More fun with mathematics (and knitting)

Just about anyone with a school-aged child is aware of the controversies in mathematics education. As a former math teacher and the parent of a ninth grader, I follow it pretty closely. The other day I read an article from a fellow arguing that algebra ought to be an elective in high school, that not many people ever have to use algebra in real life, so why make everyone suffer through it. He was especially critical of word problems and claims that there are no real life word problems that anyone would ever want or need to solve.

I guess he only knits rectangles.

I get lots of blog hits from folks looking for shawl calculation help. Many people knitting a triangular shawl from the top down want to know how many pattern repeats they can finish before they run out of yarn. I gave a method (using algebra) in this post and a follow-up in this post.



I recently started Ene's Scarf, my first triangular scarf/shawl knit from the bottom up. Meaning: cast on a terrific number of stitches, then decrease regularly until they are almost all gone, bind them off and block out to triangular shape.

Again, this isn't really a triangle, but a trapezoid. Cast on 375 stitches, decrease two stitches per row until you are left with 19 stitches, then do a bind-off that grafts them together.

This time, I know I have enough yarn. (Elsebeth Lavold's Silky Wool. Purchased to make Cozy from knitty.com, frogged for a variety of reasons.) All I really want to know is when I have reached the halfway point for the psychological assurance. However, if I were worried about having enough yarn, I would use the same calculations --- but factoring in the extra yarn used in the cast-on row more carefully.

First: Draw a picture and determine what I know and what I want to know.




For Ene's Scarf:

C = cast on = 375 stitches
B = end (not exactly bind-off, but close enough) = 19 stitches
H = number of rows = 179

note that if one really does decrease two stitches per row, the numbers are a teeny bit off -- one would end up with 17 stitches. That's because in this pattern, there are a few rows that don't follow the rules completely, but the difference is negligible for my needs.

Total number of stitches = Area of trapezoid = 1/2(C+B)*H = 35,263

I know that I will have knit half the scarf when I reach row h with r stitches where the area of the top trapezoid with base r is exactly half the area of the whole trapezoid.

I have two unknowns, h and r. Fortunately, I can solve for r in terms of h, so I will end up having an equation with one unknown and I can solve it.

h = rows left to finish
r = number of stitches in the row where there are h rows left.

So r = 19 + 2h

Area of top trapezoid is 1/2(19 + r) * h = 1/2(19 + 19 + 2h)h = 19h + h²


So we have to solve for h where

19h + h² = 1/2(35,263) = 17,631.5

h² + 19h - 17,631.5 = 0 is a quadratic equation, easily solved by the Pythagorean Theorem.

Do you want to see the calculations? I thought not. But I'll show you anyway. There are two real solutions to this equation, but we are only interested in the positive solution. Therefore, we only care about

(-19 + (19² - 4 * (-17,631.5))^.5) / 2 = 124 (more or less)

I will be halfway done when I have 124 rows left. 179 rows total, means I will be halfway done when I have finished 55 rows.

Blueberry Shawl

I've been having trouble deciding whether to knit a new sweater using stash yarn or purchasing more Cascade 220 to remake Forecast. And if I do reknit Forecast, what color? (I could always choose to finish a work in progress, but that's never as fun as starting something new!) So I went browsing at A New Yarn which has a decent selection of C220, but not the color of the Japan sweater. They do have a different yarn in the most gorgeous blue (Sapphire in this link, I believe). That would make a wonderful sweater, but it would cost more than twice as much as a C220 version. And infinitely more than knitting a sweater from stash.

So instead I wandered around and looked at the odds and ends. A New Yarn is a non-profit yarn store that raises money for a Women's shelter. They stock some good basic yarns but also take donations. So you never know what odd balls of Rowan or Malabrigo will be scattered around. I found a skein of Shetland in a tweedy blue-purple. It has a really old looking label and the colorway is Blueberry --- not one I can find currently for sale.


It is probably not a coincidence that I chose a blue-purple colorway. Not exactly the same as the Japan Sweater, but pretty close.

In one week it became a Flower Basket Shawl. I chose this pattern because I wanted something I knew would be easy to do without stitch markers since I have kinda lost mine all over the house. I knew the pattern would be easy to memorize and I knew it would be easy to add pattern repeats to maximize using the available yarn.

US 7 addi lace needles
9 pattern repeats
86 grams, 340-350 yards used
blocks to 63 inch wingspan 24 inches deep (could have been blocked deeper with less wingspan as well)

Sukoshi kanko-ga shitai-desu.

