I forgot in my last post on my crocheting technique, Back to Math Basics, to explain further how I use the following table and how I arrived at it’s contents:
| Row | x2 | x3 | x4 | x5 | x6 |
| 16 | 32 | 48 | 64 | 80 | 96 |
| 17 | 34 | 51 | 68 | 85 | 102 |
| 18 | 36 | 54 | 72 | 90 | 108 |
| 19 | 38 | 57 | 76 | 95 | 114 |
| 20 | 40 | 60 | 80 | 100 | 120 |
| 21 | 42 | 63 | 84 | 105 | 126 |
| 22 | 44 | 66 | 88 | 110 | 132 |
I used some algebra (or possibly finite mathematics) to achieve the process for inserting the six additional stitches equadistant around the circumferences of the cap.
Let the row be represented by a; let the incremental stitches be represented by b; and, let the insertion position for the additional stitches be represented by P. Then,
P = ab-1
Using the table above, at the beginning of a round, I stitch a-1 stitches and insert the a stitch in the same stitch. For row 16, I started off with 15 stitches and put the 16th stitch in the same stitch as the 15th, then I continued counting 15 more stitches (or to the number 31, since that is ab-1 or (16×2)-1, and inserted the second additional stitch, which is also the 32nd stitch, in the same stitch as the 31st stitch. How many times can I type stitch in a sentence? 🙂
When I reach my safety pin which marks the end (or beginning) of the round, I should have reached the 96th stitch, after which I slip stitch into the first stitch of that round.
Algebra doesn’t always lends itself seamlessly to application in crochet, but an algorithm works perfectly. For example (using no particular programming language, but rather just generic easily understood syntax):
Row = 16
MaxRow = 22
IncreaseBy = 6
Stitch=1
AddStitch=1
While Row < = MaxRow
While AddStitch <= IncreaseBy
While Stitch < Row
Stitch=Stitch+1
EndWhile
AddStitch=AddStitch+1
EndWhile
Stitch=1
AddStitch=1
Row=Row+1
EndWhile
I think that algorithm works, however clumsy it may appear. I’m sure I could do it with less loops and/or recursively, but I’m too far removed from my programming days to dredge up those memories. I may research a bit to remind myself of some more aesthetic algorithmic techniques and revisit this in a later posting.
Still, I find it fascinating to confuse what otherwise could be a boring bit of crocheting. Besides, I always love to tout all the math my fellow students complained about in high school, whining that they would never use algebra or geometry or trigonometry, etc. in the ‘real’ world.
Ha!