HOW TO KNOW HOW MANY LEADs AND HOW MANY
BIGHTs WILL BE
ADDED BY A GIVEN ENLARGEMENT ON A SQUARE TURK'S HEAD KNOT
( this
is a sort of follow on the enlargement of SQUARE THK ( [L -
B| = 1 ) from FOUR
very basic minimalist THK )
Those not wanting or not able for any reason to use the H48
program I wrote that gives
the results of any enlargement on any THK ( not Square ones only ) can
use this basic help.
THIS BASIC HELP WORKS ONLY FOR
THE
CASE ENLARGEMENT OF
SQUARE TURK'S HEADS KNOTS.
HOW TO FIND THE RESULT
OF A GIVEN ENLARGEMENT.
A short pondering led me to find a rule of thumb (and a
mnemonic) on
how to get the
smallest possible addition of LEAD and BIGHT : + 2L +2B
( for square THK only )
You must
start with writing the Number of LEADs ( a LEAD leads in the LOWER
is your
mnemonic ) characterizing the "starting" THK.
*** 2L 3B (
example given )
the left side 2
(L) is smaller that the right side 3
(B)
so INCREASE the LEFT side = LEFT enlargement ( LEFT side of SPart-WEnd
vector )
*** 2L 1B this time the lesser side is
the RIGHT side ( 1 -B- ) so INCREASE the
RIGHT side = RIGHT
enlargement
Another way rather quick way is ( same cases as
above
) :
- always state the LEAD /PART first ( a LEAD leads will be
the
mnemonic ) <
and >
the arrow point gives the side
of the SPart-WEnd vector where the
enlargement is to be made.
L >
B then RIGHT side of the SPart-WEnd
vector -------------------->
L <
B then <
---------------------- LEFT side of the SPart-WEnd vector
HOW
MANY L and B will be added WHEN IT IS NOT the
2L 2B already
seen
that
you want.
it will be a BIgger
enlargement so BIght
will come first in the
'divinator' ( this is your
mnemonic )
B >
L ( number of BIGHT greater than number of LEAD ) this means
that you go for a
RIGHT side of
SPart-WEnd vector------------->
B <
L ( number of BIGHT smaller than number of LEAD ) this means that you
go on
the <--------------
LEFT side of SPart-Wend ( as
the arrow points)
We know which enlargement type it will be.
How many L are added
and how many B :
simple enough.
Use the number
of LEAD and BIGHT of the pre-enlargement THK
B >
L RIGHT ENLARGEMENT will be the biggest of the two
ADDED
LEAD (L - 1) * 2
(
L>1 )
L - 1 ex
= 10L 11B L - 1==10 -
1 =
9
9 * 2 = 18 18 L will be added
giving 28L ADDED
BIGHT (B - 1 ) * 2
(B>1)
B - 1
ex 10L
11B
B - 1 == 11 - 1 =
10
10 * 2 = 20 20B will be added
giving 31B
B <
L LEFT ENLARGEMENT will be the biggest of the two
ADDED
LEAD ( L - 1 ) * 2( L>1 )
ex 11L
10B (11 - 1) * 2 =
20 giving 31L
Of course my HP48 program would tell you that a 31L 34B can be had from
a 12L 11B
but here you will have to find yourself your OWN DUMB RULE to easily
get it;
AN AWFUL LOT OF LUCK TO YOU !!! ;-O)
Added 2009
August 29th
BURNING TRACKS : ANOTHER ' STYLE ' OF ENLARGEMENT
giving a
different result from the results given by the usual enlargement
processes ( those were
explored in Summer 2008 in Turkshead-2
and Turkshead-3
with drawings, photographies
and text.
MELTING THE TRACKS ;-) Click on the thumbnail to
open a
big picture
(
quite slow
if connection speed is less than
1024 bps )
in another tab or
window.
Photo is courtesy of JIMBO ( Jim
LONG ).
Any comment just send me an email that I will
forward to Jimbo. (see
bottom of page for mail )
Best way (will be less slow to download that a web page full of
drawings) to show what
I have found is via a PDF file.
The gist of
it is that by "tweaking" a bit one of the two already
explored enlargement
processes one
can obtain a ' new perspective'.
This
preoccupation with enlargement processes is that they allow the knot
tyer not
to rely
on a whole batch of
stupidly memorized recipes but on knowledge and intelligence.
So we have only a handful of
knot ( root knots ) to know by rote (and even they are not
fully memorised with just a wee bit of
concentration and thinking one can "find again "
those
basic knot just by a small
effort of thinking along the right tracks.)
For a 3L 2B
THK
:
-- Enlargement Process on the RIGHT side of HP1(SPart-WEnd vector )
will
lead to a 5L 4B THK
-- Enlargement process on the LEFT side of HP1 will lead to
a
7L 4B THK.
In
each case
it is going from 2B to 4B
WHAT
IF I SHOW YOU THAT IT IS POSSIBLE TO GET 5B
instead of 4B
and
enlarge
a 3L 2B to a 7L 5B ?
A big thank you to
JIMBO for having been the guinea pig reader and pointing
some things in need of clarification such as HP, SPart-WEnd,
not given in
full spelling at least the first time or not explained as what is
Half-period
( people wanting a bellyful on HP Half-Period : simply explore the
Turkshead
pages )
Added 2009 December 28th
Nautile's tutorials on
HOW TO MAKE STANDARD HERRINGBONE KNOTS
Nautile's EXCEL
Worksheet : this is an adaptation to VBA Excel of
my HP48GX
program for Turk's-HeadKnots ENLARGEMENT of
Publication_3 ( see user's
tips there )
Download available here for
*** stand alone application ( Windows for sure, but may also
works with Linux and Mac with the .dll placed in the same folder.
*** User's manual
A tip = first download the User's manual and after reading it decide if
you want to go for
that application.
Another tip = so as to by-pass Net filter the .ZIP file was
renamed .000 so once you have
it on your computer hard disk rename it back to .zip and open it with
something like the
very useful ( and free ) 7zip
PLEASE SEND FEEDBACK about how it is working and with what OS.
present
version is V-2-0 : this does the whole finished knot
diagram 'at once'
This flavour draw the grid half-period after half-period at your speed
while you are making
your knot.
version V-2-0 == the current HP is in red while
the already laid HP are put in black
The last laid HP stay in red
versionV-2-1
( retired ) == the last HP, at the next push of
the button, is draw in black after
having been in red
in the' finished knot' diagram.
present
version V-2-1-1 this one correct a
small bug affecting the COLum-coded type
in the last HP in version V-2-1
Writing a multi-strand version.(
GCD>1) for the HP after HP is mathematically a whole
different kettle of fish !
Just give a swift glance at my old
exploration of that in Multi-strand Non Regular Knots algorithms (some bad typing and awkward formulation or sentence I will
have to put
right - read it
again before putting the link and realized I
omitted proofing in the past-)
2010 Oct11th
the multistrand version is working. Have to polish it for a stand alone
application.
VERY
STRONGLY SUGGESTED READING:
on the Turk's Head cordage route :
THK AND MATHEMATICS (mathematics made very easy to get, have
no fear) Part ONE Part TWO