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Counting Examples

Page history last edited by DerekSmith 14 years, 1 month ago

How to count the Overs Index for a knot


Knots are three dimensional. When a knot is finally made, some parts of it lay over other parts without actually having any binding effect, much like a coil of rope has no binding effect even though the rope may lay over (or cross) itself many times. It is only where the cord crosses itself to effect that we are interested in in order to count the OI of a knot.


The simples way to count a knots OI, is to relax the knot and 'open it up'. Spread the knot out until you have managed to lay the knot out in almost a two dimensional form with no more than two layers of cord at any one point. Move the parts of the knot around until you have arranged its parts into the simplest form, that is with the least crossing components. There is additional advantage to be gained from this step, in that it allows you to see the components of a knot, how these work together, even other ways to construct the knot.


Having 'laid out' the knot, then proceed to mark the cord at every point a cord crosses another. Then total these 'overs' to find the OI for the knot.


Example 1.


Let us first consider the simplest knot of all, the overhand knot.

Make the knot, then mark the cord each time one cord crosses another. The marked up knot should have three marks as shown in this picture.


There are three crossing points, so the overhand knot has an Overs Index of 3 -- OI-3. If you look at the OI-3 page, then you will see the overhand knot is recorded there.


Example 2.


Slightly more complicated, we will now repeat this process using the Reef knot. Make the knot and mark it up each time one cord crosses another. The marked up knot should have six crossings as shown here.




The Reef knot has an Overs Index of six. Look on the OI-6 page and the Reef knot is there along with other knots such as the Granny knot which share the characteristic of having an OI of 6.


Example 3.


The jug hitch or bag hitch is considerably more complicated because the cord lays three layers deep as these two images show;

The completed Jug Hitch


Jug hitch edge view showing the three layers of cords.


To count this knot, pull it open and lay it out until the cords are only two deep. Mark these each time they cross as in the following image.



Count up the overs. The Jug Hitch has an Overs index of 12 -- OI-12 and will be registered on the page OI-12


Counting Cylindrical Knots


Some knots cannot be laid out flat as in the above examples. The cylindrical knots are such knots because they are effectively made around a central axis. To count the OI of these knots it is necessary to open them up on this central axis. The example knot we will be using is the lovely Fiador Knot.


First tie the knot, my favourite site for instructions is here


When you have dressed the knot to its correct shape, take a cylinder and push it through the centre of the knot - that is, open the knot up on its axis like this:-


image to be inserted here of expanded knot.


Then as in other examples, proceed to mark every crossing as you progress around the knot.


image to be inserted of marking up.


You will probably notice as you mark up, that every cord as it enters the knot has two crossings. As there are 8 cords entering the knot (four from the top, and four from the bottom) you should expect the total number of overs to be 16. Indeed, when you finally count up, there will be 16 and the Fiador knot has an OI of 16 and will be registered on page OI-16

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