues of The Braider searching that ) a mighty ally in this knowledgeable ( and how ! ) author.

Article one
Article two
Article three



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Copyright 2005 Sept - Charles Hamel / Nautile -
Overall rewriting in August 2006 . Copyright renewed. 2007-2014 -(each year of existence)

Url : http://charles.hamel.free.fr/knots-and-cordages/

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