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Proportions of blankets, shawls, etc. per the Golden Rectangle/Golden Ratio


Gran

Question

I have started making my lap blankets/throws and shawls according to the proportions of the Golden Ratio/Golden Rectangle.

 

Here are a couple of links:

 

http://www.math.harvard.edu/~ctm/home/text/class/harvard/101/00/html/www/gallery/gold/

 

http://en.wikipedia.org/wiki/Golden_ratio

http://mathforum.org/dr.math/faq/faq.golden.ratio.html

 

An easy formula for the Golden Rectangle is: The Length x .618.

 

The Golden Ratio is the length/width x 1.6

 

I find the proportions very pleasing.

 

May be this will be of some use to someone else here.:)

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I followed every word Ah Leah said.

 

But maybe that's because I'm best friends with a person getting her Master's in mathematics at an Ivy Leaguer. Sheesh, that girl is smart.

 

I think a lot of people give up on trying to understand math because they had bad experiences with it in school as kids, so then that part of their brain shuts down. It's easier to say, "You get it 'cuz you're just math-oriented" rather than "Maybe I could get it if I concentrate and ask questions."

 

I'm not a math geek by any means, but I :manyheart the mathy conversations I have with my mathy friend. I borrowed some elementary math texts from her and am working through them this summer at my own pace and leisure. My favorite so far? Topology. Go torus tic-tac-toe!

 

~ Joy

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Thank you, Ah Leah, for enlightening the Village:no .

 

I would like a show of hands from all of you out there that can figure out what these two are talking about:think 'cause I'm WAY lost.

 

 

Honey, you know mommy stopped being able to help you kids with math around 5th grade, so what makes you think I understand this??? I mean, I'll stick to fast typing court reporting stuff. Do you know what nunc pro tunc means? Huh? Well do you???:devil maybe a little ex parte or a motion in limine??? Yeah, that's what I thought:manyheart

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Okay, on the Golden Ratio stuff.

 

I just remembered seeing as a child a Disney feature called "Donald in Mathmagic Land." And it has a very good description of the Golden Ratio and where you can see it. Sounds goofy, I know, but maybe seeing it in action would help some of the folk who are having trouble visualizing it?

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Just an FYI for all you Fibonacci folks - according to the DIY website, this Friday's episode of Knitty Gritty is supposed to feature Fibonacci knitting. I know it's knitting, but it would still be interesting to see how they use it for the striping.

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nunc pro tunc is latin meaning now for then. It's when a trial court corrects a non-judicial error in a judgment that has already been made.

 

ex parte is with one side absent.

 

motion in limine is when one side makes a request to the court before the trial starts to exclude certain evidence from ever being presented.

 

Do you seriously think I was actually tuning you out all those mornings going to school?

 

and back to the original topic

 

IT'S NOT THAT HARD.

PROMISE.

 

Ok, here is a classic golden rectangle (that I totally stole from google image search):

240px-Golden_rectangle_detailed.png

PAY ATTENTION TO UPPER AND LOWER CASE LETTERS.

Let's say that all sides b are equal to 5. So, multiply 5 by the golden ratio (1.618) and you get 8.09. This means that side a is equal to 8.09. So, if you were to remove rectangle A from the shape, then one side would be 5 and one side would be 3.09, because a-b equals 8.09 - 5. If you multiply 3.09 by the golden ratio, you get 5. It's a golden rectangle. See?

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This is great stuff! I have used Fibonacci numbers on several occasions for striping patterns in shawls--

You can use two alternating colors and have two Fibonacci sequences going in opposite directions:

21 1 13 1 8 2 5 3 3 5 2 8 1 13 1 21

 

This makes a nice stripe pattern.

 

I have also used PI as a pattern--using two colors of yarn and alternating them, using each digit in PI as the number of rows:

3 1 4 1 5 9 etc...

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I love the golden ratio!! Ah Leah, I understand your explanation fine but then again I'm pretty much a math geek. The purses and baby blankets I've crocheted mostly follow the golden ratio... I first got the idea when my calculus professor had a lecture on the golden ratio but I never thought to bring up the concept on here...

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KateCrochets, I've only been doing proportions of the whole, and not designs.

 

I'm glad others like the Golden Ratio in crochet, too. I find it restful, energizing, and lovely to behold!

 

Sakurasaku, your Fibonacci-striped socks are beautiful! If you apply the concept to the Giant Granny Square Afghan, could you post a photo, or your pattern, or sell them? Your stripes are terrific!

 

And I'm definitely one of those who needs the numbers manifested in hands-on, relevant-to-me applications. Hence, the divine proportions of crochet.

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Wow, this is a really neat thread! And actually will be useful for a project that I'm working on right now. I'm making an afghan to look like the Irish flag for my brother for Christmas, and was wondering how to figure out what the length of it should be. I just eyeballed the width to what seemed like a good size. So now, I just need to go home and measure the width and then multiply it by 1.618 and I'll know how long it should be. :cheer

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:eek Oh My!!! Ah Leah that was extremely confusing the first time you explained it but when you did it with the diagram and someone else said to multiply the widtth by 1.618 I worked it out. Cool stuff. I actually have written it like this to remeber cause i think it's easier:

Golden Ratio [1.618]

[say b is 5]

Side a = b x Golden Ratio

= 5 x 1.618

= 8.09

 

If y'all had've wirtten it like that in the first place would have been alot easier to understand. Algebra YAY!!!! That's my specialty!!!

