Friday, January 21, 2005

Of Geometry and Shawls

Cripes it’s cold around here!  The outside temperatures have ranged from a few degrees below to a few degrees above zero all week.  In part, this precipitated a discussion of a particular corner of the living room - you know, the one piled to the ceiling with my knitting and crochet projects?  All those projects were also sitting in front of the radiator which wasn’t, until this week, an issue because we hadn’t turned the heat on (cooling, in this apartment, usually being much more of a problem than heating).  However when we woke up one morning and it was 58ºF in the living room, we figured that was a mite too chilly.

Project bin

Neat…for now :)



So I went through everything, threw out some things, and put other things in the cabinets and the closet.  The current projects now reside in a neat, pink, box and the radiator is free to…radiate :)

The narrow scarf is about 10” long and going nicely, though constant moss stitch, without the interest of a cable to break it up is somewhat tedious to do.  Still, it’s only 15 stitches wide so it’s not bad.

The shawl is coming along very nicely and I’ve gotten to the point where I think I can relax about having enough yarn.

Shawl in progress

Moving right along…



Warning, Geekage beyond this point!

I had been wondering about how to figure the width since there are now enough stitches on the needle that it can’t be stretched out for accurate measurement.  Then I remembered my high school geometry.

The shawl is a triangle.  If a line was drawn from the bottom point up to the center of the top, that would create two right-triangles.  And the measurement of the sides of right triangles can be done, courtesy of Pythagoras!

A2+B2 = C2, right?

So I measured the line from the bottom point to the top center - 24”
And the side from the bottom point to the top right point = 31”

We’re solving for B2 here which will be half of the width of the top of the shawl.  So we’re going to subtract A2 from C2.

C2 = 961
A2 = 576

961 - 576 = 385

The square root of 385 (acquired by simply entering the number into your handy, dandy calculator and hitting the square root button) is about 19.6. 

Calculator

Square root button



That’s half of our width so the whole width is about 39”, plus a bit.  I managed to roughly confirm this by jamming half the stitches onto one end of the needle and stretching out the remaining half to measure.  That indicated a width of more like 41”, but I imagine I stretched the stitches out a bit more than necessary.  In any case, it was close enough for a rough estimate - the shawl isn’t going to be fitted after all and the measurements will increase with blocking anyway.

Cool, eh?

I’ll be working on the shawl over the weekend and I’m up to the heel on the peppermint stripe sock.  Frankly, I’ve been putting it off because of the whole toe-up thing, but I know it’s not really any different than doing a heel from the top down.  I just have to make myself do it - and then I’ll be surprised all over again, as I always am when turning a heel, at how easy it turned out to be.

Have a great weekend!

Babbled by Robbyn on 01/21 at 11:47 AM
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  1. well, geekage maybe *but* isn’t it just great to see ‘numbers in action’- whenever i used to hear the children wailing about how they would never use algebra and geometry i would think that once they entered the real world they would see how beautiful math is-

    congratulations on the organization no matter how momentary it might be- whenever i look at the chaos my assorted projects have created i have good intentions about straightening them up (but we all know about those roads paved with good intentions, don’t we?)- in the meanwhile i often spend as much time looking for the sleeve, pattern, needle, etc as i do actually using them-

    stay warm there- wish i could share some of our upper 70s temps with you- we’re in shorts and tees with open windows here today-

    stay happy-

    Posted by .(JavaScript must be enabled to view this email address)  on  01/21  at  02:16 PM
    Location : going round the bend

  2. That’s way too many figures for me, but the shawl is looking terrific.

    Posted by Pamela  on  01/21  at  02:52 PM
    Location : UK

  3. Barb - Yeah, I would have been one of those kids.  Couldn’t see the use until after I was out of school but then - oh baby!

    Pam - Thanks :)  It’s a fun project.

    Posted by Robbyn  on  01/21  at  06:55 PM
    Location : On the Isle of Capri...

  4. Mine is exactly 40” on the needles, unblocked of course.  I prefer the color you choose more each time I see it!  Great job!

    Posted by Laura  on  01/21  at  07:50 PM
    Location :

  5. Laura - Thanks - bu I think your color is pretty nifty.  I went back and looked at the yarn pictures you posted when you first bought it - yummy stuff!

    Posted by Robbyn  on  01/21  at  08:30 PM
    Location : On the Isle of Capri...

  6. Not to be supper geek, but… you do know A**2= B**2 + c**2 only works for right triangle, right?

    (Ok.. I am a super geek….)

    Posted by lucia  on  01/21  at  11:59 PM
    Location : Greater Chicago

  7. Lucia - That’s why the shawl is divided in half from the bottom point to the top center - to make two right triangles.  Once the measurement is found for half the top side (the top leg of one of the right triangles) it can be doubled to give the width of the shawl :)

    Posted by Robbyn  on  01/22  at  12:30 AM
    Location : On the Isle of Capri...

  8. I’m a little behind in reading and just saw your bag.  It’s fabulous!  You’ve also made super fast progress on the shawl.  Seeing your progress makes me feel like I’m knitting right there with you.  I’m not even going to comment on the math stuff - it’s way over my head!  I’m just glad it’s working for you.

    Posted by cheryl  on  01/22  at  01:53 PM
    Location : Toronto

  9. Cheryl - Given what you’ve been through this week, being behind in your reading should be the least of your concerns :)  Thanks about the bag - it was fun to do and the shawl is coming out better than I have any right to expect.

    But I’ll take it :)

    Posted by Robbyn  on  01/22  at  04:32 PM
    Location : On the Isle of Capri...

  10. The square root button circled - girl, you crack me up….and make my brain hurt so early in the AM! Once you went through it, it made perfect sense…but I never would’ve thought to do it to begin with!

    By the way - did you see the new show “Numbers” last night? Makes me want to go back & study math instead of history!

    See what I miss when I somehow don’t get here every day? A lovely pic of you & cat! How content you look. I hear ya on the tail…Arnold is getting a little TOO interested in my knitting.

    Posted by Bron  on  01/24  at  11:30 AM
    Location :

  11. Bron - Numbers?  Nope, but I’ll have to look for it - sounds like it’s right up my alley :)  Thanks for mentioning!

    Jade sends regards to Arnold and passes along that persistence is key to lap position and maximum warth :)

    Posted by Robbyn  on  01/24  at  01:50 PM
    Location : On the Isle of Capri...

  12. Ahh! I should have read more carefully! 

    It’s beautiful by the way.

    Posted by lucia  on  01/24  at  06:58 PM
    Location : greater chicago

  13. Lucia - No biggie and thanks very much :)

    Posted by Robbyn  on  01/24  at  10:05 PM
    Location : Digging out from under

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