We interrupt blog silence to say so long, we are off to Japan. We have passports, rail passes, hotel reservations, two cameras --- but no laptop or cables, so photos when we return --- and the list of things to do includes at least one yarn store.

I did finish the Victorian Lace Today Large Rectangle and it is large. I didn't block it to its extreme, but to the extreme of my blocking board at 32x82 inches. I could probably have gotten a couple more inches in both dimensions. I love it anyway. And as for running out of yarn, I had 300 grams and used 286 grams. The calculator on ravelry says that is 1359 yards. I am too lazy to double check or to double check my calculations from when I worried about running out. The pattern calls for 1200 yards? I used the same weight of yarn as called for, I knit on similar needle sizes, but my finished dimensions are larger. So whatever, I had enough yarn.

Here's a photo of me trying to get all arty. I am imagining being lost out on the moors in winter with nothing but the pile of shawls I grabbed as I ran away. Would Jane's have been lace?



My latest knitting is a sweater that I really want to wear in Japan. However, it's not quite finished yet. Using Forecast, from Knitty 2005, I did some modifications which I am liking. Details on my ravelry page. Body is finished, button band done, buttons sewed on, ends are woven in, but the sleeves aren't going to knit themselves, so I better keep this post short. We leave in about 36 hours.

New year starting out well.

Happy New Year!

Blog was neglected for a busy December. Few random items from the past month:

• Had a bit of a scare when I tried to get dressed and my jeans wouldn't go past my knees. To my relief, I realized I had grabbed the pair my skinny 14 year old son had outgrown and are destined for the Goodwill.
  
• My car got graffiti tagged in the driveway one night. Was pretty creeped out by it, then found out that two neighbors had gotten tagged the same time. Then it seemed more random and less creepy. Plus, what seemed to be indelible marker came off easily with Citra-Solve and some elbow grease.
  
• Working retail in December has its ups and downs. At least there are stories to share. Like the woman looking for a sudoku book for her "very smart" 8 year old granddaughter. I showed her Sudoku for Dummies and she was completely offended. Said her granddaughter was not a dummy.
  
• December 3rd, I mailed 6 checks including the mortgage. All but the mortgage showed up as received and cashed within a week. I called mortgage company on Dec 17th, last day to pay without a penalty. No check. I paid on-line which cost me six bucks. Then what to do about the missing check? Just in case, I moved enough money from savings into checking to cover it. Sure enough, it appeared at the mortgage company on the 18th. Large mortgage company is fighting bankruptcy. Is it possible it is "losing" checks for a couple weeks just so folks need to pay a late fee?
  

But now it's January and things are looking up.

I just won a blog contest! Kris has been having contests to celebrate her husband Dana's birthday. I was one of the folks who guessed his favorite album from 1979 and I won a skein of Dream in Color Smooshy Sock from her on-line store. Yay for me! and Yay for Kris who just sold her house and yay for Dana for having a birthday. Check out her store. Kris sells a nice variety of commercial yarn and a great selection of Indie hand-dyed yarn.



Most of my knitting time has been spent on the Large Rectangle from VLT. I have only 25 pattern repeats of the border left (out of 82). Each repeat takes me 24 minutes. Therefore, at least 10 more hours of work. And I am thinking of knitting the Princess Shawl? Am I nuts or just very optimistic?

Hairy Math

The Large Rectangle in leaf and trellis pattern with trellis border in Victorian Lace Today calls for 1200 yards of fine weight yarn.

Many people have found that they require more yarn than called for in VLT patterns.

I have three skeins of a fine weight Domy Heather, 100 grams, 475 yards each. A total of 1425 yards, 19% more than the requirements from the pattern.

Will I have enough?

You can skip the math and go right to the conclusions if you wish.

The main body is 94 stitches wide. 30 pattern repeats, 16 rows per repeat. Plus 5 set-up rows.

The border has an 18 row pattern repeat. There are 24 repeats on the long sides, 9 repeats on the short sides and 4 repeats at each corner.

The number of stitches in each row of the border varies, from 19 to 24, averaging 21.9 stitches per row. Not including the spit splicing, the ends woven in or the grafting of 20 stitches to finish the shawl:

Total number of stitches in shawl is 77,914

94 x 16 x 30 + 5 x 94 + 18 x 21.9(48 + 18 + 16) = 77,914

My first skein got me exactly 17 pattern repeats (plus 4 initial rows).

17 x 16 x 94 + 94 x 4 = 25,944

Therefore, I have enough yarn for 77,832 stitches.

