Oh the math! “magic formula”

There are many knitting programs that will perform the necessary calculations, as well as a variety of knit calculators. The diophantine formula is the basis for what is know to some knitters as the “magic formula”. In the early 1980s Alles Hutchinson authored a small book on the subject. There is a bit of personal leeway in the results, and the formula may be used in calculating even complex shapes with the proviso that one has the patience to break such shapes into series of simpler ones.

There are many online resources for information and calculators to sort out the math, including a triangle calculator

Using the gauge to match the previous post of 4S and 6R per inch the calculation for the pie divided into five triangles  breaks down into the web calculator result pictured below:

The longhand method for same calculation which follows and also translates to: bring into hold 2 stitches for 4 times, 1 stitch for 80 times. Stitches in shaping are proofed as above: 88 stitches shaped over 84 rows.

 

Knitting math and pies

Math is non always fun, and is downright dreaded by some. One instance in knitting wherein basic calculations are required is in obtaining stitch and row gauges. I have known one hand knitter who would purchase yarn (not necessarily the one used in pattern), knit happily away, and try the finished product on everyone she knew until she found an accommodating body shape and size. If the large number of family and friends did not oblige, sweaters were stored until such a correct body appeared. Predictable results require careful measurements and some basic formula calculations.

Using home knitting machines to produce circular forms one resorts to breaking down the round object into pie wedges, which in turn are knit as triangles with straight line outer edges. The outer final circumference curve is controlled in a number of ways, one is by creating a far greater number of pie slices. For this exercise I will work with 5 segments. 

There are some math constants. One example: to find the circumference of a circle its diameter is multiplied by pi = 3.14. If the diameter of our knit is 44 inches, its circumference will measure 44 X 3.14 = 138.16 inches. Using the rule of 5 or less than 5, this measurement is rounded to 138 inches.

The radius becomes the width of the pie wedge. In this instance, it would measure 22 inches. Let us assume our gauge is 4 stitches and 6 rows per inch. The radius is converted to stitches: 22 X 4 = 88 sts. The circumference becomes rows:  138 X 6 = 828 rs.  If subdivided into 5 slices, each slice would be composed of 166 rows.

To knit the pie slice, short row are used ; since they happen every 2 rows, our row number for outer edge is divided by 2, yielding the total of now 83, which in this exercise I will round off to the even # 84.