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.

[funkyreporter]

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

[Gran]

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.

[Ah Leah]

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

 

Ok mom, here you go.

A "golden rectangle" is like this.

 

You have a square. We'll call this B. All sides of square B are equal to Number B. When rectangle A is added on to square B, the length of rectangle AB is measured as A. When you subtract measure B from Measure A you get the width of the smaller rectangle A, which, when separated from square B is also a golden rectangle. The golden ratio, which is = the square root of 5 divided by two, or 1.618. So, if you have a square with all sides equal to 10 (so, side B=10), then you multiply 10 by 1.618 which gives you 16.18, thus giving you side A of rectangle AB. When you remove rectangle A from rectangle AB you have 16.18 minus 10, which equals 6.18. When 6.18 is multiplied by 1.618 you get 10 (well, 9.999924 or something, but friggen close enough. I don't feel like actually doing the math).

 

Fibonacci sequences are fun. It goes like this. F(n) = 0 if n=0 OR 1 if n=1 or f(n-1)+f(n-2) if n>1. So, for instance, the first fibonacci numbers are denoted as Fn, for n = 0, 1, … , are: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711. See? you add every two numbers to get the third number. 1+1=2 2+1=3 3+2=5 5+3=8, and so on, ever increasing. To put this in a rectangle, let's say we have a square with all size equal to 8. There is another square ajoining that with all sides equal to 5. A square on top of that square has all side equal to 3. Next to the three is a square with all sides equal to two. Below that is two small squares with all sides equal to 1. I know that didn't make much sense, so here's a little drawing:

 

I hope that a) I didn't sound like too much of a math geek and b) that made sense.

[RachelG]

Ok mom, here you go.

A "golden rectangle" is like this.

 

You have a square. We'll call this B. All sides of square B are equal to Number B. When rectangle A is added on to square B, the length of rectangle AB is measured as A. When you subtract measure B from Measure A you get the width of the smaller rectangle A, which, when separated from square B is also a perfect rectangle. The golden ratio, which is = the square root of 5 divided by two, or 1.618. So, if you have a square with all sides equal to 10 (so, side B=10), then you multiply 10 by 1.618 which gives you 16.18, thus giving you side A of rectangle AB. When you remove rectangle A from rectangle AB you have 16.18 minus 10, which equals 6.18. When 6.18 is multiplied by 1.618 you get 10 (well, 9.999924 or something, but **** close enough. I don't feel like actually doing the math).

 

I hope that a) I didn't sound like too much of a math geek and b) that made sense.

 

Whaaaaaat? (Math was not my best subject!)

[Ah Leah]

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.

[funkyreporter]

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??? maybe a little ex parte or a motion in limine??? Yeah, that's what I thought:manyheart

[Ah Leah]

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):

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?

[ankey]

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...

[funkyreporter]

Yup, I love the Golden Ration too:no

 

Ah Leah, you are a strange creature... you said you weren't good at math... you LIED:D

[Ah Leah]

Yup, I love the Golden Ration too:no

 

Ah Leah, you are a strange creature... you said you weren't good at math... you LIED:D

 

I'm not good at math at ALL. You saw the report cards.

[KateCrochets]

Ahhhh, Phi!

 

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

 

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

 

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

[Bookchick29]

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.

[KateCrochets]

It's where each number is the sum of the two numbers preceding...

 

1 1 2 3 5 8 13 21 34 . . .

 

There are several patterns out there for Fibonacci afghans and sweaters and the like (more knit, that I've seen), and usually just goes up to 5 or 8 rows, so that the color sequence would be 1 row A, 1 row B, 2 rows A, 3 rows B, 5 rows A, 1 row B, 1 row A, etc etc. It's quite cool looking!

 

(How does this relate to phi? It converges on phi. That is, the ratio of each number to the number before it approaches phi)

[Krystal16]

Well, this would explain a lot. I'm a math geek as well - numbers and ratios and statistics and the like have been a part of my brain for as long as I can quantify (joke intented).

 

Seems that my mind has easily adapted this to be "roughly" two-thirds, and nearly all of my afghans (that aren't a fixed pattern and thus not relevant) have wound up "near" 2/3 by my eye-balling them. I wonder if I was to go back and measure if they would really wind up to be the golden ratio...subliminally deliberate, of course!

 

I've always thought of crocheting as numbers and partially related to a subliminal urge to categorize and quantify a la O.C.D.... it's my math brain trying to escape while my body is trapped in stay-at-home motherhood.

 

Ah Leah, simply because you did poorly in math classes does NOT mean that you lack the capacity to understand math concepts that baffle others. Time and again it's been shown that grades do not reflect aptitude. Grades simply show an abillity to conform to test-taking, and from the little I've gleaned, you're not exactly a conformist....in any way.

 

But, I digress...or is that converge?

[tbird]

If this math stuff appeals to you, you might enjoy Ruthie Mark's new book, called "Geometrics." It's designed for crafters, not math geeks, and explains how to take ideas like the Golden Ratio and apply them to different kinds of patterns, like circles. It's very fine.

 

And if you are really hard-core, Google for "hyperbolic crochet." *Doing* it is a lot easier than it sounds...and it comes up with some of the coolest organic shapes I've ever seen made in yarn.

 

Yours truly - the astrophysicist*

 

* Not enough jobs for rocket scientists, so now I do computers.

[Ah Leah]

Ah Leah, simply because you did poorly in math classes does NOT mean that you lack the capacity to understand math concepts that baffle others. Time and again it's been shown that grades do not reflect aptitude. Grades simply show an abillity to conform to test-taking, and from the little I've gleaned, you're not exactly a conformist....in any way.

yes yes, I've heard the spiel many a time. I actually am really bad at math though. Still haven't managed to pass pre calc, and I've taken it three times now, at three different schools. I'm really terrible at math. Some people have suggested dyscalculia but I really don't want the label of a learning disorder. So, I'll just go along my merry way, stopping now and then to confuse people with random knowledge from my plethora of mostly useless information.

[Lisaizme]

I'm gonna send this thread to my daughter, who is majoring in physics because she loves calculus and there's LOTS of calculus in physics...

 

and see if she will comment on it.

 

She may just think it's more of her mom being weird about crochet though.

 

I've got a sierpinski shawl somewhere in this house.. that I'm going to have to frog I think. Don't have enough yarn to finish it and the yarn I started it with isn't made any more

 

I'll try to make a pic before frogging.. it's truly awesome. (Looks kinda like a Tri-force.. for those who are familiar with Zelda)

[funkyreporter]

There sure are some smart people here:think

[tbird]

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 :-)

[Lisaizme]

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

 

She's at FSU (Florida State) while Mom & Dad and Bro are still in TX.

 

There's definitely a math gene going on in the family.. lots of us like it, but not all of us chose our majors based on love of math.

 

When I tell people she's majoring in Physics, I often get the comment, "Boy she must be smart". I tell them "Well, if I wasn't there at the time, I'd swear she wasn't mine." I like math quite a bit, but science leaves me cold.

 

I'm still waiting for her to reply what she thinks.. or any comments on the Golden Ratio

[Aggie May]

I just go by what looks pleasing and to Heck with Math.

 

I think I almost got it though so the descriptions must have been good because I am no Math Nerd.

We only did Arithmetic when I was at school.

Have fun.

Colleen.

[Krystal16]

That was me liking the math in crochet