25,944 x 3 = 77,832


I am 82 stitches short on yarn. But the border is done on smaller needles. I will optimistically knit on.

Reading Lace

Did I mention that I've gone back to my old job? I think I drafted a post but didn't finalize it. Yes, the day my kid started high school (full time after two years of part-time school/homeschool) I started back at the bookstore.

Some folks fantasize about working at a bookstore just as some fantasize about working at their LYS. Truth is, it's not all standing around reading and having happy chats with customers about good books. And the pay? Um, small business, retail, part-time, those are not words associated with getting rich. But it does have its rewards and it is only part-time. The owner pleaded with me to come back. I don't know how much of that is that I was a model employee and how much of that is that I'm a warm body and they were desperate. Probably a little bit of both, but that's OK. I felt wanted and that's usually a good feeling. She doesn't know about the blog, but I'll have to write as if she'll find out eventually. That's OK. She's a great woman but she does drive me nuts sometimes. And I may mention that here. But nothing that I wouldn't say to her face. I am pretty candid and there isn't much that I wouldn't say to her face, regardless.

I will get access to galleys again and the discount is nice. I already have a list of books I want to order. I'll space them out to keep purchases less than my salary, but that is hard! My knitting book collection could use some expanding, especially Lace books.

Lace! Oh, how I love you!

When I started reading blogs I would read about folks who memorized lace patterns. Patterns that seemed infinitely complicated to me. And sure enough, my first lace projects were hard. I never got comfortable with the pattern in Cece. I persevered and finished the sweater, but each row was slow. Cozy, well, I could never get that pattern figured out. So many mistakes I ended up frogging it. It was only a few different pattern rows, but I never could figure out where I was.

Either something changed or I chose easier patterns, because lately I have been able to read the lace on my needles better. Most of Estonian Garden Wrap was done watching TV. This weekend I cast on for the Large Triangle in Leaf and Trellis in Victorian Lace Today. And to my surprise, I have A) become faster --- already have 10 of the 30 pattern repeats finished and B) Memorized the pattern. I haven't checked the chart since about repeat number 6. And even then it was just a glance or two. What I still cannot get over is that it is so mathematical, so logical, so easy to read, yet the result is so fluid and graceful and curvy.



I am using some wool I got from a vendor at Madrona. The photo does not do it justice. I was told that it was dyed by none other than Judith Mackenzie herself. That's not on the tag, which just says Davidson Corporation. I don't remember the vendor, but she was clearly associated with JM and Jessica was with me at the time and seemed to know the vendor. Anyway, the yarn is a beautiful green, a richly heathered deeply layered green. I loved the yarn at first sight, but didn't realize just how heathered it was until I started knitting with it. How do you dye yarn so heathered? It almost seems impossible, like that it must have been dyed before being spun, but I don't spin so have no knowledge of that.




I've been dyeing some lace myself, some Zephyr. I don't like strongly variegated yarns for lace, but have become so attracted to hand-dyed yarns that commercial dyed yarns just seem flat and one dimensional. My method of dyeing the Zephyr is to slowly add one color after another to get depth and variation within a limited palette. So far I have sold two skeins and have two more available at Yarn Forest. I have one more that I dyed to keep, but it is red. And we've been finding that photographing red is a challenge. And silk is a challenge with its sheen. So getting a picture I like of that will have to wait until I have more time.

Swans or peacocks?

Time for a question.

For Mystery Stole 3, I dyed some yarn. Melanie, the stole's designer, said that the theme would be best expressed in a black or white stole. (we now know that the theme is Swan Lake; a ballet I have not seen.) I chose to make a very dark green kettle-dyed yarn. This swatch is a pretty good representation of the result, which ended up more blue-green than green.


I kept up with the clues, knitting the stole, up through clue 3. Does it look swan like?


It's nice, but I am not feeling the love. Perhaps I am just not a stole person. Or maybe my idea of a stole is more like a wrap --- wider than 20 inches. My finished Leda's Dream is a generous 24 inches wide and I love how it wraps around me, but this one won't. The yarn, Henry's Attic Carrera, is lovely, but I just don't think it's the right weight for the stole. So I set it aside for a bit.

Meanwhile, after finishing Leda's Dream, I've been hankering to start something new --- Fiddlestick's Peacock Feathers Shawl. I dyed some yarn, Zephyr, thinking that I wanted something similar to the Carrera, a subtle variegated blue-green but also with an occasional blip of red and yellow, peacock-like. Well, I , um, forgot to add black so I got completely different results.


