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
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
pour ceux qui seraient plus à l'aise avec la langue française qu'avec
la langue anglaise une adaptation a été faite.
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
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
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 ;-) :
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.
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
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.
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.
