Nautile aka Charles Hamel's personal pages

page 4
page 1    page 2     page 3    page 4     page 5    page 6    page 7   page 8
  page 9   page 10    page 11   page 12   page 13    page 14



This time I invite you to a small moment of recreation : 
I propose a little game how about  playing with ropes, topology and letters (capitals letters).

Can you class this alphabet letters in these classes.

This was inspired to me by Ernest RANUCCI 1972 work Using letters of the alphabet
to look at topological concepts

Now for another trick :
try to class the letters ( capital  and then lower case for a third game ) in three classes :

               having no hole,        having one hole        and        having two holes.

Result for capitals I am giving  here



No need to be afraid, it is easy to use even if it must have been not at all easy to 'prove'
on mathematical and logical grounds.

You can drive a car without being a car mechanic or and engineer at Detroit, cannot you ?
You can use a house cleaning product without being a chemist ?

Well you can use these moves without being a topologist.

When trying to transform one knot into another configuration, to find an 'equivalent' knot,
you are not  allowed to undo and lay again the rope, no re-threading of any part, no cutting
and no gluing, only 'smooth, continuous' action, you may only 'move' it with  Reidemeister's

There are 3 distinct types of moves :

- tackling ONE crossing
- tackling TWO crossings
- tackling THREE crossings



If you want to apply the Reidemeister's moves it will be that much easier if you close your
real rope knot.

It will have the added advantage of 'desensitizing' you about topology and there seems,
from past  sorry experience on Igkt forum, to be much need of that cure in the knotting
world. No offense intended just as there is no offense intended in a medical diagnose.

Similar trick it was that I used when writing what I have named the Drawing Sequence of
Crossings (DSC) and the Great Sequence of Crossing ( GSC)
Which leads us to...



You need - it is compulsory it is in fact - to take the greatest care in avoiding
 useless crossings to get the only number of crossing that is useful :  
the minimum number of crossings.

Here is a small elementary training problem and its solution.

If you let live useless crossings  you risk having
- - a trefoil (overhand) masquerading as a quintefoil
- - or let a Non-knot live as a make believe knot.

A trefoil is just the topology appellation of the reef knot.
Cinquefoil is a real 'in the rope' knot too.



Having in mind cladistics, clads or 'grouping' I think it can be useful to get the sign of crossings.

Cladistics !!! Ha! another desensitization cure to prescribe may be ? 

Here an overhand turn  is signed 'plus' while an underhand is signed 'minus'

Now, in drawing or in cordage,  make a left and a right overhand knot.

Try to think "S" and "Z" .

Just look at that to convince yourself that PLUS/MINUS is equivalent to RIGHT/LEFT
which is equivalent to "Z" / "S".

Here is an easy trick to get the sign of the crossing :

Put one of your hand flat, palm down on the strand that is in the upper position in the
Strand is entering by the heel of the hand and exiting by the tip of the middle finger.
The lower strand in the crossing is supposed to enter the base of your thumb and exit at its

Simple :

- - - if you have to use your RIGHT hand to get the correct configuration then it is a
crossing of sign PLUS.

- - - if you have to use your LEFT hand to get the correct configuration then it is a crossing
of sign MINUS

Another mnemonic trick that came to my mind :

Cross your forearms in front of you.

Only 2 ways to do that, just as it is for the strands in a crossing : either RIGHT or LEFT
forearm goes in the Upper position ( that is the one that is nearer to your trunk if
forearms are held more or less vertical or the one nearer the sky if they are held more or
less horizontal ).
It is the direction pointed to by the "upper hand" forearm to that is  be retained as the
correct answer.

So the forearm which has the "upper hand" has its hand pointing in the correct direction for
the letter and it is giving the "oblique bar" of the letter :

LEFT hand is pointing to Your RIGHT so it is "RIGHT" and the left forearm draw the
oblique bar of the Z.

RIGHT hand is pointing to Your  LEFT so it is "LEFT" and the forearm draw the oblique
bar of the S.

Another illustration
SUMMARY for signing

Another potential tool : the lettering of crossings.

You may even want to go playing mathematician and use Gauss or Dowker's notation.

A curiosity is here. One can be 'transform'
(Please if a link is broken be kind and send me an e-mail )

Signing or lettering crossings can be a useful tool to differentiate or regroup knots, I hope
you will be willing to keep that in an open mind.


Go to page 5 of  bat's belfry

Copyright 2005 Sept - Charles Hamel / Nautile -
Overall rewriting in August 2006 . Copyright renewed. 2007-2012 -(each year of existence)

Url :