Tag Archives: math

In which I do a bunch of math

4 Replies

If you’re a mathphobe, be warned. There’s gonna be a lot of math in this one.

Because I’ve got a pile of yarn and a plan. But not too much of a plan, because obviously that wouldn’t be fun.

So, I’m making a blanket- with a largeish gauge (I’m using US9s) in a lace pattern that I found… somewhere on the internet at some point in the past. I know that’s not great, and I would love to cite the original designer, but I literally have no information, except that it was a charted Japanese stitch pattern, probably from a stitch dictionary. Which one? I have no idea. (If you recognize it, please let me know and I’ll happily share the source.)

Anyway, I worked up a decent-sized swatch, I know I’m going to do this all-over lace pattern with a simple garter border, and I have a big pile of yarn. But how many repeats to cast on?

I could just guess, but that never ends well. Either I end up with a weirdly small blanket or I run out of yarn halfway through a king-size monstrosity. I’m aiming for a nice throw blanket this time. Big enough that the newlyweds can snuggle underneath it, but not so big that they will be celebrating their silver anniversary before it’s done.

I grabbed some tools. A pad and pen (I’m still old-school when it comes to math), a tape measure and my trusty kitchen scale.

First, I weighed the swatch: 30 grams. (I’ve got 12 skeins of 100 grams each, so 1200 grams of wool to work with.)

Then I measured the swatch. The whole blocked swatch was about 7.5x 9 inches, or 67 square inches.

So if 30g=67 square inches, I can do a little math to figure out that I can use my 1200g to work about 2680 square inches.

Then the next question is, If I have 2680 square inches to play with, how wide should the blanket be? In my head, the blanket is about 50 inches square… ish.

So I divided 2680 by 50, leaving me with 53.6. So, if I cast on 50″ across, I’ll have enough yarn for a 53″ long blanket.

Each repeat is about 3″ across, plus an inch and a half for each border, so dividing it out, that will give me 16.16. But, of course I can’t do part of a repeat, so I’ll round down to 16.

So to get my stitch count, I’ve got 6 stitches for the edges, plus 14 x 16 (14 stitches per repeat, 16 repeats), which gives me 230 stitches.

So now I’m off to cast on and cross my fingers that I did my math right!

Math… After Dark

2 Replies

When I start a project, I like to finish it.

And sometimes, when I’m working on something particularly tricky, I want to finish it right now.  Which can lead to mistakes.  Especially when I get stuck on a bit of particularly tricky math.

Which has led me to make a rule for myself:

No math after dark.

I’ve burned myself too many times with this.  I start working on a particularly tricky part of a pattern, or find a mistake, then next thing I know, I’ve deleted and re-jiggered a weeks’ work in an evening.

And invariably, there ends up being some massive mistake in my “fix” that takes three days to re-fix.

(When I worked in an office, I had a similar rule- no mass emails after 4:00, especially on Fridays.  The few really big email mistakes I made always happened when I tried to send out emails right before leaving work.  Like when I accidentally sent invitations to a group of about 50 “no” applicants to interview with our company.  Whoops!)

I’ve been working on a fairly complicated design lately, and I’m 90% of the way there- I just have a few more tweaks (and a little ripping out and re-knitting) before I’m finished.  I almost finished yesterday, but felt myself starting to get carried away last night (and the growing urge to delete big swaths of data that I was sure were wrong).

But, this morning the sun’s shining (as much as it ever does in Seattle at this time of year), I’ve got my fully-caffeinated coffee and I’m ready to tackle some more math.

Wish me luck!

Project Tea Cozy: The Spout

1 Reply

It’s spout time!

My original idea was to make a gusset for the spout, in the same way that I would make a thumb on a mitten.  But then I cast on, started knitting, and promptly forgot about that.

Oops.

