## Saturday, 30 January 2010

### Thimbles are all about geometry and trigonometric function

Today's post is one of my "how I do" series but a bit heavy on a technical side. It may not make sense clearly to you, but it's not your fault. English is not my first language and I have never participated in math class in English. I would appreciate it if you could let me know, after you read this, where and how to improve it so that it becomes easier for everyone to understand.

When I first made a thimble, I made a mistake by packing too many stitches in one section. The reason I tried to make too many is a simple misunderstanding. The centre of the ring is fatter than the top and bottom because of the padding, thus I thought I had to make more stitches so that the body of the ring is nicely covered. But I was wrong. Unless the angle of the thread is too extreme or the ring is unusually fat, you don't need to worry about whether you are making enough stitches for body coverage.

You may have noticed that I said "section" instead of "segment" as before to refer the space all the stitches are made. From now on I will call them sections although I don't plant to replace the words in the old posts at the moment.

Now, like origami, thimble making is much like geometry; simple zigzag thread forming various designs and number of sections, order of stitching, and to which directions to go decide the design. However how many stitches you make in one section depends on the angle of the thread. It's trigonometric function, sounds scary doesn't it.

The above is a diagram of simple bi-coloured scales, number of sections unknown. When I talk about the angle of the thread I usually mean angle a (not clearly appeared in the picture though) and I meant angle a when I left a comment on Debi's post however, it's easier actually to explain when concentrate on angle b so from now on, it's angle b when I say sharp or otherwise.

When you have less sections, in other word wider sections, in other word again more space to stitch, the angle of the thread becomes sharper like below;

When the angle of the thread becomes sharper, the more coverage the thread makes at the middle of the body because the width of the thread becomes wider.I have realized that my English is better than my drawing :( Does the picture make sense? A horizontal black line above is a position where the two threads cross, i.e. the fattest part of the body and segment line a is a width of a thread at the top of the base where you make a stitch, segment line b is also a width of the thread (in the same width naturally) but segment line c is an actual width that covers the body. The sharper the angle becomes, the wider the actual width of the thread at the middle of the body becomes. That means the size of the sections (or you can say the number of the sections) dictates how many stitches you have to make in one section. The narrower the sections the less coverage the thread makes at the middle, and more stitches required while the wider the sections the more coverage and less stitches. Actually you can calculate how many stitches you have to make if you like.

My mould is 50mm in circumference and when sections are 8, I make 20 stitches in one section and it makes total 160 stitches while when sections are 10, the number of the stitches in one section is 18 and it makes total 180 stitches. The difference is 20 which amazingly coincides the number of the stitches I make in one section of 8. The size of the base is the same but the total number of the stitches varies depending on the angle of the thread, i.e. number of the sections of the ring.

Having said that, when the angle is too sharp then what will happen? You are of course going to make less stitches but the coverage at the edges cannot catch up with the one at the middle so either you cannot fill all the section at the top/bottom of the ring with stitches or you have to make stitches rather sparsely. I don't think either option looks very good. You can adjust it a little by adding more padding at the centre, i.e. makes your thimble very fat, so that there would be more room at the middle of the ring. My limit is 7 segments for 50mm mould ring. Perhaps I can make do with 6 but not very sure if I like the result.

Here is a summary; as you see below two diagrame, the first one has sections half as small as the second one's , i.e. the second one's thread has to form a sharper angle.

I have merged two diagrams so that you could see the angles more clearly:

When you work with red thread for the first diagram, say you make 12 stitches in one section while with blue thread for the second diagram 21 stitches. Since the section of the second diagram is twice as wide as the first one, when compared you have to make 3 more stitches to fill the TWO sections of the first diagram, which is the same as ONE section of the second diagram, and this is all to do with the angle of the thread. The sharper the angle becomes, the more thread coverage at the middle, and as a result less stitches over all.

Of course you don't need to know all of this to make your thimbles but counting the number of stitches is vital to deviate to more complex designs. When you practice next time, why don't you count the stitches and see if you could always finish off with the same number of stitches? Knowing how many stitches you can make, or rather, you are planning to make, is essential for thimble making. When you can make exactly the same number of stitches every time, then you can make do with one or two more/less stitches in the same size section when the design requires it. Say I want stripes, a set of three rows of stitches stripes, like, a set of red, red, and white. As I told you, I make 20 stitches for 8 sections, that makes one stitch short so I try to pack a little and make 21 stitches, 7 set of 3. Maybe red, red, white stripes are too bright, and perhaps I would like to add another row of red after the final white, that requires total 22 stitches, 7set of 3 plus 1. Then I can either add two stitches on top of my usual 20, or make one less stitch, i.e. 19 stitches of 6 set of 3 plus 1. Both can work fine. Adding 2 to 20 is not difficult and it maintains the original design of 7 stripes while one less stitches is easier although it changes the design a little bit.

I will host another Share Your Thimbles for February. I am thinking to continue to limit the design to bi-coloured scales for one more month and then in March it will be anything you can make with forward stitches. So please count your stitches in February so that you will be ready to explore more complex designs in March. Happy stitching.

1. Hi Chloe Patricia,

I think this is a great post. You described this exactly the way that I would have. My only suggestion to make it better would be to include two pictures to show how there is a greater distance across the thread when the angle is sharper: one with a sharp angle and one with a shallow angle. Then the reader can clearly see the difference instead of just imagining.

I like your description about how knowing the usual number of stitches helps you to modify it for specific design ideas. Your posts are always so helpful. Recently I went back and revisited the old ones about making the thimble base and making the stitches. I learned even more details from them now that I have made a few thimbles.

I'm looking forward to the next opening of the Flickr group!

2. I am enthralled with the mathematical reference to the art. It had always intrigued me.

3. Debi, thank you for your comment. I am not sure if I understand " a greater distance across the thread" means (probably not) however, I went ahead and added a couple of pictures and a bit of an explanation. I would be grateful if you could tell me more how to improve this. CP
The Muse, thank you for leaving coments, You can make your own thimbles. It won't take much, material wise and time wise, and I am happy to help if you need help. Just let me know by leaving a comment explaining your concerns and I will get back to you. CP

4. great post
never imagined that the trignometry which i learnt at school would be so useful!thanks so much for the detailed explanation

5. I think I've understood,lol!
As English is not my fierst language too, I had to read this post several times.
I'll count my stitches next time for sure! But I think its number depends on the thread we use, isn't it?
From DMC range (that's what we have available here to compare)which one must we use?

6. I mean my first language...:(

7. Yes, definitely a useful post. It makes me feel as if I'm taking a special 'Making thimble rings' online-course with Chloe Patricia. It's a good feeling!

It does make me pause though. I've been wily-nily changing ring size and thread. To progress, it would make more sense to stick to one size and one thread.

Chloe Patricia, may I ask, do you ever change mould size, to achieve a specific angle, number of segments and/or stitch count? Or is that not done?