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Knot and Braid Theory help


Two years ago, I wrote a paper for Bridges about using Knot and Braid Theory to assist in designing a braid to tie into a knot.  The amount of Theory used is very basic, intro type stuff (self taught from a few chapters of Adams plus Wolfram Alpha online documentation).  I was rejected for being inaccurate/mistakes while at the same time not spending enough time defining (basic to the subject matter!) terms.  :'(  I believe that any inaccuracies were due to cutting an 8 page document down to 4 for page count purposes... >:(  but I'd like someone to proof read my math before I try to post/publish the info anywhere else.

So do you, or someone you know, have a reasonable grasp of basic knot and braid theory?   :o  Did you learn it in a school or spend more than a couple of weeks bootstrapping yourself?   :-[   Can you help me proofread my concepts?   ;D  Do you have the time to read and comment on an 8 page math paper (with lots of pictures!!  :) )?

I like to think that my theorizing which resulted in physical objects that I believe illustrate my points are more or less proof that I'm not completely off-base or just incredibly lucky?

i kinda have my own model of understanding and decoding, perhaps off the beaten trail.
But still, would not mind seeing if can sharpen my talon(t)s against this and see where it goes/what ya go.
Perhaps open positing link would give more general output of many, with that more tangible input of link for all.
i think all support structures are a given geometry(s) in given material(s); and what seems like light magic is yes, really math/geometry and sine/cosine the decoder ring/key that tensions input against controls of nips, grips and frictions are applied with; especially where specifically ALL Bends and Hitches input where clean running linear force of any length that then gets radial control asserted/converted inside knot microcosm of arc/deformities. 
Linear focused force, dispersed to radial to be then controlled easier.
Opposite flow and thus result, of opposite target of taking a radial explosion force and concentrating it's total sum to focused linear, like to fire bullet or piston.

I didn't want to publicly post until I was sure I didn't have some egregious errors but I guess this forum has a fairly small and specific reach....?  So here's an expanded 9 page draft.  Still needs more polish and I'm debating adding in a bunch more "diagrams" like screen shots of Mathematica/Wolfram Alpha output... plus I just noticed that I've left a temporary photo caption in there...  So be kind!!!   ;D

Endgame since Bridges was a bust is probably something for Knotting Matters/Knot News and/or The Braid Society Strands plus maybe a monograph?  If I get enough feedback in time, there's an Instructables making with Math contest....   ;)


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