Author Topic: Symmetric bends - definitions  (Read 6759 times)

sgrandpre

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Re: Symmetric bends - definitions
« Reply #15 on: October 30, 2017, 06:18:48 PM »
In the correct dressing state that is #1415 (Double Fishermans) - each half - ie, each double overhand knot strangles the SPart in an opposite direction relative to the other. For example, one side strangles an SPart in a clockwise direction while the opposite side strangles an SPart in an anti-clockwise direction.

If both sides strangle the SPart in the same direction - it wouldn't be #1415 anymore. It would be a 'derivative' of #1415 deliberately tied in such a way as to achieve a  particular symmetrical outcome. So again, this is simply forcing a change in the basic structure to achieve an outcome.

You make a good point.  The point symmetric version of the knot is not in fact #1415. 

However, #1415 as shown in ABOK is in fact rotationally symmetrical (about the axis that comes straight out of the page).  That is to say, if you rotate the image so that the top of the page is now facing downwards, the knot will be identical. 

Dan_Lehman

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Re: Symmetric bends - definitions
« Reply #16 on: October 31, 2017, 12:18:59 AM »
In the correct dressing state that is #1415 (Double Fishermans) - each half - ie, each double overhand knot strangles the SPart in an opposite direction relative to the other. For example, one side strangles an SPart in a clockwise direction while the opposite side strangles an SPart in an anti-clockwise direction.

You make a good point.  The point symmetric version of the knot is not in fact #1415. 

However, #1415 as shown in ABOK is in fact rotationally symmetrical (about the axis that comes straight out of the page).  That is to say, if you rotate the image so that the top of the page is now facing downwards, the knot will be identical.

!?  I don't follow the "opposite direction" assertion : they are of
like handedness, which IMO is same direction.

In a simple test of "symmetry", my take is that if one
moves from one half/end to the other and nothing
changes except for perhaps *mirroring* geometry,
... .:. "symmetric".


--dl*
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agent_smith

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Re: Symmetric bends - definitions
« Reply #17 on: October 31, 2017, 01:16:35 AM »
Quote
!?  I don't follow the "opposite direction" assertion : they are of
like handedness, which IMO is same direction.

This actually depends on ones perspective. And I think we are talking about 2 different things here... although we both understand the underlying concepts.
In terms of handedness, yes they do have the same chirality.
But, when tying #1415 double fishermans, you do have to do one of 2 things:
1. Tie the first strangled double overhand knot then - perform a 180 degree rotation before tying the opposite strangled double overhand knot
2. Alternatively, hold the ropes statically (no rotation) - tie the first strangle, then tie the other (but you will have to reverse the direction of one of the strangles from your perspective.

I'm sure that you are aware of this..when teaching new knot tyers to tie #1415, a common error is that they end with one of the strangled knots tied in the wrong direction (very common error).

EDIT: Added a photo showing typical tying error (one of the strangled knots is tied in the wrong direction...its all a question of perspective)... OR another way to describe this is 'Reference frame'. When tying this knot - you need a reference frame to be able tie each strangled double overhand knot in the appropriate direction, otherwise you will end up with the wrong geometry (per attached photo below). Beginners make this mistake all the time (and I even noticed the same error with a bunch of climbing guides earlier in the year - where virtually all their 'prusik loops' had the #1415 double fishermans knot incorrectly tied).

Mark G
« Last Edit: October 31, 2017, 06:29:37 AM by agent_smith »

Dan_Lehman

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Re: Symmetric bends - definitions
« Reply #18 on: November 02, 2017, 01:07:44 AM »
1. Tie the first strangled double overhand knot then - perform a 180 degree rotation before tying the opposite strangled double overhand knot

How things get fouled :: THIS is my conjecture to
what Clyde Soles did** in The Outdoor Knots for
the "square fisherman's" (squaREef with strangled tails).

And so he in fact ended up making/photographing
instead a "thief'd fisherman's (arguably better,
in that with some slippage in the base knot the
strangles will be drawn to abut it and thus
be more secure vs. loosening!

(**As, presumably, he was working with a short
length of play rope, not many metres of it.)


--dl*
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agent_smith

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Re: Symmetric bends - definitions
« Reply #19 on: November 07, 2017, 03:04:23 AM »
Diagram showing the 'Point inversion symmetry' as advanced by DDK (where are you DDK...please come back!)

Roger Miles wrote a technical book on "Symmetric Bends: How to join two lengths of cord".

Here is a negative criticism of his work...
[ ] the photo image quality (in general) is poor
[ ] the blueprint line drawings are hard to follow - the concept is good but the execution is bad
[ ] he introduces complex subjects with little background explanation as to their meaning and/or how they were derived
[ ] his '+' and '-' bends weren't really explained with detailed side-by-side images showing precisely what he means (somewhat vague assumptions from my point-of-view)
[ ] it is heavy on math - while this is not 'bad' per se...its just that he offers little explanation for the equations and computations (it is assumed that the reader is a mathematician) . he does not state explicitly who the book is aimed at (but he does encourage all to read and experiment).
[ ] he should have illustrated his book with many more drawings to support his theories (a picture speaks a thousand words)

The positives...
This was a 1995 publication - essentially before the digital age
[ ] in fairness to Roger, he likely didn't have access to quality camera and/or how to take quality photos of knots
[ ] he likely didn't have access to computer software drawing programs - so he probably had to draw the blueprint line drawings by hand (tedious work)


...

Anyhow, I am hoping to make things easier for the interested reader (with the benefit of the digital age and higher quality images)...
Mark G
« Last Edit: November 07, 2017, 03:07:23 AM by agent_smith »

 

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