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.
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.
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.
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
... best
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.