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.

My kid, now a high schooler

Zach finished middle school sans pomp and circumstance. He could have gone to graduation and played Pomp & Circumstance, but he didn't really feel like an 8th grader, nor, as a part-time student, did he feel the need for the ritual. Seating is limited so we were altruistic in not attending, gave up our tickets so some other student with more than two relatives could force them to sit in a hot, crowded auditorium for a tedious ceremony invite them.

Friday he biked up to Matthews Beach to meet with a group of kids for their own end of school celebration. Candy and Capture the Flag. Coming home on the Burke-Gilman trail, he took a tumble when he let his front wheel drift off the pavement. Nothing serious, just got some ugly road rash on his elbow and a scrape on his rib and hip. (In addition to helmet, he wears biking gloves. I don't know if his hand hit the pavement too, but gloves are great for avoiding road rash on one's hands. I never bike without them myself.)

We cleaned him up and he seemed fine. Even played some DDR Friday evening. Saturday we went to Icicle Creek Canyon to go camping, hiking and drop him off at music camp. Well, he ended up sleeping the entire three hour drive, then continued to nap on and off most of the afternoon while we set up camp and hung around. No wonder. I am sure he didn't break a rib or get a concussion, but he must have slammed pretty hard on the pavement and was feeling pretty sore. So instead of anything ambitious, late Saturday afternoon when he perked up we took a short hike, then Sunday did another short hike. The area is beautiful.

By Sunday his elbow was scabbed over with no sign of infection. We dropped him off at camp with strict instructions though, if it starts to look bad, streaky red or hot he is to alert the staff and make sure it gets looked at. His main question was ought he put a bandage on it, so as not to gross out the girls. Nah, I said. Just tell them he fell off his bike to avoid hitting a kitten.

My week

• Snaked the bathtub drain.
  
• Contemplated getting hair cut short to avoid that chore again.
  
• Mowed the lawn.
• Almost fell for Google's April Fool prank.
  
• Knitted on but did not finish

sea silk triangle shawl

green pullover sweater (EZ meets Pippa)

mini-clapotis in angoravalley Lacewing


sleeves for fibonacci sweater

• Renewed car license tag on-line.
• Found out I had waited to long to have it mailed to me before current tag expires.
• Took bus downtown to pick up car tag. Spent $2.50 in bus fare because I refuse to pay $4.00 to have the tabs sent to a local agency.
• Treated myself to latte and muffin downtown.
  
• While downtown, went shopping and bought myself new underwear. It had probably been 10 years since I bought underwear. I can now get hit by a car without embarrassment.
• Took car to shop for 90K check-up.
  
• Vacuumed car. Helped put roof box on car.
• Arranged temporary stop of newspaper, mail and milk for next week.
  
• Arranged foster care for Tasty Chicken for the week.
  
• Looking forward to a week of car-camping in SE Washington, emphasis on Washington State History and geology. History because it is a state educational requirement and we are homeschooling history. Geology because geology is fascinating and Washington's geology is visibly fascinating.
  
• Logged into checking account at credit union about two dozen times looking for IRS refund.
• Once the refund arrived, wrote checks for and mailed mortgage and property tax bill.
• Finished a marathon Harry Potter reread of all six books.
• Inspired The Nerd to reread them also. He's also finished.
  
• Discussed same with The Nerd and hypothesized about Book Seven.
• Tutored math at The Nerd's middle school
• Found out that he got into his first choice high school, even though for the upcoming school year, it has the longest waiting list of any Seattle public school ever. Very relieved.
  
• Found out what a close call it was. District uses a distance tiebreaker. This year, the boundary for enrolled vs wait-list was 1.81 miles from school. Mapquest puts us at 1.79 miles.
  
• Updated alumnae email and snail mail addresses for upcoming 30 year high school reunion
• Started searching airfare prices for Fall trip back East.
  
• Discovered that waiting a week to purchase airfare for reunion increased the cost by 35%
• Found out that by flying into Baltimore instead of Dulles, I could reduce airfare back to original estimate.
• Purchased ticket. I'm confirmed to attend Reunion and my niece's wedding on East Coast in October. Just me. Not going to disrupt high school attendance in the first semester.
  
• Started thinking about what shawl/stole/wrap I should knit for the events.
• Took The Nerd to an open house of a youth kayak racing club.
  
• Passed a Float Test at a local pool. I only needed a renewal if I want to take another sailing class which is a long shot. Really I did it so The Nerd would have company taking his float test, necessary to take a sprint kayaking class. Float test: wearing long sleeves, long pants, tread water for 9 minutes, then put on life jacket while treading water --- not as easy as it sounds but there's a trick that helps. Nice lifeguards share trick.
  
• Signed The Nerd up for the beginner sprint kayak class and braved Spring Afternoon Greenlake traffic getting him there and back again.
• Walked around Greenlake for the first time in years. Anyone free on Tues or Thurs at 4 PM and want to walk the lake with me? (starting April 17th)
• Rest of today will be packing, organizing, grocery shopping for trip. We leave tomorrow morning. Fort Vancouver here we come.
  

Catching Up

Greetings from the family room.

I usually blog, surf the net, read the news, correspond with family and friends from my computer, situated in a sunny corner of the kitchen. Centrally located, it allows me to monitor meal preparation and offers easy access to the coffee pot. But the wooden chair is not super comfortable. Zach was given an old computer sans peripherals which he set up using our TV as the monitor. I hijacked it for the morning so I could blog in the comfort of a beanbag chair.

Time for some random catching up. Let's get the hard part over first. The sad part. Elaine, maybe you should stop reading now, ok?

