I recently heard about the trident loop, googled it but only found two different references,
one from the Wikipedia and the other one from here:
http://library.wustl.edu/~manynote/trident.gif
The thing is..., both of them are different! Although they both are neat and elegant, I don't know which of them
is the "true trident loop", or to which of them the tests mentioned in the Wikipedia article apply.
Thanks...
Dave Fred has done a good job of bringing rigor re knots to Wikipedia; the presentation
there, taken from one of Budworth's many books, is accurate. The image in your cited
other source differs in the topmost two crossings--one by the '3' and the one left of it at
an arrow point, which both should be reversed re Over/Under of parts (yielding an Overhand
of the same handedness as that formed in the SPart--which isn't immediately obvious in
the image, but note where the eye bight is drawn from: that makes the Overhand).
Apparently, Robert Wolfe communicated this loopknot idea to Budworth but it never (?)
made the pages of
Knotting Matters--at least, I've not found it in a quick search of
issues immediately preceding GB's particular book ('97). However, at km58:28-9 (Winter
1998), Wolfe does present a quite similarly formed loopknot which he (or the editer)
calls "Pyramid Loop?".
It's worth remarking that the so-called "Trident" LK follows the rule of association of bend
& LK that is imputed for the Butterfly siblings: i.e., the LK is formed by joining BOTH ENDS
of the bend. Compare this with the imputed kinship of Bowline & Sheetbend, as well as
Rosendahl's Zeppelin Bend with a LK promoted as its sibling--where the SPart's end forms
the eye and re-enters the knot qua opposing SPart of the bend. Only just yesterday it
occurred to me to question both of these sorts of correspondences, and think that e.g.
Ashley's #1016 Single Bwl on a Bight is the match to the "Left-Handed" Sheet Bend
--where BOTH legs of the eye assume the posture of an opposing SPart of the bend.
(And so I've now a few fiddled corresondents for Rosendahl's Bend, and the variation
for the (right-handed) Bwl, to sketch. In this line of thinking, one might find that the
Overhand & Fig.8 LKs naturally have this sort of relation of parts, though a full imple-
mentation of the concept would put in another & encombering course of parts.)
Frankly, I rather like the LK for #1452 that reeves the end back into the SPart's
Overhand as though it is the opposing SPart of the bend.
--dl*
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