Part 4, research point 2 – the Golden Mean

From the course notes:

 [Essentially] the Golden Mean is a proportion in which a straight line or rectangle is divided into two unequal parts in such a way that the ratio of the smaller to the greater part is the same as the ratio of the greater part to the whole

This site (Maths is Fun) describes the Golden Mean and its relationship to Fibonacci numbers thus:

… just like we naturally get seven arms when we use 0.142857 (1/7), we tend to get Fibonacci Numbers when we use the Golden Ratio.

Maths is Fun,B

Sometime last year, watching the live stream from the NASA clean room where they were building the Mars 2020 rover, I noticed a Fibonacci moment when all the engineers had arranged themselves unawares into an approximation of that classic formation. I doubt I’ll forget what this is called but I impressed myself by just recognising it as a thing in the first place, never mind that it had a mathematical descriptor!

Screen capture of the LiveLab stream with my roughly drawn Fibonacci spiral added in orange pastel.

Much the same applies to the rule of thirds which describes the best (and worst) places to have the focus of your painting. Again, a mathematical descriptor leading to a rule about imagery.

I see the point but I also see how breaking that rule – and if breaking a rule doesn’t kill you or anyone else why not do it? – can be unexpectedly jarring and may be the thing that causes a painting to stand out. I don’t think Magritte had conformity in mind when he painted The Son of Man, perhaps he had ya boo to you and your rule in mind. It’s that thing about knowingness, understanding a standard enough to subvert it deliberately for your own purpose.

To me a rule is only useful if it keeps you safe or clarifies messages. Driving conventions for instance, and for me the much abused Oxford comma which can ensure you don’t make some outrageous attributions such as:

My heroes are my parents, Superman and Wonder Woman

[unlikely, try that again with an Oxford]

My heroes are my parents, Superman, and Wonder Woman

[that’s better]

Taken from BHP Headquarters Meme Monday at

I can’t help thinking that, with so much of art history being dominated by men, many of them in the past also being engineers and gadget buffs (lenses and the camera obscura for instance), that something intuitive has become mathematicised and ossified into a rule. I wonder who in contemporary art explicitly considers these rules in their own work.

For me, my current task is to internalise these rules so that, in due course, I’ll be able to mess with them to good effect.



Post script: I hit send in the middle of trying to conceptualise the rationale for primarily perceiving the golden ratio as pleasing and then formalising it mathematically. After a quick search, I came up with a Guardian article from 2009 in which an engineer, Adrian Bejan, describes his thoughts about the biosocial reasons for it. He says that an animal’s world:

[…] whether you are a human being in an art gallery or an antelope on the savannah – is orientated on the horizontal. For the antelope scanning the horizon, danger primarily comes from the sides or from behind, not from below or above, so the scope of its vision evolved accordingly.


Whether intentional or not, the [golden] ratio represents the best proportions to transfer to the brain.


This is the best flowing configuration for images from plane to brain and it manifests itself frequently in human-made shapes that give the impression they were ‘designed’ according to the golden ratio.

I find this ethological conceptualisation appealing, especially as it confirms my view that the perception, driven by a sense of pleasure, preceded the mathematics. It would seem that a preference for the golden ratio/Fibonacci arrangement is in-built and all we need to make it work for us as artists is to have our explicit attention drawn to it.

I have listed the Guardian reference, unfortunately the academic paper referred to there is behind a paywall.


Maths is Fun. [online] Available at,B. Accessed 5 June 2020.

Oxford Comma. [online] Available at Accessed 5 June 2020.

McVeigh, K. 2009. Why Golden Ratio pleases the eye: US academic says he knows art secret. The Guardian. [online] Available at Accessed 5 June 2020.

Learning outcome 4: evidencing reflection, learning, and self-advice.

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