The Geometry of Art and Life

By: Adam Marelli

“What should I read to learn about composition?”


It is a simple question with a million answers.  Most photographers will agree that composition is essential to photography.  Otherwise, how do you place subjects in a frame?

Leonardo DaVinci

But if you ask where you should go to learn about composition, the answers vary enormously.  Some might tell you to study the Golden Ratio, others will say that you can just use the Rule of Thirds, and another group will tell you to figure it out intuitively.  All three of those approaches will never lead to an understanding of composition.  Why?  Because if you want to understand composition, you’d like to understand why its inventors were not artists at all.


As a quick reference, here are some clarifications to the points that you may read online, which are usually well intended, but terribly inaccurate.

Not correct use of Golden-ratio-ii

The Golden Ratio: As seductive as it seems, the Golden Ratio and the Rectangle of the Whirling Squares do not fit into a 3:2 aspect ratio.  Whenever you see a Golden Ratio spiral drawn over a photograph like in the above image, it is safe to assume that whoever is doing this does not know anything about composition.  It is interesting to learn, but it does not fit into the shape of a 35mm negative.  (See Jay Hambidge’s The Elements of Dynamic Symmetry for more on this idea.)


The Rule of Thirds: This is the most basic interpretation of the concept known as “rabattement.”  It is a French term that means, “rotating the short side of a rectangle on to the long side to create a division of the whole rectangle.”  Learning rabattement will allow you to understand why the Rule of Thirds, as it is presented in photography, is so basic as to render itself nearly useless.  (Wikipedia has a nice GIF to visualize this process here.)

Francis Bacon detail

The intuitive approach: While there are without a doubt a handful of individuals in history that seem to express a “gift” for art, music, architecture, mathematics etc., taking an intuitive approach to any subject where highly trained professionals operate will forever short change your potential.  For those who are worried that “learning” will inhibit their creativity, I will defer to an expert on the subject, a Mr. Leonardo Da Vinci, who cautions artists against the gap when your artistic desires exceed your ability, or as he puts it:


…when your views are in advance of your work.

Plato Timaeus

The study of composition is at least 3,000 years old.  One of the oldest texts that speaks explicitly about it is Plato’s Timaeus.  In an effort to make sense of the design elements in the universe, Plato formally introduces ideas like Platonic Solids and the Golden Ratio.  While academics argue about their origins, Plato can certainly be credited with popularizing the ideas.


Since then, the divisions of space (later known more simply as composition) have been explored by some of the greatest mathematical and artistic minds in history.  Figuring out something that took 3,000 years to evolve on your own is not ambitious; it is absurd.  The aim of the Greeks, the Romans, and the Renaissance were to make sense of the world around them.  They all searched for patterns of growth.  This led to the study of the biological world and the mineral world.  From what they observed, different sets of mathematical divisions governed things that were living, like trees, from things that were not, like crystals.  Based on their studies, artists and architects experimented with applying systems of design to their creations.  And while this is easily mistaken for a “God complex,” it appears that most architects and artists proceeded in a humble manner.  They revered the creations and nature and rarely verbalized the superiority over the natural world.  They were more like nature’s apprentices.  You could call it an attempt to make sense of the chaos of life through the observation of nature.


Where does that leave the photographer in this long history lesson?  Usually very lost.


The next logical question is how can a photographer use any of this stuff when they pick up a camera?


If the path to understanding composition was clear, I imagine less people would ask about it in the first place.  But one of the reasons that composition can be hard to study is that it is a complex history, which is partially shrouded in secrecy.  Now before anyone starts talking about a new world order or secret societies, let me assure you … it is possible to study, understand, and use composition without turning into a mason or talking to aliens.  But there were artistic guilds and scientific societies that guarded their research.


During the Renaissance in Europe, secrecy in a guild was mandatory.  On top of that, any artistic, philosophical, or scientific findings that contradicted the Catholic Church could result in death.  Fortunately for a contemporary photographer, these ideas can be studied without ruffling any institutional feathers.


Composition came way before photography was even invented.  So if you want to learn about it, it’s best to study a book that puts the history of composition into perspective.

Vitruvius 10 books on architecture

Where did composition come from?  The origins of composition are in music, geometry, and the study of nature. Names like Plato, Archimedes, Vitruvius, and Pythagoras figure heavily in this conversation.  The funny thing is that none of them were artists.  They were mathematicians, philosophers, and one was a builder.  When the artists of the Renaissance rediscovered the works of the Egyptians, Greeks, and Arabs in the 15th century, it flung open the door to design and at a bigger level of creation.  Artists took these ideas and ran with them.


When we look at what artists do, we can say at their most basic level artists create.  When they are not busy making things “that your kid could do,” they are presumably making interesting things.  Someone who wants to “create” might take a cue from nature.  It seems sensible, right?  Regardless of any belief system, nature is a heck of a designer.  Her endless forms, shapes, and variety continue to mystify us today.  The more we think we understand, the more we realize we are not even scratching the surface of how nature really works.


This is the starting point for writer Matila Ghyka in his book, The Geometry of Art and Life. His short novella (it is less than 200 pages) explores the historical roots of composition.  It connects many different types of design with unified theories.

Light at the end Adam Marelli

He does not take sides in the arguments.  I never got the sense that he wanted to convert anyone into thinking composition was anything more than a tool.  He presents examples from science, art, and architecture so thoroughly that the question is not whether you believe in composition, instead it is:


“With so many approaches to design, where is the best place to start?”

Leonardo DaVinci Star of Bisangoli

Ghyka is a curious historian looking for clues about how entire systems of composition came to exist.  Fortunate for the photographer, he breaks apart the types of composition for practical use.  A rich history of harmony, proportion, and space come to life.  It can be heavy on the math at points, but the photographer does not need to get bogged down in the proofs.  Keep in mind that artists are not interested in making mathematical illustrations.  They have historically simplified more complex ideas for practical application.  Which is exactly what any decent photographer will aim to do with their study of composition.


When we pick up a camera, we play with composition whether we intend to or not.  It is the great accident of instant reproduction.  But if we ever intend to create – rather than record – our eyes need help from our minds (plus a little help from our hearts, but we will save that for another day).  Why not then learn how others have made good use of its tools and learn to use them ourselves?


The Geometry of Art and Life

I read the book at least once a year as a reminder that,


The work of the scientist and the artists alike is the presentation of Form, Pattern, Structure in material or mental images.


For the work of either to fulfill its end it must be communicable: the hearer, reader, or beholder of the work of art must in the end find coherence and feeling from the images aroused in their own mind and the verifier of the scientific theory must be able to reproduce in their own mathematics and experiments the measurable facts communicated.


–Dr. Martin Johnson (quoted by Matila Ghyka p. 172 in The Geometry of Art and Life).

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