parallax tramps - photo blog

the golden triangle

photo blogPosted by christian rollinson Sun, October 19, 2008 13:20:49
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.

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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.

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