It's pretty, but not what I had in mind. So now I am stuck. What to do now? Should I keep going with the Mystery Stole and the Peacock Shawl or should I frog the Mystery Stole and use that yarn for a new peacock shawl?

Times like these sure make me wish I could knit faster. Then frogging wouldn't seem so harsh.

Leda's Dream

Summer is in full swing, but Fall seems to be in the air here in Seattle. All it took was one chilly morning to get my neighbors, friends and random strangers at the grocery store all talking about --- and looking forward to --- Fall. And rain. And grey skies. Seattleites tend toward two camps: those that complain that only a dozen days with temperatures above 80 degrees F (26 degrees C) does not a Summer make and those who complain that four days of temperatures above 90 degrees (32 C) are just too damn many and when it is going to get rainy and cold again.

Me. Well, I'm in the latter camp. Sure, I am happy we've had enough warm weather that my tomatos are going gangbusters, that we've had so little rain I haven't had to mow the lawn for a few weeks, but shortening days and the need to put on a sweater occasionally are not things to mourn. I know we still have many weeks of good weather, more berries to ripen, more time to play and hike and camp.

A little crispness will give me a reason to wear something soft and cozy, Leda's Dream Stole, design by Melanie Gibbons. This was Mystery Stole number One. I wasn't even a knitter when she created this knitalong, but she sells the pattern for two bucks. Very clear instructions, very clear charts, well worth the investment.


Now what I really need to invest in is blocking wires. I blocked this by pinning it out and it looks much better than before, but still doesn't look finished. I'll get some wires and redo the blocking.

Details:
yarn is one strand of Zephyr and one strand of Madil Kid Seta knit together. Both are dark grey, the slight variation in the color along with the silk content of each yarn make for a rich depth of color I have found impossible to photograph.
US 6 addi lace needles.

Modifications:

• slipped the first stitch of every row.
• used a centered double decrease (slip 2tog, k1, pass slipped stitches over) instead of the slip 1, k2tog, psso in the pattern, except, I used the angled decrease for the wave edging.
• cast on 12 fewer stitches that the pattern called for, and knit fewer repeats (26 of the Wing of the Swan pattern)
  

Blocked dimensions: 24x70 inches.

Mysteries

I have already finished Mystery Stole Three Clue Two!
just kidding! But it is downloaded, printed and 28% completed.

Since two of the big wheels in knit-blogdom, Bonne Marie and Stephanie, blogged about joining Mystery Stole 3 (signups close any minute now) the number of members doubled in a couple hours. I trust Melanie can take the excitement. Why would so many people be willing to invest their knitting time and money into a project where they don't know what it will look like? And me, I even dyed yarn specially for this.

The first two clues have each have about 5000 stitches. Not too overwhelming, especially in installments. I do expect to be finished with clue two today or tomorrow. Lace provides such a fun challenge. Melanie has added to that with a hidden theme. She won't reveal the theme for a while, but we do know that a stole closely following the theme would be either white or black but she warned us not plan to use this as a wedding shawl. Most likely the theme is a tragic love story. (Madame Butterfly? Swhan Lake? Othello? Knitters have been guessing.)

I do enjoy knitting for intellectual puzzles. New stitches, new stitch patterns, new yarns, new yarn combinations, new colors all stimulate the desire to knit. Erika offered a different sort of kntting challenge, when a while ago she discovered a handwritten cryptic pattern in her great aunt's knitting books. Numbers, letters in knitting shorthand and just a few words. Two important words --- sleeve & body --- told us that it's a sweater. The 'k' is clearly a knit stitch, but nothing else was evident. Page one seems to be missing, this starts on row 29. What's the size, the gauge, the cast-on? Can we reconstruct a pattern from it? To follow the discussion so far, go to Erika's blog, find the search box in the right hand column and search for Helen.

If you do, you can see many different interpretations were considered. I took a mathematical approach. How many k's, o's, sp's were in each row? How did the number of stitches change from row to row? In answering those questions, I finally narrowed it down. The only way I could make it work was to identify the o's as yarn overs and the sp's as a double decrease. That's the crux. Who, at first glance would think of a double decrease?

Basic pattern. multiple of 6 plus 3.

DD = double decrease. I slip two together knitwise, knit one, pass two stitches over.

Row 1: K3 *yo DD yo K3* repeat in asterisk til end of row.
Row 2: Purl
Row 3: K6 *yo DD yo K3* repeat til last three stitches, K3
Row 4: Purl

repeat for pattern.

