The golden ratio

We're all familiar with rule of thirds as a compositional aid in our photography...

rhapsouldize

selfishtears

But how familiar are you with the golden ratio and it's permutations? Discovered by the ancient Greeks, the golden ratio is a geometric formula which leads to an aesthetically pleasing composition. Any image following this rule is thought to be visually harmonious.

(skip to the next photo if you don't like maths :D )

The formula starts with a square (shown here in blue)

Now we divide the base of the square into two equal parts (point x) and use this as the centre of a circle (the radius of which is shown by the arrow between x and y).

Using this radius, we extend the base of the square to give us a rectangle which ends at point z.

So we now have a rectangle [c], made up from the square [a] and the extension [b].

With me so far ;)

It's this relationship between a and b that we're interested in. The ratio of these parts is 5:8 (or 1.618 to1), which is very close to the ratio of 35mm film, which is 24mmx36mm(1.5 to 1)

Henri Cartier-Bresson was aware of this, and as a result never cropped any of his images. Every photograph he displayed was a full 35mm frame, just as it came from his camera.

Donald McCullin, best known for his war photography, once said of Bresson 'Henri really introduced the concept of perfect composition into our thinking. He was the first to teach us to compose within the specific shape of the 35mm frame and to utilize the very nature of that camera and format'.

Here we see the rule of thirds grid overlayed with the golden ratio grid in yellow. Both are similar, but the rule of thirds is a simplified version. Notice how the lines relate to the formula diagram above.

Examples of the golden ratio ...

josh

zuzana

arthur mola

Another example of the golden ratio can be found in the Fibonacci spiral.

In the Fibonacci sequence, each successive number after 1 is equal to the sum of the two preceding numbers (i.e- 0,1,1,2,3,5,8,13,21,34,55, etc.)

This is a visualisation of that sequence using the tiling of squares, with the rectangles repeating and increasing size.

Notice again how the rectangles within rectangles correspond to the ratios above.

If you then join the corners you get a fluid logarithmic spiral....

...which is the reason spiral staircases can be so beautiful.

bryan marshall

electrified clown

sanctamonius

It's possible that we are genetically programmed to recognise the ratio to be pleasing to the eye.

sandro di carlo darsa

But the main point of this piece is not the golden ratio in grid or spiral form, but the lesser known golden triangle.

We draw a line from the top left to the bottom right of our golden rectangle, and another line from the top right towards point 'y' until it hits the first line. We now have three different triangles, and placing components roughly within these portions gives a harmonious composition, as does the use of the geometric lines as a guide. Also, placing a point of interest just within the smallest of the triangles (the saddle) gives a pleasing composition.

laith

cmphotography

I was amazed to discover the maths involved in some of my favourite shots...

chris weeks

treamus

darren abate

jason lee perry

thorsten overgaard

severin koller

I also noticed elements within photographs that corresponded to these angles...

table lines....

chris weeks

shafts of light...

riccardo

and body shapes...

nhat nguyen

obsidian fox

flipo

I always knew these images looked 'right', but never quite knew why.

Now I do. It's the golden ratio.

***************************************************************************************

There's a fantastic web page available here which allows you to load your own images and view them with a variation of the golden ratio over them as a compositional aid.
The golden ratio is also prevalent in nature. Take a look here.

-Christian

Comments

[Scott]

Wow. Great blog! I'm going to have to check it when I get home! Surprised to see a shot I took 11 years ago up there!

[C Weeks]

i was stoked when i got an email from christian telling me he saved this as a draft of a previous blog post on uber.

seriously, you will not find that shit on wanker's site. wanker doesn't even know this stuff.

you'd be better off knowing this information rather than knowing most "gear-related stuff" for sure.

happy this was posted!

[Brian Webb]

Very good article and definitely an interesting read. That being said, sometimes I feel that too much analysis of an artistic medium does more to constrain then to expand.

[2REP]

great article to explain the Golden Ratio, I only know the rule of thirds before reading this :D

Thanks Christian!!

[Tabish Bhimani]

Hey Chris! good to message you after so long. I was actually aware of the golden ratio, the phi, for the past 5 years now. that said, it's fascinating how you've composed your images in the ratio, without really realizing.

Oh and your fuck count? Ze-fucking-ro.

[miss-maple]

that's ace! i'll try some of my pictures, interesting post:) i'm happy that it haven't died with uber:) (poor uber, btw)

[Thorsten Overgaard]

Super. Love it. I'm not for people "figuring out" or "measuring" a photo, but I like it as a home study. When I do photo seminars, part of it is composition were basically all rules on composition and aesthetics goes. But the main think is to see the picture and frame it "it's there."

This is great homework and I've never seen it laid out so applicable. One could also go shoot for one composition, like one can go shoot, limiting one self to say a 50mm only.

[Chris Livsey]

Excellent summary. There's always a pedant though :-) You should never say never, well very rarely.
HCB did crop two shots that we know of. His, arguably, most famous "Behind Saint-Lazare Station" Place de l'Europe, Paris 1932. One print exists of the full frame and it is reproduced in " Scrapbook" Thames & Hudson 2006 Pg 87 . The other... do your own research :-)

[peter]

good encapsulation
lot of writing on the golden triangle
good and bad

[Stewart Bywater]

Great post. I think I saw it on Uber too, but it's good to see it again. Very clearly explained and nicely written. Good job mate!!

S.

[Namelast]

Great article, I remember it from Uber, thanks for reposting it here!!!

P.S. as a side note... HCB did crop some of his photos... He was great, but not unerring ;)

[Sonny Thakur]

This is simply amazing. It takes a great eye to notice all the details in the photos and im not surprised it was through Christian's. Great entry, bookmarking and archiving. :)

[Michael]

good and informative writeup.

but linking to people on uber is pretty useless.

[severin]

of course i know this... but i never think about it.. i shoot how i feel like.. but often it ends up in the golden ratio.

nice examples here.. and cool to see one of mine up there.. wouldn't have thought about this one in the golden ratio ;)

cheers

[meredith]

leave it to christian to write a post like this :D really interesting and cool post. i was surprised to open my rss feeder and see my shot at the top :D thanks!

[Christian Rollinson]

thank you very much everyone for the great comments, and michael, sorry about the links to uber, but i did the draft just before uber went tits up again! a lot of the people are on the facebook/friends of uber page so you can find them there.

[Luca]

very very nice and interesting post!! i just love it! I study physics at the university... and I see maths everywhere... I'm very happy to see it also here!! :)

[cha]

i'm not sure i'll agree with maths then, some of these shots don't look aesthetically pleasing to my eyes, mostly in your golden triangle thing, it seems to be more random as a rule, one of these shots isn't even 1.5/1 ratio.
what about central compositions, that seem to have a lot of success ? do the greeks have any input on that ?
hehe

cheers anyway, that mustve been a lot of work writing all that.

[Arthur Mola]

i remember this post from uber- loved it then and it was nice to see it again!

interesting! :)

[Mark Greenmantle]

Rockin post with a great selection of captures shown that most of us already know and love. Funny how I'm often drawn to see golden ratio shots more than rule of thirds when I shoot.... though them turning out that way or not is another thing. Rules are there to be broken. =)

[Isaac]

So wonderful to have this back here (it was impossible to find in Uber "shortly" after it was originally poster).

[zabong]

This is one of the best posts I ever saw on the net. There are some pictures I really love, and a good theory of why they work.

[Kim Long Vo]

I loved this post when I first read it. Wish the images still worked though. =[

[xanax]

Please one more post about that.I wonder how you got so good. This is really a fascinating blog, lots of stuff that I can get into. One thing I just want to say is that your Blog is so perfect