# Golden Meaning

April 14, 2015 12:59 PM Subscribe

Graphic artists depict the golden ratio – in pictures

Alex Bello blogs about the book: Golden Meaning: 55 graphic artists reveal the maths of the golden ratio

Another look, from Creative Review

Malika Favre's image on her blog

The Golden Ratio in Art Composition and Design

Alex Bello blogs about the book: Golden Meaning: 55 graphic artists reveal the maths of the golden ratio

Another look, from Creative Review

Malika Favre's image on her blog

The Golden Ratio in Art Composition and Design

My problem with this sort of thing is that you would

One of these are in the golden ratio; can you tell which?

posted by BungaDunga at 2:01 PM on April 14, 2015 [3 favorites]

*probably*not notice a difference in any of these designs if you changed the ratio to 1.6 or 1.5 and redid them all based on it.One of these are in the golden ratio; can you tell which?

posted by BungaDunga at 2:01 PM on April 14, 2015 [3 favorites]

The Guardian: "the golden ratio, which is the number 1.618."

It repeats this misinformation 2 more times.

posted by signal at 2:09 PM on April 14, 2015 [1 favorite]

It repeats this misinformation 2 more times.

posted by signal at 2:09 PM on April 14, 2015 [1 favorite]

Was hoping for an illustration of horseshit.

posted by potch at 2:20 PM on April 14, 2015 [4 favorites]

posted by potch at 2:20 PM on April 14, 2015 [4 favorites]

Yeah, post-hoc Golden Ratio hunting is one of the worst fields for curve-fitting special pleading. People love discovering golden sections in the work of Old Master artists, but in fact nobody much was talking about the Golden Section until the C19th.

posted by yoink at 2:42 PM on April 14, 2015 [2 favorites]

**Paper chromatographologist**'s link is a good one.posted by yoink at 2:42 PM on April 14, 2015 [2 favorites]

*Was hoping for an illustration of horseshit.*

Wombat shit is totes golden rectangles.

posted by yoink at 2:44 PM on April 14, 2015 [3 favorites]

My horse only shits in golden ratio spirals.

posted by Joseph Gurl at 3:02 PM on April 14, 2015

posted by Joseph Gurl at 3:02 PM on April 14, 2015

There's a useful gem buried in the horseshit, though. A fine way to tighten up a design of pretty much anything is to use a consistent ratio throughout. Doesn't matter as much what the ratio is - 1:1, 1:1.618, 1:2, 16:9, etc. If you have each element relate to the next smallest and largest elements with the same ratio every time, you'll find some visual harmony.*

Which is why people who slavishly follow the rule often do indeed get good results. It's the consistency that matters, not the numbers.

* Note that this too can become a rule to be slavishly followed. It'll never work for every single part, so don't sweat it when you have to break it.

posted by echo target at 3:26 PM on April 14, 2015 [7 favorites]

Which is why people who slavishly follow the rule often do indeed get good results. It's the consistency that matters, not the numbers.

* Note that this too can become a rule to be slavishly followed. It'll never work for every single part, so don't sweat it when you have to break it.

posted by echo target at 3:26 PM on April 14, 2015 [7 favorites]

___ ___ ____ ____ ( _ )/ _ \ | ___| ___| / _ \ (_) | () |___ \___ \ | (_) \__, | ___) |__) | \___/ /_/ () |____/____/posted by Wolfdog at 4:03 PM on April 14, 2015

That golden ratio photoshopped face next to the original is slightly terrifying.

posted by Metroid Baby at 7:29 PM on April 14, 2015

posted by Metroid Baby at 7:29 PM on April 14, 2015

Huh. I always thought the golden ratio was something else entirely--a rectangle of such shape that when bisected width-wise, the two new, smaller rectangles produced have the same ratio of width to length as the original rectangle. This ratio is 1 : square root of 2.

