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.