Mathematics – Page 4 – Into the West

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!

Sunday afternoon became more distracting as it approached evening. Aside from the numbness and tingling which reasserts itself every few minutes, I find it difficult to count stitches and determine multiples of double digit numbers in my head while remembering the end goal of max stitches for that row all while the rest of the family watches a movie or taunts the Rotts into playing boisterously.

At row fifteen, I stopped and took a break for a bit. I read a few pages in Grand Conspiracy. I then found a piece of paper to write out the next seven rows numerical stitch pattern. For example, until row twenty-two, I need to increase each row by adding six stitches evenly spaced around the round. I wrote the following quick chart to aid in my stitch counting:

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 made it to row eighteen last night before retiring to bed.

Part of the reason I enjoy crocheting, or music (which is tangential I know) has to do with all the finite math involved with the patterns. And the best part of all, at least when working a circular crochet pattern is the chance to use my favorite mathematical constant. Stretch your memory back to the days of algebra and geometry and remember the simple formula for determining the circumference of a circle:

Can’t remember? Well, let me remind you using the photo above. If the diameter of a circle is 10.25 inches, the circumference is the diameter multiplied by the constant pi:

C = dπ

Or, as illustrated above:

C = 10.25 * 3.14159

C = 32.2

I have four more rows of increasing before I crochet a band of a half dozen single crochets (with no increases in stitches). After that, I start decreasing. The pattern reduces to a head band circumference of 18.25 inches, which is too small for Rachelle’s inflated ego, er I mean head. Her cranium has a circumference of over 22 inches. So I’ll have to do yet more math to determine the proper stopping point during the reduction.

I’ve decided not to take this Brimmed Cap project with me to work today, even though with the vanpool I have over an hour I could be crocheting to and from work. Mondays (and Fridays) I usually have to tote quite a few things with me (like a week’s worth of lunches and a laptop). If I don’t finish the cap this evening, I’ll probably take it with me on the commute Tuesday.

Category: Mathematics

Algorithmic Crochet

Back to Math Basics

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

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

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

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

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

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