Helen's notes look a lot more complicated because she's making a sweater from the top down, with raglan increases following the stitch pattern. Can you see in the swatch below where I increased? Swatch is done with Brown Sheep Cotton Fleece on US7s. This would make a nice simple lacy summery sweater.

Sweaters

I covet this:From Louisa Harding's Modern Classics.

The softness, the delicacy, the style! Hard to tell from the photo, but there are 4 different lace columns asymmetrically repeated. If I could only knit one more sweater in my entire life, this would be it.

The book has some wonderful designs and some terrible instructions. Charts where the keys don't match the symbols in the chart. Sweater sets where the outer sweater has two inches less ease than the inner one. Complex stitches -- such as p2tog tbl --- that are not described in the glossary, while pages are devoted to describing simple stitches. (Does every book need to explain knit and purl?) And the chart for this sweater is a confusing jumble that would be impossible to follow without previous lace experience. If I make this sweater, I'll use Ann Budd's book of sweater patterns for the details and use the pattern for inspiration.

Having used Ann Budd and Elizabeth Zimmerman's percentage system, I am slowly learning how *I* want a sweater to fit, which is different than either Ann or Liz. For instance, Ann tends to have the sleeve circumference at the armhole at 50% of chest measurement. EZ says to make this 33%. Well, Ann's proportions are part of my problem with Franz's Cambridge Jacket, the arms are too big. EZ's proportions, on the other hand, mean my Fibonacci Sweater's sleeves are turning out to be tighter than I would prefer. I suspect that the differences lie in how much ease one wants or expects in the chest measurement. I have not a clue how to modify a set in sleeve design for more or less ease in the arm, but EZ's percentage system for a raglan can be personalized just fine.

I am still puzzled about cardigan designs. I read over and over that the backs and fronts must match, and sure, in pullovers that's easy to accomplish. But Cardigans have button bands. Therefore, I would assume that designers would account for the width of the button band and make the fronts a wee bit narrower than 1/2 the back. That's not the case though. In almost all patterns I have read, each front gets exactly half the number of stitches cast on for the back. Why?

So far, the sweater on the left, Diamond Mesh from Knitter's Magazine, Summer 2007, is the only exception I have found. The back has six more stitches than the sum of the fronts. (I like this sweater a lot.)

Wait. One more exception. That red sweater above I covet? It has the traditional button band knit on sideways, 6 rows worth. But the fronts added together have two more stitches than the back.

Lace

My list of finished knits includes a large proportion of lace.

Branching Out in Noro Cash Iroha
Mountain Stream in Madil Kid Seta
Cece in Elizabeth Lavold Silky Wool
Spinner's Shawl in Corriedale - Romney from Oregon Trail Natural Fibers
Flower Basket Shawl in Handmaiden Sea Silk
Estonian Garden in Frog Tree Alpaca

Lace satisfies an itch, an itch to try new technique, new fiber, new color, new pattern. And once you've bound off, just block and you are done! No sleeves to seam, no zippers to sew in. Well, Cece is a sweater, but is very simply constructed.

It's no surprise then that I have two lace shawls on the needles. Both are designed by Melanie.

Leda's Dream is almost half finished. I am knitting this on US6 addi lace needles (would have used 7's if addi would only make them) combining one strand of Zephyr and one strand of Madil Kid Seta. I love it, especially the Swan's Wing lace pattern, which I believe is from Barbara Walker. The central all-over pattern is also easy to learn and looks good. I could see a lightweight afghan knit with just that pattern and a garter strip border. She designed this as a mystery stole, offering the pattern for free in serial form two summers ago. Now she sells the pattern for a very affordable 2 dollars.

I joined Melanie's second mystery stole last summer, but never started. Turned out that the design never called to me. But I couldn't resist joining again this year. Why, when I have so many ideas of what to knit, would I join a group to knit a stole where I would not know the final design til late in the game? I don't know. Figured it couldn't hurt --- I wasn't required to cast-on. Well, we got the first clue and I have cast on, using some hand-dyed Henry's Attic Carerra and addi lace US5s. We still don't know the final shape of the stole, but it won't be a triangle. After 100 rows, there are 99 stitches on the needles, and Melanie says that's as many as we get. So, is this going to be knit on the bias or will it have pointy ends? Time will tell. The outer pattern is a variation of the Swan's wing pattern from Leda's Dream. I love the way she made that work, especially in the corner.