My chickens. I haven't really blogged about the chickens in a long while. Well, recall that Amelia had gotten sick, was getting better but moulted and the other girls were picking on her? Well, we may have underestimated how much she was picked on until it was too late. She started escaping from the yard so we sent her to a friend's coop to see if she'd be happier. Alas, she started escaping from their yard and the third time she escaped, she was gone for good. We searched all the neighboring yards, but no signs of anything. We suspect coyotes.

The four remaining birds were doing fine, handled the cold and wet winter fairly well, but alas, more predation a couple weeks ago. Something came into the yard and ate three of them. This time, the carnage was obvious. Sigh. We suspect raccoons. Annie and Lucy were laid to rest in Nancy's pet cemetery aka side yard, and Orpie met her end at a separate event and is at peace in our yard, not far from gerbils Vivek and Rollie.

Tasty has surprised us all and so far avoided the same fate. She has also learned how to get out of the backyard, but not so much escaping as exploring. Fortunately the neighbors are all pretty cool about it, except for one neighbor's downstairs tenant who claims that Tasty scares her cat. They have a bird feeder situated in a tree about 10 feet from the entrance to her garden apartment. And of course right below the feeder is a great spot for Tasty to collect all the dropped food. When Tasty is over there enjoying a snack, her poor cat is too freaked out to come home. Tenant knocks on my door and I grab the tupperware of corn I keep in the fridge and coax Tasty home.

Chickens get lonely and need to be in flocks. (However they also are mean to each other; pecking order is not just a metaphor. go figure) For Tasty's long term health, we've had a note posted in an urban chicken newsletter offering her up for adoption. No takers yet though.

On to other topics.

The Nerd's application to Transition School, an early entrance program at the University of Washington, is in and being considered. We will find out this week whether he advances to the next stage and be invited to an interview. I have no idea what the likelihood of that and they interview about40 candidates for 16 slots, so the odds are still low. His grades and scores are mostly good. His ACT scores are respectable for a 13 year old, but are perhaps not high enough for Transition School. But he is in his first of two years of eligibility so there's a good chance they will say try again next year. That wouldn't be the end of the world, as we've been able to have him skip 8th grade next year so he will be in high school in the fall.

I've got a cold, my throat hurts, my head hurts. It's not too bad though, I've been able to listen to archived This American Life podcasts and knit. Franz offered to make me soup, but I made his volunteer efforts easier by having a craving for Chicken Tom Ka Gai from Marlai Thai. It hit the spot.

I've been knitting way too many projects, for my sake more than others, I will list them below in no particular order. I don't really mind knitting on multiple projects at once, because they all have different size needles --- easier on my hands to switch around --- and they require different levels of concentration.

• Franz's Cambridge Jacket. while exploring the possibility of reknitting the sleeves, I decided to unseam the sleeve caps and see if reseaming them will help. I suspect it will. Current state: One sleeve is about 5/6th unseamed.
  
• Ribbi Cardi. All done except one sleeve. I have started the sleeve but haven't gotten far. The stumbling block is that knitting the sleeve done entirely in k2p2 rib is tiresome and the increases look sloppy, although I have tried many variants on Make1. I'll finish eventually though. If I ever do something like this again, I think I might knit the sleeve cap using a provisional cast on, then pick up the stitches on the bottom and knit the sleeve proper using decreases instead of increases. Can't help but think it would be tidier.
  
• Moebius shoulder bag ala Cat Bordhi. Her Moebius Cast-on is fascinatingly clever. The felted bags are constructed by knitting the shoulder strap as a moebius strip with an after-thought opening for the bag. I have almost finished the shoulder strap, using Lamb's Pride bulky. It has an i-cord bind off which is really really slow, given that I had about320 stitches to bind off. I have less than 100 stitches to go. I think the bag part of this will be a fast knit.
  
• Tartan Plaid. Yup, the reason I have so much Lamb's Pride lying around ready for a felted bag is because of choosing colors for this jacket. I haven't abandoned it for good, but am unsure about its potential as a wearable FO. I love this jacket, I covet this jacket. I have the back and one front completed and one sleeve halfway finished. They look great. But I am worried that seaming is going to look like crap. The pattern has no specific instructions for how to seam the slip stitch pattern and I just can't see how it can be done in a tidy fashion given the bulkiness of the fabric. I plan to purchase some Lambs Pride worsted in the appropriate color for the seaming. I figure my next step will be to procure this yarn and practice seaming the pieces I have finished. If I can make it look good enough, that will encourage me to finish.
  
• Pippa/EZ hybrid. Using my hand-dyed Aurora 6 which is very similar to DB Baby Cashmerino (the recommended yarn for Pippa) but is 100% wool, I've started a pullover using EZ's percentage system and the mock rib detailing from Pippa. Knit in the round from the bottom up, it will probably become a raglan crew neck. Coolest thing about it is the tubular cast-on k1p1 ribbing along the bottom.
  
• Vintage bawneen cardigan. I dyed most of the rest of the vintage bawneen in semi-solids and started a striped cardigan. Knit in the round I will steek it where the colors change. I'm sort of copying a store-bought acrylic V-neck cardigan that I have had for years and always (inexplicably) get lots of compliments when I wear it. Seriously, I keep almost throwing it into the Goodwill bag, then every once in a while I find everything else in the laundry so I wear it and everyone notices and says how nice it is.
  
• Micro Clapotis. Inspired by Erika's micro clapotis scarf, I started one myself. This is a portable project being knit on bamboo straight needles, which make it a quiet knit --- good for knitting in public during a talk or concert.
  

That's about it. A few random things in the closet go unmentioned, a Dulaan hat, a warshrag. And the log cabin which is a long term project, I knit on it occasionally when I want completely mindless garter stitch for TV watching. But I don't feel any anxiety about finishing it.