Does the ratio of 1 : 1.414 have any special name and/or significance?

posted by obscure simpsons reference at 7:49 PM on April 14, 2015

Does the ratio of 1 : 1.414 have any special name and/or significance?

posted by obscure simpsons reference at 7:49 PM on April 14, 2015

*Huh. I always thought the golden ratio was something else entirely--a rectangle of such shape that when bisected width-wise, the two new, smaller rectangles produced have the same ratio of width to length as the original rectangle. This ratio is 1 : square root of 2.*

Yeah, that's ... well that's european paper sizes I guess. Which sometimes people absolutely do incorrectly claim is the golden ratio.

What the golden ratio is is if you have a golden rectangle, you can cut a big square off of one end and you get another golden rectangle. Which is exactly how all the pictures of golden spirals in golden rectangles do it.

posted by aubilenon at 8:35 PM on April 14, 2015 [1 favorite]

*Yeah, that's ... well that's european paper sizes I guess.*

Jun Maekawa has a nice origami book about using a4 paper because of that ratio and how to design around it.

posted by klausman at 10:24 PM on April 14, 2015 [1 favorite]

I've got a reprint of an early 1900's book which says to just avoid obvious to the eye small number ratios like 1:2 or 2:3 and so on.

posted by sebastienbailard at 10:29 PM on April 14, 2015

posted by sebastienbailard at 10:29 PM on April 14, 2015

Hmm, I'd guess that if a rectangular region is 1:2 it can easily appear to consist of two 1:1 regions, so avoiding small number ratios helps create a feeling of overall unity. You'd also want to avoid proportions that are very near to small number ratios.

There's an area of math that quantifies how well an irrational number can be approximated by rational numbers, and I'm pretty sure that it says that the smaller the terms in an irrational number's continued fraction, the worse it is approximated by rational. It'd take a lot of time to explain exactly what a continued fraction is, but if you consult the continued fractions for φ and √2 you can see that they use all ones and all twos, respectively, and so are very poorly approximated by rationals. (For comparision, check out the continued fractions for π and

Personally, I think this is taking a general guideline and pushing it really hard mathematically beyond the limits of our perception, but it is fun.

posted by benito.strauss at 12:31 AM on April 15, 2015

There's an area of math that quantifies how well an irrational number can be approximated by rational numbers, and I'm pretty sure that it says that the smaller the terms in an irrational number's continued fraction, the worse it is approximated by rational. It'd take a lot of time to explain exactly what a continued fraction is, but if you consult the continued fractions for φ and √2 you can see that they use all ones and all twos, respectively, and so are very poorly approximated by rationals. (For comparision, check out the continued fractions for π and

*e*, which have large numbers in their continued fractions.) So this does support the idea that φ or √2 proportioned rectangles hang together best of all.Personally, I think this is taking a general guideline and pushing it really hard mathematically beyond the limits of our perception, but it is fun.

posted by benito.strauss at 12:31 AM on April 15, 2015

I have totally used 3/2 as an approximation for sqrt(2) and it was plenty good enough, plus it's really quick to multiply all four of every pixel's diagonal neighbors by it.

posted by aubilenon at 12:48 AM on April 15, 2015

posted by aubilenon at 12:48 AM on April 15, 2015

echo target: "

If you choose 1:1, your doorknobs are going to be the same size as your skyscrapers.

posted by signal at 8:59 AM on April 15, 2015

*Doesn't matter as much what the ratio is:*"**1:1**… If you have each element relate to the next smallest and largest elements with the same ratio every time, you'll find some visual harmony.*If you choose 1:1, your doorknobs are going to be the same size as your skyscrapers.

posted by signal at 8:59 AM on April 15, 2015

The irony is that the only people who think this sort of thing is cool are those that think the Golden Ratio = 1.6180....blah blah blah.... When any self-respecting mathematician is trying to remember what the real transcendental number is.

