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TURK'S HEAD
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Without the freedom to make critical remarks, there cannot exist sincere
flattering praise
- Beaumarchais.

INTER-BIGHT CODED KNOTS MADE ON A  THK SHADOW (cordage route)
inter-bight = row-coded for horizontal mandrel ==column coded for vertical cylinder


There is a program doing the thinking part for you if you are the lazy type downloadable
in Publications_2.

Here are the three documents pertaining to that :

Row-Umanual
ROW- THE BRAINLESS RECIPE
HOW TO USE THE SLIDE RULE


Added 2009 January 10th :

EMU 48 STARTER help




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READING TIPS (IFFy sort,  but you really cannot do without) FOR
THOSE ENVISIONING PROGRAMMING
ON  :

-REGULAR NESTED-BIGHT KNOTS  (RNBK)
      *** STANDARD  ( with Herringbone Pineapple somewhere in there )
      *** ASYMMETRIC
      *** PERIODIC
or
--INTER BRAIDED KNOT

The Braider :   first is Volume , second is issue


I / 14      

II / 19  -   II : 21  -   II / 22  -   II / 23  -   II / 24  -  II / 25  -  II / 26  -  II / 27
II / 28  -  II / 29  -  II / 30

III / 31  -  III / 33  -  III / 34  - III / 35  - III / 36  -  III /42  - III / 44
for  the RNBK

and

IV  / 53     to    IV / 56 for INTER BRAIDED KNOT

following is a VERY SHORTENED perspective on  STANDARD RNBK ONLY.



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ABOUT SO-CALLED PINEAPPLE
BETTER SAID
STANDARD HERRINGBONE PINEAPPLE KNOTS



To get the whole story just buy from Dr J. TURNER Book 4/1 1991
BRAIDING - STANDARD HERRINGBONE PINEAPPLE KNOTS
just over 200 pages of articulated explanations made
clear by bright minds.

I use a lot of material from there as "fair quote".

-- one reason is that is because I cannot make it better.
-- second reason : may be you will be clairvoyant enough to buy this book.

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Prologue :

To succeed in the world it is not enough to be stupid; you must also be
well-mannered
.
Voltaire

Well I may be stupid or not but certainly I am not well-mannered when faced with
absence of critical thinking (in the highest meaning of this concept) with 100% falling back
on handed down and then swallowed whole "creed and belief" in the knots world !


Une erreur ne devient une faute que lorsqu'on ne veut pas en démordre.
Ernst Jünger

An error becomes a fault only when one does not want to let go of it.
Ernst Jünger

 problem seems to lie in :

“It ain’t what ya don’t know that hurts ya.
What really puts a hurtin’ on ya is what ya knows for sure, that just ain’t so.” ~~
Uncle Remus


Thanks Jimbo my friend for that one, but we both know that they will not let go, except
a  microscopic contingent,  that is for those happy few that I put on the public place what is
done for my sole egoistical satisfaction .

or Stephen Hawkins :
 "The greatest enemy of knowledge is not ignorance, but illusion of knowledge ",
...of that some ex-spurts and their admiring cohort of followers have heaps of.

*************************************************************

All this is the result of old notes of mine being entirely written again to include
my very recent encounter with SCHAAKE & TURNER ( S & T ) writing.  ( quotes from
them will be in green
in the main text of this page )

My old notes were done with the intent of opening trails for a future algorithm (hence a way
to code a program) dealing with  those knots since to me it clearly  appeared plain stupidity
to commence without having a sharp, detailed and precise perspective.

This classification rest upon mathematical criteria and not on personal whims.

This "objective" sorting, has internal and external validity, it is indeed to be bowed to if one
want to stand a chance of  making a working algorithm in any computer language.

I had advanced well but was still  far from being at the end point attained by S & T who
remain to this day the masters of all this topic ; they very clearly exposed the hard facts.
(sorry for those who find S & T writing  "unclear" ; I am not absolutely sure that it is not
a case of  "pilot error"  or rather "reader error" that explains it.
A sort of "hospital mocking charity")


I have always been quite irritated by the way people use " pineapple" about any knot
without neither rhyme nor reason.

A bit of 'history' :

Bruce GRANT ( Encyclopaedia of Rawhide and Leather Braiding ) qualified it
"the King of the braided knots" ; I cannot quite follow that opinion having no great interest
in ornamental knotting beyond its geometry but any how tastes and colours are not to be
discussed as they say in France.

GRANT clearly stated what was a Pineapple and it is the unthinking and unsophisticated
vox populi by the intervention of so called ex-spurts (to steal my friend Jimbo's way of
writing that word  -  seems to echo some "pissing contest" )  that made the silly jump to
a non verified equation : nested bights = pineapple.

-----------------------------------------------------------

GRANT  ( Encyclopaedia of Rawhide and Leather Braiding )

 page  134

... b
est covering I know for this foundation knot  is one I call the Pineapple Knot. It is
one of the most practical knots in braiding. As the bights or scallops on each edge are
staggered   toward the center, the knot closes on the end when tightened and, in fact,
will close on both end and completely encompass a spherical object.The pineapple 4
can be intervowen to make it larger, yet its outside bights remain the same in number,
 enabling it to close over....
It is the King of the Braided Knots, and you will find many uses for it. The Argentine
gauchos use it to cover buttons and call it the button knot"

and he then quote only ODD number of LEAD

page 420

The Pineapple or Gaucho Knot......Where the HERRINGBONE knot

( plate 171 has an interweave of two Turk's-heads of the SAME NUMBER OF  
PARTS AND BIGHTS , the pineapple knot is an interweave of two Turk's-heads
OF THE SAME NUMBER OF BIGHT BUT DIFFERENT NUMBER OF PARTS...

and he does not give anything other than odd number for the LEAD

page 416

 " It might be of interest here to say that Turk's-heads and woven knots have engaged
the attention of many profound mathematicians and a ponderous literature has been
written on them. They follow rules as inviolate as those of the planets, and the winding
and intricate, even labyrinthine, twisting can be calculated to a nicety"


I just hope that Grant knew how well  'planets' applied because as I have shown in
THK MATHEMATICS ( One and Two ) they can be drawn as hypotrochoids,
those types of cycloidic curves were used by astronomers !

----------------------------------------------------------

This sort of knots  'fall under the umbrella' ( an expression that I find absolutely  funny
--funny as in bizarre --  and  cannot resist borrowing) of another appellation :
the HERRINGBONE PINEAPPLE  Knots (HPK). 

*************************************************************

ALL knots belonging to that group  are made by INTERLOCKED THK
(see my THK OR NOT THK ) :

"True" THK of same dimension as far as number of BIGHTs is concerned.
There is only a bit of phase shift to accommodate the interlocking.

They also have an ODD number of LEADs .

Either
they ALL share a common ODD number of LEADs
or
they come in two different SETs of different ODD number of LEADs.

In one SET all have the same ODD number of LEADs
in the other set they still have a common  ODD number of LEADs that is different by
2 units from the first SET
.  

*************************************************************

 

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Copyright 2005 Sept - Charles Hamel / Nautile -
Overall rewriting in August 2006 . Copyright renewed. 2007-2012 -(each year of existence)

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