The Magic Formula

Hello Everyone - Here are my notes on the Magic Formula - for those who are interested in working out their own patterns.
These notes assume that you can work with cms. *(see below for help with cms)

The Magic Formula

First, you need to have converted the horizontal and perpendicular cm measurements into stitches and rows by means of the stitch, then row measurement per 1 cm (the multiplier).

1. Enter the multiplier e.g stitches per 1 cm, so 28 sts per 10 cm = 2.8 per 1 cm.
2. Enter x for times. Some calculators require x to be pressed twice.
3*. Enter the measurements to be translated to stitches.
4. Press = for the answer.
5. Repeat from 3* until all stitch conversions are complete.
6. Enter the multiplier for rows and repeat from 2, reading rows for stitches.

Note: if you have a pc, you can use the calculator in Accessories. You need to place the multiplier in MS (store) and press MR (recall) to multiply it with the next and subsequent cm readings .

The Magic Formula

This is an equation discovered by Diophantes an ancient Greek mathematician, which removes the necessity of converting remainders in division sums to fractions. It was first used in Japanese knitting patterns to show the increase breakdowns along horizontal lines like sleeve to armhole seams, in the late 1960s, although it was not realised at the time that you added a 1 to the divisor to ensure you were not casting off at the end of the sleeve what you had just increased and that you had some straight rows in the same breakdown sequence after the last increases on the sleeve .

Until the late 1960s, there was much guesswork involved in the writing (and working) of knitting patterns. As knitters we cannot work with bits of stitches and rows but only with whole numbers. The MF is the basis of calculations made by the knitting machine charting device and computer software for garment patterns.

There is a +1 involved in all Magic Formula sums which knitters find very puzzling. I often take a box of 35 matches to workshops to explain how break downs are worked out. Say 35 are divided into 8 piles ! is a match.

! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !
! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !
! ! !
but there are 3 remaining and we cannot have remainders in a MF sum. We therefore give 3 piles an extra match and the extra match is the +1
! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !
! ! ! ! ! ! ! ! !
If I were increasing one stitch 8 times in 35 rows, the answer would be every 4rs x 5 and then every 5 rs x 3. If we wanted to finish at row 35 and cast off, we would add one to the divisor, making 9; we would then have 4 x 8 and 3 x 1. We could say 3 represented the straight rows to the last row (no increase there).

There are 3 main expressions of the Magic Formula . Please read alongside illustrations:

1. For the regular decrease or increase of stitches in rows along a diagonal as in underarm seams, V-necks, darts, raglans and bias knitting of any kind i.e knitting diagonally from corner to corner. In Expression 1, there is always a hidden right-angled angled on each side of the diagonal (one marked * in illustration). The diagonal in each case is the hypotenuse of the triangle. Where a design is complicated and two or more diagonals are seen along a line, then the triangles need to be traced and the sum worked out for each stage.

2a. For the even distribution of extra stitches which have to be decreased or increased for features like cuffs, waistbands and yoked sweaters (sometimes the increases are grouped more towards the middle)

b. For the even distribution of stitches/rows in button hole bands and for distributing shaping groups of stitches along the length of a sideways knitted skirt.

3. For the creation of flares and mitres using the short row technique and in skirts, polygon knitting and sideways knitted yokes, as well as for breakdowns for colour changes in holding position geometric intarsia. This particluar form of intarsia usually involves breakdowns every other row.

Note: you may have to even out charting device breakdowns as it clicks on every row!

*WORKING WITH CENTIMETERS

Your 3 questions: what is the gauge in cms per 100sts per 100rs; per 40st
x40rs; per 40sts x 60 rs?
Your gauge: 8.3sts per inch x 29.9 per inch. 1 inch = 2.54 cms
(to the nearest workable figure)
To find readings per 1 cm, divide your numbers by 2.54, so 8.3 ÷ 2.54 =
3.27 sts per 1 cm; 29.9÷2.54 = 11.77rs per 1 cm.
If you are working out horizontal and perpendicular stitch and row
breakdowns for a garment pattern, keep the numbers up to 2-3 decimal places
until you get to the final stitch and row count. The calculator does the
work for you anyway. To work out breakdowns along diagonals, you need the
Magic Formula.

Incidentally, I am using the calculator in the computer (you can bring it
out of Accessories and minimise as you read this). I have it minimised
just now ( * = x, / = ÷ , and ÷ is achieved by Alt +0247 - numeric keyboard
- see Accessories/Character Map).

Write down the numbers on paper first, as the Calculator does not seem to
be movable and has just obscured this sum! Yes, I'm working with it in
front of me now! It must have heard me; it has shot conveniently into the
top left corner!

To find cms per 100sts 3.27sts = 1cm,
100sts = x(unknown as yet)
To find x, cross -multiply( 3.27x =100). To get x, 100 ÷ 3.27 = 30.58 cms
per 100 sts - Answer To find cms per 100rs 11.77rs = 1 cm
100rs = y(unknown as yet)
To find y, cross multiply (11.77y = 100) To get y, 100 ÷ 11.77 = 8.5 cms
per 100rs - Answer
To get the breakdowns for a 40 st x 40r reading (Form Computer) multiply
each reading by 4 and move one place to the left (i.e ÷ by 10). The
answers: 12.332 cms per 40sts and 3.4 cms per 40rs
To get the breakdowns for a 40 st x 60r reading (Brother/Knitking),
multiply the sts by 4 and the rs by 6 and divide each by 10.
The answers: 12.332cms per 40sts and 5.1cms per 60rs.

To get the 10 cm breakdowns for a 40st x 60r swatch,
supposing you have no green ruler (Knitmaster/Studio/Singer):
for stitches divide 400 by 12.332cms = 32.43 sts per 10 cm;
for rows, divide 600 by 5.1cms for 10cms =117.65 rs per 10cm.
For the readings for 1 cm - move 1 place to left 3.243 and 11.765.
Now we are back to where we started, but you say, there are discrepancies,
especially in the sts per 1 cm. The reason is that I have evened up some of
the decimal places as I have gone along. I believe that 2.54 cms per 1 inch
is not entirely exact to several decimal places! The point is though that
the whole stitch and row numbers are the same.

To work with the Magic Formula , prepare your garment drawing with cms
converted to stitches and rs- along the horizontal and perpendicular lines.
Here's a quick way of using the computer calculator. Enter your sts per 1cm,
say 2.5. Press MS. The multiplier has gone into store.
For each measurement you enter, press MR (recall) first x the measurement.
Try it now. Bring up the Calculator.Press C to clear. Enter 2.5 and press
MS. enter x 2 = 5, MR x 4 = 10, MR x 6 = 15. Got it?

Feel free to make copies of the Graphic Lessons for your personal use. The following copyright notice must appear on all copies Copyright (c)Kathleen Kinder, 1997, 1998.

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