Author Topic: Two "Eskimo"-like Janus TIB bowlines.  (Read 4237 times)

xarax

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Two "Eskimo"-like Janus TIB bowlines.
« on: December 02, 2013, 05:14:06 PM »
   There many more "Eskimo"-like Janus TIB bowlines than common Janus TIB bowlines ( as the one shown in (1)). The two "twin" bowlines presented in this thread - "twin", in the sense that they can be derived by collapsing the one or the other eye of a "base" Double TIB bowline, in a manner similar to the collapsing of the one or the other eye of the bowline on-the-bight, shown in (2) - satisfy an additional condition : the continuation of the returning eye leg, which becomes the Tail end, goes through the nipping loop for a third time ( as it happens in all Janus bowlines ), but it also goes through the "Eskimo" collar - so that the lines  follow smooth paths = trace wide curves ( around two, at least, rope diameters ) throughout the knot s nub.
   The interested reader will find out immediately that this loop is very easy to tie in-the-end. To tie it in-the-bight, he will have to spend a few more minutes, I am afraid... :) 

1. http://igkt.net/sm/index.php?topic=4697.0
2. http://igkt.net/sm/index.php?topic=4687.0 
This is not a knot.

xarax

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Re: Two "Eskimo"-like Janus TIB bowlines.
« Reply #1 on: December 02, 2013, 05:15:22 PM »
   The "back" view" of those knots :
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SS369

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Re: Two "Eskimo"-like Janus TIB bowlines.
« Reply #2 on: December 02, 2013, 10:41:21 PM »
Thanks Xarax.
I'm intrigued by the double loop.
Any chance that you would provide a loosened photo of it? Please and thank you.

SS

xarax

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Re: Two "Eskimo"-like Janus TIB bowlines.
« Reply #3 on: December 03, 2013, 03:44:25 AM »
   This double loop can be loaded from both ends. From the one, it is a double bowline based on an "Eskimo" nipping loop. From the other, it is a double bowline based on a crossing knot nipping structure. By the same token, the one single loop, when the one eye is collapsed and it is turned into an "Eskimo" collar around the returning eye leg of the other, is a two-collar ( Janus ) "Eskimo"- like bowline ( the "A" loop ) - and the other single loop, when the other eye is collapsed and it is turned into a link around the returning eye leg of the other, is a two-link crossing-knot bowline ( the "B" loop ).
   To tie the "A" "Eskimo"-like bowline in-the-end, you have first to tie the one of the four possible simple "Eskimo" bowlines - as shown with the blue rope. Then, as shown with the yellow rope, you have to form the second Janus collar around the Standing end, and, with the second leg of this collar, you have to retrace the path of the first leg, till its lowest point. Finish the loop by making the Tail end exit out of the knot s nub, now by retracing the path through which the Standing end enters into it - just as we do in most of the TIB bowline-like loops (1).
   In the tying diagram I have chosen to show the interweaved nipping structure / collar structure of this particular "Eskimo" bowline as a Carrick mat. Notice that, although the (yellow) line, as it forms the Janus collar around the Standing end, can follow a clock-wise or a counter-clockwise path, the generated knots are both TIB, and their difference is minor and insignificant - so we do not have to pay any attention to this detail.

1. http://igkt.net/sm/index.php?topic=4695.0
« Last Edit: December 03, 2013, 12:52:51 PM by xarax »
This is not a knot.

xarax

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Re: Two "Eskimo"-like Janus TIB bowlines.
« Reply #4 on: December 03, 2013, 02:13:38 PM »
  I have shown the interweaving of the nipping and the collar structures at the heart of the "base", simple "Eskimo" bowline as a Carrick mat, in an effort to offer some quantitative definition of "vast:

  Now we can dispense with any vain overreach for some pejorative qualitative definition of "vast" for a quantitative one

  In general, in a "Eskimo" Carrick mat the returning eye leg passes through 6 crossing points ( 5 when it crosses the nipping loop s line, plus 1 when it crosses itself ), so it can follow 64 x 2 = 128 different paths within and/or around the nipping loop ( x 2, because it can enter into the nipping loop from the "higher" or the "lower" entry point of the mat ). Then, to form the Janus collar, it turns around the Standing end, following a clock-wise or an anti-clockwise direction, so the number of different paths is duplicated again, and reaches 256. Then, it enters into the nipping loop for the third time, through one of the 4 openings, going from the "front" to the "back" side of the mat or vice versa, so the number is multiplied by 4 x 2 = 8, and reaches 256 x 8 = 2048. Then, it enters into the "Eskimo" collar, through one of the 4 openings, so the number is multiplied by 4, and reaches 8.192  ( that is, not even 10.000 !  :).
   Of course, many of those knots are not stable, and some of them degenerate into some others, so the total number is not so vast - but still it is not very small. Now, even if the 1 / 8 of them is TIB, we are talking about dozens and dozens of different TIB "Eskimo" Janus eyeknots like the one presented in this thread - an interesting challenge for the brave knot tyer !  :)
« Last Edit: June 06, 2015, 11:15:14 PM by xarax »
This is not a knot.