# The Beauty of Geometry III

In my previous post I said I’d explain the link between Fibonacci numbers and a device we photographers often use. It’s a little technical but not very difficult to understand so bear with it!

Many plants arrange their leaves around the stem in a pattern in which each new leaf is positioned at an angle close to 222.5° around from the previous leaf (it has been demonstrated that this maximises the amount of light and water reaching each leaf). This image illustrates this pattern well. If it’s not clear how, I’ve created a version of it where each of the pairs of coloured lines represents this angle. The ratio of this angle and the angle of a full circle (360/222.5) is 1.618 (rounded). You may already recognise this special number: if not remember it for a moment.

The Fibonacci sequence (described in detail on Wikipedia) is a series of numbers in which each number is the sum of the two numbers before it. It looks like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34…. Starting at 2, the ratio between any pair of successive numbers in the sequence gets progressively closer to 1.618. Recognise that ratio?

That ratio happens to be what is commonly known as the Golden Ratio, a ratio many photographers may be familiar with as a compositional aid. If you’re not familiar with the idea, Wikipedia explains the Golden Ratio in detail and Digital Photography Review has a good article illustrating its use in composition, as does photoinf.com. This looks suspiciously similar to the well known Rule of Thirds, which I think is just a simplification of the Golden Mean proportions.

Ironically, this image uses neither for its composition, proving that rules are made to be broken!

An interesting theory Adrian, but I have to take issue with the term “Rule of Thirds”…

There’s another “rule”, that of symmetry, that more often than not contradicts the “rule” of thirds. So. with luck they cancel each other out and we’re left with no rules.

Which is how photography ought to be, no rules – just good photographs!

I share your wariness of “rules” in photography George.

To be clear, none of this was intended as an endorsement of the use of “rules”, I was merely drawing attention to links between seemingly disparate domains of knowledge.

About the “irony” of not using the mentioned rules for composition in this particular capture, in fact, it doesn’t really matter.

It doesn’t matter that you intentionally (dis)obeyed the Golden Ratio rule, it is the brain of the spectator that decides.

As a matter of fact, the spot that most captivates my attention in your photo is the little white button (burgeon) near the — surprise — upper left intersection of the golden mean lines.

I never found more than speculation about why the human brain focuses attention to portions of a bordered image this way — I personally guess it is a consequence of evolution in a Fibonacci world — but it thrills me each time I think of its puzzlement, nevertheless.

Very beautiful captures, your last ones (like all the blog, you know I think it so). I like the somber but at the same time calm, almost mellow tones, so much more surprising as we see them in monochrome.

Fibonacci numbers? oh no …. my high school math headaches are coming back

Fibonacci introduces another idea it seems, that of rhythm. It’s beautifully illustrated in your composition of the leaf pattern, which to me has a distinct rhythm around the center focus. Rhythm can be found in many forms… photography, painting, architecture, music, poetry, nature. One of the many reasons I love your blog is not only your great images, but your fun and fascinating discussions as well :^)

Beautiful capture!