Proportions, Space, Framing

This is a slice through a Nautilus shell. This particular one is in the Zoology Museum in Cambridge, where I photographed it with my iPhone.

I tidied up the reflections and the background, but otherwise, this is a Nautilus shell as the Nautilus made it – except sliced in two.

The Nautilus has ninety tentacles that it waves about in the water to take food that passes. The shell is its home.

It starts out small, and as the Nautilus outgrows the shell it builds a bigger compartment around itself. You can see the little tubes that are its last contact with the compartment it vacates before it seals it off.

The Nautilus builds about 30 compartments during its lifetime. And in doing so it makes this spiral of air-filled compartments.

The compartments that have been sealed off are water tight, which is why a whole Nautilus shell without the creature that lives in it, floats.

I made a joke about the stupidity of Brexit, pointing out that during its life, at no time does the Nautilus abandon its shell in the vague hope that it will find another one as well fitting.

Here though, I just want to talk about the shape of the shell.

There are classical design rules. They are the rules that classical architecture follow. A certain height to a certain width, a certain distance to another certain distance.

Quite the opposite of building economically at the expense of craft and the love the product. That is, building to formula of whatever shape will satisfy the building regulations for the least wastage of plasterboard sheets to line out a room on a housing development…

Some people believe that the reason the classical design rules are as they are is because their appeal is hard-wired into our brains because of the way the world around us is constructed.

Or to put it another way, there is evidence of ‘rules’ of composition throughout nature, and these may explain why an extended form of these rules exists in classical art and design.

The Fibonacci Series in Nature and Classical Design

The Fibonacci mathematical series is simple. Start with the numbers 0 and 1. Add them together. Add the answer to the larger of the two numbers that have just been added. Repeat, and repeat, and repeat. That’s a Fibonacci sequence.

0 + 1 = 1
1 + 1 = 2
1 + 2 = 3
2 + 3 = 5
3 + 5 = 8 etc.

And as the series progresses, two things become apparent.

The first is seen if we construct rectangles with sides that are in the ratios of the series (1:1, 1:2, 2:3, 3:5, 5:8 etc) and set them one on another so that sides of the same length are laid on top of one another. If we then draw a line that curves to follow the corners of the rectangles, it forms a spiral.

And that spiral is the spiral that is echoed in nature – in seashells and fruit and flowers and endless features of the natural world.

The second interesting thing we can see as the series progresses is what happens to the ratio of the larger number to the sum of the larger and smaller numbers,.

In the example above I only got as far as 5:8, but if we keep going, the ratio approaches a number, a fixed ratio. It is that described and used in art and architecture throughout history certainly back to the Ancient Greeks, and which is known as the Golden Section.

Another way to express it is Phi (pronounced Fee), which is 1.618.

Take a length, any length. Divide the length by 1.618. The ratio of that part to the whole is what is called the Golden Section.

Here’s a a yellow rod. The red part if the length of the yellow rod divided by Phi.

The Golden Section is the ratio of the red part to the whole length of the rod.

And that relationship is used over and over in the classical tradition of design in art and architecture.

Turn the two parts of the rod at 90º to one another and we have the proportions of a room, or a picture frame.

Perhaps someone could make a digital camera with a sensor in that proportion.


  1. I would venture to say that those who have an innate sense of balance – a “good eye”, if you will – make better photos – so a big fat “NAY”! to your digital correction suggestion, David 😉


    1. Film manufacturers have tried lots of different ratios. There is the 3:2 of most consumer film cameras. There is the 6:4.5, 6:7, and 1:1 of medium format film cameras. And there is the 5:4 and other arcane ratios of large-format film cameras.

      Digital camera manufacturers broke ranks with traditional film aspect ratios with 4:3 and 16:9.

      A sensor of the Golden ratio would be approximately 5 by 3, which sits somewhere in among the ratios that have already been used.

      I hear you about balance and a good eye. In the forums, camera buffs often come back to saying they dislike the 3:2 ratio of 35mm film cameras. Personally, I think that as viewers, we work with what is in front of us and accept it. But perhaps some part of our hard wiring would like 5 by 3.

      Liked by 1 person

  2. Margy says:

    Excellent story! We had some Christmas photos taken recently. My daughter wanted to print and frame a few and discovered that some of them didn’t easily crop to a standard size frame!


    1. Thank you. Yes, and if one adds a mount of, say, two inches all around to a photo, then that means different proportions for the frame compared to the print.


  3. Tamara says:

    Such gorgeous proportions! Great all ’round post, David.

    Liked by 1 person

  4. reb says:

    I thought of Fibonacci as soon as I laid eyes on the picture. Math was never my strong point, but I’m fascinated by it, nevertheless …

    Interesting point about Nautilus/Brexit. I’m trying to keep up with all the twists and turns in the news, but it’s hard, as so much is going on on this side of the Atlantic.


    1. Channel 4 News interviewed the Norwegian Prime Minister. She smiled so nicely while she said that she would veto Britain entering EFTA because Britain had shown itself to be a disruptive and abusive partner. Theresa May is still insisting on no new referendum but ministers within her party are reported to be pushing her that way. The same with MPs in the Labour Party – but Jeremy Corbyn doesn’t want a new referendum because he wants Britain out of the EU for his own reasons – read for some insights.

      I read a lot about the USA but not so clear about Canada – what’s the news?

      Channel 4 News:


      1. reb says:

        Will look.

        Not Canada, I follow the American news on CNN.

        Liked by 1 person

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