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That's, um, really CONFUSING:eek !

 

I sent the link to my daughter, Ah Leah... I'm sure she'll like the idea.

 

I'm not saying it's a bad idea, I just don't think I could crochet anymore 'cause I did very poorly in math... and geography... and science

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Someone gave me the idea to use for something else and I then thought, "Hey, why not for blankets?". I get help with the math sometimes and just figure the inches and crochet away. Or you could extrapolate from given Golden Rectangles: 5 x 8, 8 x 13.

 

I don't really know much about it. I just like it and it does have a fascinating history. The math folks can talk about the Fibonacci numbers and the Golden Ratios. I just jot down the figures I need and happily get my hooks and thread or yarn.

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Yeah, theory is SOOOOO not my thing, either. If's and P's and all that crud were about as far as I could get. If I couldn't apply a rule directly, I was dead in the water... thus, APPLIED mathematics as my major!!! I have a friend that just went BACK (at 30+) to get her masters in Physics, and I'm thinking....oh, I could do that! (After being a SAHM for 8 years now, I can still do DiffEqs in my head...)

 

Just maybe.... :D

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You know, I was a HUGE math geek when I was really young. I mean, 5 years ago, I would have totally understood everything in this thread. I got 7 semesters into a degree in Computer Engineering, which involved a lot of calculus, physics, etc. I was a science/math GENIUS... but then I dropped out of school to move to California and stopped working on that stuff.

 

And now? Now, I can barely follow the discussions in this thread! I went to sakurasaku's link on the Fibonacci socks and, while I obviously *get* the concept, trying to follow the description left me cold. I wonder why that is?

 

Maybe I should work on practicing with math more, although I don't need it in my line of work anymore. I just have to say, I'm really disappointed!

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I think the discussion of the Fibonacci sequence on the socks page would be more effective if instead of writing the patterns out -- to show the variety -- the author had made little swatches showing the various effects. Makes it more concrete.

 

But you know, your post got me thinking about this again...and then I was reminded (don't ask me how) about *Spirographs*. Man. Could you use Spirograph drawings as inspirations for doilies and motifs, or are they all too complex?

 

I think I feel an E-Bay attack coming on...

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Ahhhh, Phi!

 

It's one "H" of a lot cooler than Pi :U

 

You may have also heard of it as the "divine proportion", especially if (a) your mom is math teacher and this was a fun dinner-time conversation or (b) you read The DaVinci Code

 

You know it has it's own webpage? Probably more than one, but http://goldennumber.net is a very intersting one, especially the http://goldennumber.net/neophite.htm .

 

But I really think Robert Langdon's explaination of Phi to his students in DaVinci Code is one of the best introductions I've seen for the non-math friendly crowd :U

 

Thanks for the thought, Gran! I had never overtly thought of using it for proportions, though I :manyheart using a Fibonacci sequence of rows. (Fibonacci is most def. my favorite series of all time)(wow i sound like a huge dork)

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I would LOVE to take credit for the socks, but it's just some site I found a while back when I was researching the use of the Fibonacci sequence in fiber arts. The socks do look cool, right? I wish I had done that. :D

 

If I successfully apply the formula to the Giant Granny Afghan (sounds funny..."giant granny"), I will definitely share it with the 'Ville.

 

Oh that's an awesome idea. :hook I hope you can apply the formula, I'd love to be able to do a pattern like that. I'd consider myself a math geek, as I got as far as Calc III in college, but once I hit Statistics and Linear Algebra, that all went out the window! :lol Vectors are NOT my friends..

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I majored in physics too! Where's your daughter in school?

 

I can't keep quiet about this topic. ;) I didn't know there were all these physics gals around! I'm in grad school for physics. It's a great conversation stopper. "So, what do you do?" "I'm in grad school." "Oh, yeah? What are you studying?" "Physics." "Ummm....okay." :lol

 

Didn't someone earlier in this thread say that they'd always liked the math in crochet? It's certainly one of the things that appeals to me. It's math, but it's all finite numbers and you end up with an actual cool *thing*. I was no good at math when it was all abstract. I like getting my hands dirty :-)

 

That's why I'm in experimental physics, not theory. ;)

 

Using the Fibonacci sequence is a GREAT way to do stripes that look cool with hardly any design effort. Check out this link. I have been meaning to use the concept on Erin's Giant Granny Square Afghan at some point.

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I majored in physics too! Where's your daughter in school?

 

Didn't someone earlier in this thread say that they'd always liked the math in crochet? It's certainly one of the things that appeals to me. It's math, but it's all finite numbers and you end up with an actual cool *thing*. I was no good at math when it was all abstract. I like getting my hands dirty :-)

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Sakurasaku, your Fibonacci-striped socks are beautiful! If you apply the concept to the Giant Granny Square Afghan, could you post a photo, or your pattern, or sell them? Your stripes are terrific!

 

I would LOVE to take credit for the socks, but it's just some site I found a while back when I was researching the use of the Fibonacci sequence in fiber arts. The socks do look cool, right? I wish I had done that. :D

 

If I successfully apply the formula to the Giant Granny Afghan (sounds funny..."giant granny"), I will definitely share it with the 'Ville.

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