So, I had a big rectangle of knitting that wrapped nicely around my teapot.  I knit it until it reached the split between the spout and the ‘body’ of the pot, in between two stripes (so I wouldn’t have to worry about making a hole and maintaining the colorwork pattern at the same time).  First I thought I would make a simple 8-stitch button hole, but that didn’t seem right.  I thought it would make the tea cozy pull funnily, and I want a little cuff around the spout of my tea cozy.  So, I decided to do a slight variation.

I knit to where I wanted the hole to be, then transferred 12 sts to a stitch holder, then I cast on 4 sts using a backwards-loop cast on, and knit the rest of the row.

img_3357The way I made the hole reduced my total stitch count by 8, so now I was working with 112 sts instead of 120, but that felt right to me. After all, I was going to decrease for the top of the cozy in a few inches.  I continued knitting, following the established pattern without any more shaping until I got to the top of the 10 colorwork repeats I had planned.img_3366And, when i put the unfinished cozy on my tea pot, it fit surprisingly well!  I still have to seam it on the bottom and the top needs to be knit.  The spout hole fit really well, sure the safety pin is pulling a bit, but the when I knit up those stitches into a little cuff around the spout, I’m sure it’ll fit like a glove!

 

Stoichiometry and Knitting

6 Replies

calculator[1]I don’t get to use my college degrees very often (they’re in a couple fairly impressive-sounding branches of biology and chemistry), but sometimes I get to use a technique I learned in school.  It always makes me happy to use to use things my professors never would have expected.

For example:  Stoichiometry.

Never heard of it?  Not a problem.  Stoichiometry is a fancy chemistry word for a really useful way to do conversions.

If you’ve ever figured out how many stitches there are an inch of sweater or how many rows you need to knit to make a  foot of scarf, you’ve probably done stoichiometry without even knowing it.

Here’s the idea:

You know how if you divide a number by itself, it equals 1?  (Like:  2/2=1)  Stoichiometry tells you that you can do the same thing with words, units, and variables (remember x from high school algebra?).

So what does that mean?  Let’s take a really simple example:

1We can cancel out the “sts” from the top and bottom, so the answer (1) doesn’t have any units.

Now, that example is kind of useless to us, right?  So let’s use stoichiometry to do something that really is useful.  Figuring out how many rows we need to knit to get a 7 inch-tall sock.

Start by making a list of everything you know:

  • Our gauge is 12 rows/inch.
  • We want a 7 inch sock.

You could probably figure this one out in your head (or just on a calculator), but let’s do it the long way for example’s sake.

Start with the number that has a single unit (in this case the “7 inch” finished length) then, build your equation, multiplying across, and making sure that you cancel out your units as you go:

4 We can cross out the units that appear on the top and on the bottom (in this case, the “inches”).

Then we just multiply across, and the answer to the problem gets whatever unit is left (in this case, “rows”)3

So, in this example, if you have a 12 row/inch gauge and you want to knit a 7 inch sock, you have to work 84 rows.

Does that make sense?  Want to do one more (slightly complicated) example?

OK:  Imagine you’re designing a sweater pattern.  You want the front to be covered with fair-isle patterned stripes that are 8 rows tall.  You want to calculate how many stripes you will need to work to cover the front.

Here’s what we know about your sweater:

  • Gauge: 6 rows/inch
  • Sweater length from hem to shoulder: 22 inches
  • Stripe width: 8 rows/stripe

So, let’s set up the formula (starting with the sweater length- remember, begin your calculation with the number with the single unit.)

5(See how I flipped the 8 rows/stripe upside down, so it’s 1 stripe/8 rows?  That’s totally OK!  And, actually really important.  Flip any/all of your numbers, if it makes the units cancel out correctly.  Just remember, if you flip your the number, make sure you flip your units, too.)

Once everything is lined up correctly, start crossing out units that cancel:

6Then multiply across:7And then divide the top by the bottom.8So, in this example, you’d need to work 16.5 Fair Isle stripes to cover the entire front of your sweater.

Cool right?  (Or maybe that’s just me being a math nerd.)

