Author Topic: new method for Turk's Head Knot  (Read 1973 times)

Ruby

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Re: new method for Turk's Head Knot
« Reply #30 on: May 01, 2023, 03:00:25 PM »
like the famous  Fibonacci sequence equation F[n]=F[n-1]+F[n-2]
there is an equation for golden ratio THK:
TF[n]=TF[n-3] + double + split

Jan van Leiden

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Re: new method for Turk's Head Knot
« Reply #31 on: May 01, 2023, 03:03:56 PM »
Hi Ruby,

One final reflection on your equations.

You probably know there are many other ways to generate sequences of regular knots with, for example, a U1O1 pattern.

Ever heard about the Masurel Method? Its two starts produce all p/b = 4/b THK.

I found it in KM51, pp67-69, December 1995.

Jan van Leiden

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Re: new method for Turk's Head Knot
« Reply #32 on: May 01, 2023, 03:09:40 PM »
so the direction is always changing,  left right left right.....

Indeed, and that is the first part that messes up the linear equations.

like the famous  Fibonacci sequence equation F[n]=F[n-1]+F[n-2]
there is an equation for golden ratio THK:
TF[n]=TF[n-3] + double + split

If you insist on retaining your U1O1 pattern, you can lay and split tracks, and your Fibonacci Equation will hold.

For other patterns, the story may well be different.

Ruby

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Re: new method for Turk's Head Knot
« Reply #33 on: May 01, 2023, 03:41:32 PM »
hi, just checked this article,

yes, this is the easiest linear enlargement


apply LeftSplit or RightSplit of any 2-parts THK to get any 4-parts THK,

left for 4n-1 , right for 4n+1

begin with simple  THK as 2-parts  or 1-bight, we can get quite a lot THK by only apply LeftSplit or RightSplit linear enlargement.

linear enlargement is especially useful for small THK.
for 55 THKs below 10, only 3 can not be made like this: 75 85 97, and their mirror.

Jan van Leiden

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Re: new method for Turk's Head Knot
« Reply #34 on: May 01, 2023, 04:15:30 PM »
Hi Ruby,

The point is that Masurel's Method leads to 4/b that have no direct connections in the regular knot tree via Schaake and Turner's fundamental enlargement methods.

The Masurel Method has two starts, and indeed yields two 'linear' sequences:
  • 4/(4n - 1)
  • 4/(4n + 1)
Where n indicates the number of tucks in the initial Multiple Overhand Knot.

In the regular knot tree, however, you cannot get from for example 4/9 to 4/17, short of untying.

Here are the paths:
  • 1/3 - 2/5 - 3/7 - 4/9
  • 1/5 - 2/9 - 3/13 - 4/17
It is an interesting exercise to find the location of these 4/b grid diagrams in the regular knot tree.
And subsequently the p/4 grid diagrams.

 

alana

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Re: new method for Turk's Head Knot
« Reply #35 on: May 05, 2023, 08:17:57 AM »
hi, do you have an easy method to tie THK like 7Leads x 9Bights or 9B x 7L ?

I mean, tie them easily like basic 3 Leads x 2 Bights, around your fingers,
without any grid or pin or mandrel tool.


i've got nothin'!  i need a pin board,

so 7x4 is as far as i've got tying in hand,
(in 2-pass if i consult my notes)

glad you mentioned golden raito,
i have tied 5x8 somewhere,
cant find pic,
and - i needed pin board to do so -
but proportionate and appealing


i found my 5x8, except it's a 7x8 2-pass ...!
(in case anyone wanted to see how it looks)

 

anything