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

[Gran]

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.

[jimbo]

Uh, i'm more into the wooden stick formula, myself. You take a stick and check the diameter H and length O, then multiply the length by itself (OO) and then by the bark constant K and you get: H O O K.

 

 

(i made that up to impress you)

[Gran]

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.

[Krystal16]

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....

[sakurasaku]

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.

 

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

[CaliAdria]

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!

[tbird]

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...

[Brandybuck]

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.

 

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. 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! Vectors are NOT my friends..

[jenhen]

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...

[nana5boys]

This sounds toooo confusing. I like the simple patterns.

 

jaye

[Gran]

Jenhen, thanks for the ideas. I'm looking forward to trying the PI and the double Fibonacci.

[losingmymind2]

Do you mind explaining that in English? Very very simple words? Or better yet, next time I want to make an afghan a certain size, how bout I just call on you Ah Leah, and you tell me how big to make it. Because I have NO earthly idea what you were talking about there ladies.

 

Ok, nevermind I figured out the stripes...one stripe, two stripe, red strip, blue strip.

[EmEyeAaay]

That's amazing, I can't wait to try it out, I've been striping an afghan and wanting it to look random without trying to hard. I may frog a bit since I'm not to far along.

[sakurasaku]

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."

 

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.

[Bookchick29]

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.

[Sarah Jane]

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!!!

[crochetluvknot]

funky reporter Im with you i read through these posts and um i have to say i am and to i could even understand that post not for me at all.

[sem464]

I'm sorry, I'm horrible at explaining stuff.

 

Let's say you wanted to make an afghan that was a golden rectangle, and you wanted the shorter side to be 4 feet. Ok?

 

So, let's call this side A.

 

A = 4 feet

 

To find out how long the other side needs to be, you multiply A by 1.618.

 

4 x 1.618 = 6.72.

 

So Side B would equal 6.72 feet.

 

B = 6.72.

 

That's all!

 

The rest of that was explaining how one would construct a traditional golden rectangle.

 

Ok all, if you will follow the formula above and forget all the other stuff that most of us can't understand, it will help you make an afghan with eye pleasing proportions. Thanks Leah, for the condensed version.

[useratl]

And WHAT would that be exactly?????? not that I've understood anything in this thread so far, but I'll play along!

 

 

I got lucky and managed to make SOMEBODY over at crafster explain how to do some fibonacci striping so I could figure it out! I'm pleased and amazed. I mean, I get the addition thing, but I couldn't translate the needlework I was seeing into a pattern!

 

http://www.craftster.org/forum/index.php?topic=171112.0

 

good luck! Hope this helps you as much as it did me.

[Loralynn]

This thread is so cool! If I turn off the preschool programming and send my daughter to the other room I am actually understanding this!

 

I am going to show/tell my dh about this thread. Finally a way that he can relate to my crocheting!!! He has had Advanced Calc., Physics, blah...blah...blah... while going for his Masters in Structural Engineering and he really is something of a math geek! It's usually Greek to me!

 

Thanks for starting such a thought provoking thread!

[fiddleyarn]

This thread is so cool! Thanks for starting such a thought provoking thread!

 

I agree! I just read the whole thread. Fascinating concepts! Has anyone seen the crocheted coral reef? (I didn't save the web address). I once made an ---um, "interesting" piece by crocheting a small circle, then 2 single crochets in each stitch. Just kept doing that and it made neat ruffles, I think the ruffly scarves are made that way too. Chain the length. 2 SC in each chain. Repeat until it's the width you want.

[alibra]

I am getting a headache trying to figure this out...I crochet to relax and de-stress and multiply that times l.168! Geeze!

[sonnets_and_stitches]

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 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

[sonnets_and_stitches]

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?

[Etrnlife]

http://www.greatknitdesigns.com/ Using this program is the best way I know of to design blankets/shawls/circle items. Less stress on my brain. :O)

[funkyreporter]

I using a Fibonacci sequence of rows.

 

And WHAT would that be exactly?????? not that I've understood anything in this thread so far, but I'll play along!