Author Topic: Lees link Bowline (discovery date)  (Read 7173 times)

agent_smith

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Re: Lees link Bowline (discovery date)
« Reply #15 on: September 25, 2022, 07:01:40 AM »
In relation to reply #14 (per Dan Lehman):

Quote
Put a knot as a Tangle --all "ends" (S.Part(s), Tail(s), (eye legs))
run off from knot & outside the Tangle boundary.  I'm pretty much
only musing about "2-Tangles" --of simple joints & eye knots,
mostly, with 2 pieces of knotted material ID'd as "1-2" entangled
with "A-B" (1, B, 2, A the 4 "ends").

Just trying to decipher this tangle of words :)
Perhaps you are eluding to an end-to-end joining knot - from which 4 eye knots can be derived (within a chiral domain)?
If so, I've attached an image showing the correspondence between a parent 'bend' and its 'child' eye knot(s).
In this example, the 'parent bend' is Lees link joint... and the Lees link Bowline from which it corresponds.
I have not shown the other possible eye knot combinations.


...

Given that this is posted in the 'new knots' section, are you making a claim of originality?
If yes, what exactly are you claiming?

Dan_Lehman

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Re: Lees link Bowline (discovery date)
« Reply #16 on: September 25, 2022, 07:55:40 PM »
In relation to reply #14 (per Dan Lehman):

Quote
Put a knot as a Tangle --all "ends" (S.Part(s), Tail(s), (eye legs))
run off from knot & outside the Tangle boundary.  I'm pretty much
only musing about "2-Tangles" --of simple joints & eye knots,
mostly, with 2 pieces of knotted material ID'd as "1-2" entangled
with "A-B" (1, B, 2, A the 4 "ends").

Just trying to decipher this tangle of words :)
Perhaps you are eluding to an end-to-end joining knot - from which 4 eye knots can be derived (within a chiral domain)?
You want "allude" --I'm not escaping anything.
And an asymmetric e2e joint gives rise to EIGHT (8)
eye-knots --each end of the joint playing its turn at
S.Part with either of the two other-piece's ends to tie
into for forming the eye.
1-v-A joint, B & 2 ends tails
=>
1-v-2+a,
1-v-2+b
...
B-v-A+2

Quote
If so, I've attached an image showing the ...
correspondence
=> "a correspondence"

Quote
In this example, the 'parent bend' is Lees link joint...
and the Lees link Bowline from which it corresponds.
My discovered "Doubly HAH!" makes your sort of correspondence
using the opposite joint S.Part as EK S.Part.  Ha!

As for Lee's Link, X. went from one EK to bolster some
things, and to make it NSUEnds; I had already crossed
this ground --as noted above-- save for a further tucking
out of the tail through the collar (to be NSUE), which didn't
concern me --to run through all the possibilities,
just as putting it out to make your EBSB from the general
"EB" idea manifest in the EBDB (from which there are many
known extensions that could be lopped together to form
similar and ever more entangled knots).
((I think I've voiced here the note that with some 300 EKs
illustrated on some count I made years back, I can use them
each in many combinations to form a "shared-eye joint"
(what CLDay I think christens for the one? known case,
"Twin BWLs") :: and 300 additive factorial (for 1&1, 1&2,
..., 300 & 300) = 45_150!!  Do you want claims for each one?!!   :o


--dl*
====


...

Given that this is posted in the 'new knots' section, are you making a claim of originality?
If yes, what exactly are you claiming?
[/quote]

agent_smith

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Re: Lees link Bowline (discovery date)
« Reply #17 on: September 26, 2022, 12:53:48 PM »
Quote
And an asymmetric e2e joint gives rise to EIGHT
And this holds true if you want to also count asymmetric/rotated geometries - which might be dubious or unstable when loaded.
I prefer to keep the logical primary count to 4... within a chiral orientation. Reverse the chirality and you get another 4 combinations.
But, from a purely technical standpoint, you are correct when counting each and every possible combination of eye knots that can be derived from the parent 'bend' - regardless of instability or insecurity that arises from their loading profile.

And thanks for pointing out my keyboard typos... !

Dan_Lehman

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Re: Lees link Bowline (discovery date)
« Reply #18 on: October 15, 2022, 05:59:34 PM »
Let's see if I can capture the image of Lee's Link
("bowinabowl")

Given that this is posted in the 'new knots' section, are you making a claim of originality?
If yes, what exactly are you claiming?

Per your nice photo'd image,
connect the TOP two ends --of two colors--
to form the eye of the "Doubly HAH!" eye knot,
loading the white cord's opposite end qua S.Part.
Now, the tail of this could also be a S.Part (EEL),
and both of these EKs are "fore<=>aft'ings" of
the starting one.

(-;
« Last Edit: October 15, 2022, 06:02:03 PM by Dan_Lehman »