According to wikipedia the real golden ratio is the number (1+√5) /2

posted by mary8nne at 1:11 PM on April 15, 2015

According to wikipedia the real golden ratio is the number (1+√5) /2

posted by mary8nne at 1:11 PM on April 15, 2015

*That golden ratio photoshopped face next to the original is slightly terrifying.*

I think that one, and the wine/glasses illustration, are the most successful of the set in the article. The rest just shove a bunch of data down your throat and call it design, which misses the point that the Golden Ratio is supposed to be

*tacitly*pleasant.

posted by a halcyon day at 1:27 PM on April 15, 2015

As someone with some math background I'd say that when I think of the golden ratio I think of it as the positive root of

and the fact that it happens to be equal to (1+√5) /2 is just as co-incidental as the fact that it happens to have a decimal expansion starting with 1.618033988.... And I do think it's cool, because that's about the simplest quadratic equation with non-trivial, real roots.

posted by benito.strauss at 2:05 PM on April 15, 2015 [1 favorite]

*x*^{2}−*x*− 1 = 0and the fact that it happens to be equal to (1+√5) /2 is just as co-incidental as the fact that it happens to have a decimal expansion starting with 1.618033988.... And I do think it's cool, because that's about the simplest quadratic equation with non-trivial, real roots.

posted by benito.strauss at 2:05 PM on April 15, 2015 [1 favorite]

*When any self-respecting mathematician is trying to remember what the real transcendental number is. According to wikipedia the real golden ratio is the number (1+√5) /2*

Any self-respecting mathematican just had a spasm and spat the word "Algebraic!" at their screen.

posted by Wolfdog at 4:53 PM on April 15, 2015 [2 favorites]

*blushes for not having noticed*

posted by benito.strauss at 5:10 PM on April 15, 2015

posted by benito.strauss at 5:10 PM on April 15, 2015

Leonardo's theorized golden mullet is 1.61 times longer in back.

posted by BrotherCaine at 5:25 PM on April 15, 2015

posted by BrotherCaine at 5:25 PM on April 15, 2015

I've loved mathematical games and curiosities and puzzles since I was a kid, and I read Martin Gardner's columns in

Yet one of the most delightful things I came across as an adult, decades after I had first heard about the wonders of the Fibonacci sequence, and years after I had finished any formal instruction in math, was the idea that the Fibonacci numbers didn't have to be derived recursively, one after the next, that there was a closed-form expression for the Fibonacci numbers:

F(n) = [φⁿ - (1-φ)ⁿ]/√5

posted by DevilsAdvocate at 8:12 PM on April 15, 2015

*Scientific American*with relish (and his older ones, from before I was born or old enough to understand, in collected books), and so I had been exposed to the Fibonacci sequence since an early age.Yet one of the most delightful things I came across as an adult, decades after I had first heard about the wonders of the Fibonacci sequence, and years after I had finished any formal instruction in math, was the idea that the Fibonacci numbers didn't have to be derived recursively, one after the next, that there was a closed-form expression for the Fibonacci numbers:

F(n) = [φⁿ - (1-φ)ⁿ]/√5

posted by DevilsAdvocate at 8:12 PM on April 15, 2015

DevilsAdvocate, you might enjoy this: Take the equation that defines the Fibonacci numbers,

(1) f

re-write it as

(2) f

and make a wild-ass guess that

(3) f

When you plug equation (3) into equation (2) and cancel a few terms, you find that r must satisfy the equation

(4)

which is the equation that I think of as practically being the definition of φ. You have to do a bit more work, like dealing with the fact that equation has two roots, φ and 1 − φ, and correctly combining the φ

posted by benito.strauss at 9:05 PM on April 15, 2015 [1 favorite]

(1) f

_{n+2}= f_{n+1}+ f_{n}re-write it as

(2) f

_{n+2}− f_{n+1}− f_{n}= 0and make a wild-ass guess that

(3) f

_{n}= r^{n}for some real number r.When you plug equation (3) into equation (2) and cancel a few terms, you find that r must satisfy the equation

(4)

*r*^{2}−*r*− 1 = 0which is the equation that I think of as practically being the definition of φ. You have to do a bit more work, like dealing with the fact that equation has two roots, φ and 1 − φ, and correctly combining the φ

^{n}and (1 − φ)^{n}terms, but that's how φ gets in to the closed expression for the Fibonacci sequence.posted by benito.strauss at 9:05 PM on April 15, 2015 [1 favorite]

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posted by paper chromatographologist at 1:13 PM on April 14, 2015 [13 favorites]