Monday, February 08, 2016

Factors—A Math Review

There is a meme that goes round on FB “Another day gone by, and I still haven't used Algebra”--this annoys me, because  algebra includes such basic stuff as mixed addition.

The ability to look at a handful of coins in your hand, some quarters, and dimes, nickels and pennies, and to quickly, (mentally!) tally them up, and know, YES this is the correct change, is using algebra. If you go day by day, without doing that little bit of algebra, —Whoa! No wonder you are broke!

Algebra is vital for knitting—since basic counting is part of algebra. There are lots of other math skills needed and many of them use algebra-- Like deciding on a yarn--This sweater calls for yarn A, with 220 yards, and I need 7 skeins, I am using Yarn B, with 207 yards per skein. How many skeins do I need--(I see, from the comments in Ravelry, most knitters had just inches of yarn left.. so how many skeins do I need? A quick bit of math makes it clear—7 X 220= 1540, and 7 X 207 =1449...and given that information, plus the notes from other knitters, I know I need 8 skeins of yarn B—and maybe it will be cheaper to use the recommended yarn A...and I go through another set of calculations.

But the math I use most as a knitter, and a designer is factoring. I hated factoring as a kid. . Do you remember it? It is an almost lost skill in today's calculator rich environment.

Factoring is the skill you need to add up mixed fractions (among other thing) ¼, + ½ + 3/16ths—for example(and really, this is an easy one! To add the fractions, you first change them, to have a common denominator (the lower number!) So what is a common factor for 2, 4, and 16—D'oh, 16!
Now, multiply both halves (top and bottom)  of each fraction to change all the fractions into x/16.

¼ becomes 4/16ths, ½ becomes 8/16, and 3/16ths stays the same. And now we add up the 4 + 8+ 3 and get 15. and our final answer is 15/16ths. If instead of 3/16ths we had 9/16ths, our answer would have 21/16ths, and would then have to reduce the fraction (and get 1 5/16ths as an answer)

This is the algebra we all know and hate! It's the Algebra that makes us say, Wow, I need the $$$ laser tool that figures out all of these fractions, and tell me, (with me doing any of the work) the precise measurements and tells me what length I need to cut to make this...(any household project from replacing cabinet door knobs to adding a new room!)

Or we spend the money on making someone else do it... It is the algebra that Tom Silva keeps telling us is easy on the TV show This Old House.. and it really isn't that hard, but most of us are out of practice—and we never liked doing it anyway.

I find, as I design things, factoring is my friend. I have favorite numbers—and will change yarn or needles to get the gauge to that works with my favorite numbers.

96 is one favorite number, and so is 72, 64 sometimes often wins out over 60an other favorite)—though, in general I really like numbers that are in the 12 times tables! 12 has so many factors.. 1, 2,3,4, 6 and 12. Then, every other multiple, (every even multiple, like 2 X 12,and 4 times, (and so on) has 8 as factor...and ever 3rd multiple, (3 X 12, 6 X12), has 9 as a factor.. so 72 (Oh such a beautiful number) has, 1,2,3,4, 6, 8, 9, 12, 18, 24, 36, and 72.  With all these factors, the world is your oyster when it come time to select a stitch pattern for your project!

By now, you might be thinking... OK, Helen is a real math nerd... but if you want to design, and to have stitch patterns (vs stocking knit or plain knit (garter), starting with a number that has many (vs. few) factors,  creates a huge number of possible stitch patterns to chose from! 70 by comparison is more limited.. 1. 2, 5, 7, 10, 14, 35, and 70--

What is more, there are only fewer even numbers, 2, 10, and 14 . I think, (and I could be wrong, but I don't think I am,) there are many more even numbered stitch patterns than odd, and if you are limited to just 10, and 14 well, it's harder find patterns you might like. I also tend to like symmetry, and 5 repeats of a 14 stitch pattern just doesn't seem as attractive as an even number of repeats...

the fold back cuff with a chevon design.
Why all this math? Well I have started the double knit hat for D, and my cast on number is 72, and with this a starting point, I can just work out a simple pattern (like this chevron for the fold back cuff) with almost no effort... I don't need a chart, just a number of stitches (8) that is a factor of 72, and bingo, the pattern emerges like magic! I might chart the snow flake pattern I am thinking of for the sides of the hat—but with all the factors I have to work with... it will be a snap!

For me, hardly a minute goes by that I am not using algebra! I think in numbers.

Meanwhile, I've added some round to the sock too..64 isn't as versatile as 60, but 8, as a multiple has a lot of advantages.. (perfect number for sets of 5DPN's or for 2 circ's) and this pattern has 8 stitches, making is simple and symmetrical. I'd show you but my camera memory card is full, and I wanted to post this--NOW!.
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