Author Topic: Generalised Turk's-head knots  (Read 8331 times)

struktor

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Generalised Turk's-head knots
« on: November 04, 2010, 08:58:14 PM »
A Turk's-head knot is made of one line (cord).
If we take under consideration using more than one line to do it,
it can give us opportunity to set Turk's-head knots easily in order.
This is the example for 4 and 5 lead knots.
I wrote the program to draw schemes of these knots, which is available from:
http://www.narval.republika.pl/

WM

Knot Head

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Re: Generalised Turk's-head knots
« Reply #1 on: November 10, 2010, 05:49:29 AM »
Very nice ! I like the simple light weight layout. Nice work struktor. The program renders quickly and lays out the turks head in a labyrinth for making a mat fairly easy. I like it.

Brian...
Regards,
Brian Kidd

squarerigger

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Re: Generalised Turk's-head knots
« Reply #2 on: November 10, 2010, 07:30:40 AM »
Great job Struktor and welcome to the site!  Thanks for posting this!

SR

struktor

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Re: Generalised Turk's-head knots
« Reply #3 on: November 12, 2010, 08:42:22 PM »
Thank you for your warm opinions about my post.

One day, while making a Turk's head knot, I made a mistake and instead of a ring, I created a perfectly symmetrical Mobius strip.

I was really surprised and interested by this new possibility, let's call it: Turk's head Mobius knot.
I decided to define the rules of making this kind of Turk's head knot ( shape of Mobius strip)
Looking for regularity, I was generating normal Turk's head knots of even number L (Lead) using my own program.
Next, I was cutting them and gluing them together again ( virtually) after turning both ends - angle 180 degrees,
by analogy to a normal way of making paper Mobius strips.

What have I noticed? A one strand knot B5L4S1   http://narval.republika.pl/b5l4s1.jpg
can be changed into a one strand Mobius strip described above ( cutting, turning, gluing)

To my surprise also two strand knots can be changed into a one strand Mobius strip B10L6S2
http://narval.republika.pl/b10l6s2.jpg

As you know, Mobius strip has only one edge.
It is not possible for me to create ( by this method of cutting and turning a normal knot) an odd number of bights on this one edge.

After this introduction, I can ask the right question :
Does a case with an odd number of bights on the edge of Turk's head Mobius knot exist?

WM

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Re: Generalised Turk's-head knots
« Reply #4 on: November 13, 2010, 06:28:50 AM »
I was wondering if you could possibly make a way to save and print the generated diagram?

As far as you question goes, I imagine that you would have to look on the net far and wide to find something like you're talking about.

Brian...
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Brian Kidd

struktor

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Re: Generalised Turk's-head knots
« Reply #5 on: November 13, 2010, 12:24:27 PM »
After turning lower end - angle 180 degrees design is identical, but then changes lines:
 1 <> 7
 3 <> 9
11 <> 5
http://narval.republika.pl/b22l6s1_m.jpg

http://narval.republika.pl/b22l6s2.jpg

struktor

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Re: Generalised Turk's-head knots
« Reply #6 on: November 13, 2010, 06:54:01 PM »
I do it like this:

1. Press PrintScreen key
2. Paste to Paint.net , or other graphic program
3. Rectangle select
4. Crop to selection
5. Save or Print

http://www.getpaint.net/index.html

Perhaps one day, when I have more time, I will insert printing directly from the program.

WM