Of course, you don’t have to use stoichiometry to work these things out, but it’s a great tool to have in your pocket- you never know when it will come in handy.

Do you think you’d ever use this technique to calculate bits of your pattern?  Do you have a different technique for calculating things?  Or do you avoid math completely?

Husband Sweater: The Sleeves

1 Reply

I think it’s high time that this dang sweater stops looking like a muscle shirt when my husband tries it on.  Don’t you agree?

The only problem is that he’s not a fan of the fairly over-sized sleeves that the original pattern calls for.  Ugh.  Nothing is ever simple.

So, it’s time to get out my scratch paper (or rather, the back of the pattern), my calculator and start figuring out what I need to do.

OLYMPUS DIGITAL CAMERAOK.  Before I even have to start doing math I know a few things:

1.  I have 82 stitches (about 20 inches) at the top of the sleeve, set aside from when I split the body for sleeves.

2.  I need to get down to about 40 stitches (about 10 inches) at the top of the cuff.

3.  My sleeve needs to be about 15 inches (about 105 rows) from where I’ll pick up my stitches to the top of the cuff.  (I based this on my husband’s arm length, and the length of the sleeves of his favorite sweater.)

Now it’s math time.

If I need to go from 82 to 40 stitches, I need to do 42 decreases somewhere on the sleeve.

(82 sts at the shoulder-40 sts at the cuff=42 decreases)

I’ll do two decreases per decrease row, so I’ll need to do 21 decrease rows.

(42 decreases/2 decreases per row=21 decrease rows)

And, I want to space those decreases out evenly over 105 rows, so I’ll work a decrease row every 5th row.

(105 rows/21 decrease rows=5 rows per decrease row)

OLYMPUS DIGITAL CAMERASo that means, I’ll knit four rows evenly (while still making sure the stripe pattern matches up with the body), then I’ll work a decrease row (knitting all stitches, except for working two decreases at the underarm).  Easy!

Hopefully, this’ll look good.  It’s a more extreme decrease than I usually use for sleeves, but it might work.  Luckily, I’ll be able to finish one sleeve, have the husband try it on, and get his approval for the next sleeve (or, heaven forbid, find out I have to redo the sleeve!  Cross your fingers for me).OLYMPUS DIGITAL CAMERAHave you ever had to rejigger part of a pattern?  How did it turn out for you?

Husband Sweater: The Body

6 Replies

My husband’s sweater is coming along (slowly, but I’m still making progress).  It’s looking pretty good, if I say so myself.

I split off the arms a while ago and have been working on the body.

See?

OLYMPUS DIGITAL CAMERAI actually modified the body a bit from the pattern, which should make the sweater a little more fitted.  When I was measuring my husband’s favorite cardigan to pick the size for this one, I noticed that the torso was slightly tapered.  The chest measurement was 40″, while the waist was 36″ around.

I figured, why not add a little waist shaping into this sweater?  That’s why we knit, right?  To make beautiful, customized garments.

So, it was time to do some math (Yay!).

I knew I wanted to decrease 4″ (which comes to about 20 stitches, based on my gauge).  And, I wanted to arrange the decreases in pairs underneath the armpits, along the “side seams” (this sweater is knit in the round, so there aren’t seams, but you can imagine where they would be).  This means, that each time I work a decrease row, I’m decreasing 4 stitches (2 under each arm).

So: 20 decreases total / 4 decreases per row = 5 decrease rows.

I wanted the decrease rows to be spread evenly down the torso.  Based on the Emilien pattern, there are 88 rows between the armpits and the top of the hem ribbing.

So: 88 rows total / 5 decrease rows = 17.6

Because you can’t knit .6 of a row, round to 18.  So, I work a decrease row (decreasing 4 stitches under the arms) every 18th row (ish).

A couple inches doesn’t seem like it’d make a lot of difference, but you’d be surprised.  Adding just a few k2togs will change this sweater from a standard, boxy cardigan to a cool, slightly fitted one.  I hope my husband will like it!