February 2, 2015

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Let's go back. Back to work on TatHelper, Maths and Onion Rings.

I haven't worked on the things I love in the last months (almost a year). Time doesn't last as it used to when I was younger. How can it be? The Theory of Relativity in action?


Talking with a friend about the maths behind the lace, she suddenly exploted. How can you complicate something so simple and plain as the tatted lace!!!??? Have you ever thought that it was created and developed by people that probably didn't know a word about maths?

Like many others, my friend had bad experiences with maths at school, some think that they aren't good at maths, others that maths are just for scientists. But we do maths everyday, everywhere in our lifes without thinking on it.

Most of the time the problem was the maths teachers, not the child, she/he didn't show the natural side of the math and maybe, that's why there are so many people affraid of it.

Tatted lace is increbly mathemathical. It covers almost every natural curve and straight line studied by maths. Circle, parabola, opened and closed curves, curve inflections, etc.

Getting back to Onion Rings. OR is a complex shape built of 2 or more concentric rings tatted with one thread, developed in the 19th century or earlier, and previous to 2 threads shape (chains). One ring sorrounded by a bigger ring. Theorically, you can have as many layers of rings as you can tat.

But the true is that more stitches in the ring, harder to close the ring.

The relation for the first and second ring is 1 to 2.5. It means: Two and a half times DS for the second ring or outer ring. For example, if your inner ring is 10DS, then your outer ring would be 25DS ( 10  * 2.5 = 25)

Easy? Yes, quite easy. And it's maths making our tatting design easier.

The relation for the second to theird ring is 1 to 2. That means that if our 2nd ring was 25DS, the theird ring would be 50DS.

And here life limits the lace. Because the fourth ring would be 100DS. Hard enough to close it. But we can do it backwards. What if we plan it from the outermost ring to the innermost ring?

Let's call our designing friend, Mathematics. Instead of multiplying, divide to conquer.

R3 = 30DS 
R2 = 15DS  ( 30 / 2 )
R1 = 6DS   ( 15 / 2.5 )

But we will tat it R1, R2, R3. 

Another thing we have to care of, is that the small ring tends to be circular until is too small and becomes like a short straight line, looks like a knot on the thread. Getting bigger, looks like a tear if it's completed closed, or a parabola if it's half closed.

This relation is not fixed. It may vary depending on the tatter, the tension, the thread size and how tight you close your rings. 

But it can be mathematically adjusted by a precision factor too.