August 11, 2008

Taking the magic out of the "Magic Formula"

This is the first in a series of posts explaining the use of the "magic formula", a simple mathematical equation which allows knitters to calculate evenly spaced shapings in varied situations. I'm putting this here as much for my own reference as anything else. I'll be expanding upon the varied uses of the MF as soon as I get the chance to put fingers to keyboard. I'm a busy boy, so it'll probably take me a while to write the complete series. Please be patient....

What exactly is the magic formula?
The “magic formula” is a nickname coined by Alles Hutchinson, an American machine knitting expert, for a mysterious sum she discovered being used frequently in 1970's Japanese knitting magazines. This strange, but useful equation allowed knitters to precisely calculate their garment shapings, eliminating guesswork or trial and error. Although not immediately clear as to why, it worked perfectly every time as if by magic, hence the name.

The “magic formula” is more correctly known as a “diophantine equation” and was invented by Diophantus, an ancient greek mathematician credited as the father of algebra. A diophantine equation is defined as an equation in which only whole number solutions are allowed. In other words, the answer to the sum can only be a whole number, no fractions or remainders are allowed. This is exactly what makes it so useful to us as knitters, bearing in mind that we can't work with fractions of stitches or rows, only whole ones.

There are 4 basic uses or expressions of the magic formula:

Expression 1a - used to evenly space shapings along a diagonal line, such as on a sleeve underarm, a raglan armhole or a v-neckline.

Expression 1b - same as above, but shapings always occur on even rows only. This is particularly useful for handknitters who prefer to work shapings with the RS of work facing. For this particular expression of the formula to work, there has to be at least two times the number of rows as stitches.


Expression 1

Expression 2 - used to evenly divide up groups of stitches for shaping, such as on a sloped shoulder or flared panel shapings on a sideways knit skirt. Shaping can only happen on alternate rows with this particular expression of the magic formula.


Expression 2

Expression 3 - used to evenly space shapings horizontally across a single row of knitting, such as in a circular yoked sweater, or to deliberately create fullness above a ribbed border.


Expression 3

Expression 4 - used to evenly space buttonholes or other design elements such as cable panels across a knit piece.


Expression 4

I'm working on diagrams to explain everything as clearly as possible. So stay tuned!

August 11, 2008 in Knitting, Machine Knitting, Technical, Technique | Permalink | Comments (3)

December 10, 2004


Nothing really new on the knit front to disclose, currently engaged in online Christmas shopping and planning tasks to be done in the new year. 

Have to go back to Italy next week [I'm praying only a week!] to fit prototypes and decide which colours to produce them in.  I'm making all of this sound really easy, but it usually involves several hours of heated arguments to resolve anything.

Other than that, I finally managed to get round to uploading an image to the webspace I've had for ages.  You can check it out if you like, but it's temporary and there's not really anything there yet.  I plan to start working on something over the Christmas break, relying heavily on my brother for technical support.

If I have time later, I'm going to post a knit technique you can try.

Ps.  I did get the Jewelboxes, and I can confirm that they are everything they are reported to be.


As promised, I'm back.  The technique I want to present is a fashioning detail.  Referred to as "wale deflection" in the knitting industry, it's usually used only on higher quality stuff as the multiple transfer rows make it time consuming, and therefore expensive, to do.  It's not difficult to do, however, and the effort involved is minimal.  If you can do an ordinary fully-fashioned decrease, you can do this. It's perfect for those simple garments that need a little extra detailing to upgrade them into something more special and looks good anywhere you would normally use fully-fashioned shaping.


[click to see a larger image in a new window]

As you can see in the sample above, the edge stitches are deflected by the decrease[hence the name] and run off at an bias angle.  The number of rows worked between each decrease will also change the effect.  In the lower part of the sample 1 stitch was decreased every 2 rows [like a standard raglan], creating a gentle slope.  Decreasing 1 stitch every row results in a steeper slope, as seen in the upper part of the sample.

This technique works best on finer yarns and looks best worked several stitches away from the edge [my default number is six]. 

The trick is that two different kinds of decreases are used alternately. 

By machine: 

**Using a 3 or 6 point transfer tool, move edge 6 sts in by 1 needle. [one 6st fully-fashioned decrease made]

Return empty needle to non-working position. 

Knit 2 rows [or as many rows as your pattern dictates]. 

Using a single point transfer tool, move edge st onto adjacent needle. [one 1st simple decrease made]

Knit 2 rows [or as many rows as your pattern dictates].**

Repeat from **to**

By hand:  coming soon

December 10, 2004 in Technique | Permalink | Comments (3)