I prefer 'SHADOW' as it entails 'a projection' and I will make use
of that notion later.
More precisely projection on an oriented horizontal plane.
So I will use 'SHADOW', being understood that this shadow while not
showing the true
nature of crossings ( High or Low ; Over or Under),
still show every
one of these crossings
once and once
Never will one crossing be superposed on another one.
At any one place there can be only one crossing
projected, be it in a 'shadow' or in a knot
By the way it is an affirmation of mathematics : any knot
can be drawn in a diagram.
Problem is just to find the right way to do it !
can be used to 'group' or 'separate' knots.
Under one shadow several different knots can hide.
This is how
to proceed to draw them.
This is my attempt at a
depiction of the concept
using real life shadows.
Would you have been able, just by looking at the shadows to
This is what make them useful to study
knots while trying to find 'group' to be use
Remember I still hope that cladistics
principles and methods can be 'adapted' to knots and
'adopted' by the
Thinking this is a bit tangled ?
Be not in fear, I am not a mathematician, I
will not make use of the full
concept invented by John H. Conway.
Tangles can be computed, what we will not do.
Still this is a good
tool to study 'real' knots.
tangle is a knot projection (or a link projection, entire
knot or part of it)
on a plane,
surrounded by a circle (I also use
2 bars as in the previous paragraph) and the knot or link
crosses the circle exactly four times, say in the four orientation NE,
I will depart from the formalism of this idea and use 'tangle' with
more than 4 parts.
Think sheepshank as an example.
One can view the four crossings as 'fixed', and with no particular
identification as tail /
working end (WEnd) or Standing part (SPart) /
This absence of identification can be really useful in studying
the knots anatomically as
tail / working end (WEnd) or Standing part (SPart) /
Load are 'physiological' (so to speak)