So I decided to do another one - tearing this one apart. I want to do the same triangle pattern, but this time with bigger (and fewer) triangles.
I know how wide I want the shawl (about 25 inches to cover my whole back) - but I don't know what that translates into when casting on the bottom row of the (equilateral) triangle.
I google the problem and am led to math websites - where they tell me to use Pythagorus' Theorum - but I don't remember how! Besides, I only know one number (25) and that the other sides are the same length - or, if bisected, the right-angle triangle formed has one side twice as long as the other. I re-discover lots of math vocabulary I've forgotten and use that to google my problem: If I bisect the triangle, I know the bisection line is 25 - and the base is half the 3rd side - what is the length of that side?!! I try other wording: The adjacent of the right-angle triangle is 25, and the other two sides are a and a divided by 2... What is the length of a?
Terry was always better at math than I was, so I go to him - but even he has forgotten how to do it! (I wonder if my mother would remember - she was always good at math! But I have a cold and don't want to visit her until I'm better.)
Finally I called my daughter in Toronto. She was always good at math. But she's getting ready to go to work: I'll call you back later...
I measure a triangle in the shawl. The sides of the individual triangles are 19 inches and the height of the triangle is 17. (17 divided by 19 = 8.9) Does that mean that I should simply add 10% more stitches to get triangles the size I want?! Or should I count the number of knitting rows that would give me 8 more inches in height?
Maybe I should take a math class at night school, I tell Terry. I know there is a formula for this and it shouldn't be hard... I wish I could find a website that would give me the answer (rather than simply tell me to use Pythagoras' theorem to do it!) I wonder if there is a math website for knitters! (All this math thinking is giving me a headache!)
Hi Marlene, If you give us more information (the actual pattern information for the original) and how large you want the larger triangles to be, my husband who is a math major may be able to help if you still need it. Love your afghan by the way, the black, pink & purple. It has the feel of an Amish quilt.
ReplyDeleteHave a great day!
Pat
My wife asked me to see if I could be of use for your problem. She has followed your blog for a while and as a quilter herself and having relied on my math skills in the past and thought this problem would be an interesting challenge.
ReplyDeleteFrom my understanding you would like to widen your shawl from 18" to about 24". You would also like to shorten your shawl. The one question that I do not know is do you necessarily need to have equilateral triangles? Otherwise, you could make triangles with a base of 18" and the two sides of 26" your shawl should come out to be 72" long by 24" wide.
If you need more information about how to figure out the math I can send you a detailed explanation but I don't want to take up you space with a math lesson.
Thanks for the offer of help for the math! Several people offered suggestions - not necessarily the same - but I went with the first suggestion I got and I think it will be fine.
ReplyDeleteI chose the colors for the Amish-looking afghan based on the colors of an Amish quilt. I love the colors, too.
ReplyDeleteIn trying to modify a knitting pattern, I have come across the following problem: Picture an equilateral triangle sitting like a mountain. If I want the base to the peak of the mountain to be 25 inches, how long does each side of the triangle need to be?
ReplyDeleteMarlene this is where you would apply a little trigonometry. Since you have an equilateral triangle when you determine the height of the triangle you have one side of a right angle triangle and you also know that the corresponding angle is 60 degrees so
Deletesin(60) = 25 / hypothenuse,
so your length will be 25 /sin (60) which equals
28.8675 inches
since your wool has elastic properties you can probably get away with the length between 28.5 inches and 29 inches.