Divine proportions

The golden rectangle

I’ve been cruising a few sites to see what I could suggest as good examples of Art using the Golden Mean, or the Golden Rectangle, also known as the Divine Proportion. In my current avoidance and procrastination mood, I’m looking for a way out of drawing a template myself, but I haven’t found what I wanted. There are several rather dry explanations from a mathematical point of view.

Actually, the recurrence of the Golden Rectangle and the Golden Ratio in nature is quite frequent as is the Fibonacci series (1 plus 1 is 2, 2 plus 1 is 3, 2 plus 3 is 5, 3 plus 5 is 8, 5 plus 8 is 13; that is 1, 2, 3, 5, 8, 13, ad infinitum . It’s best to look in Wikipedia if you want a good mathematical explanation of it. My eyes glaze over when I see it. I find it amazing, but I don’t want to do the math. (More avoidance?) I can check my grocery bills and balance my cheque book and determine what my change should be in a financial transaction at the supermarket; but further than that, I have little interest in geometric and algebraic calculations.

In my former day job, I managed several millions of dollars per year in a major contract, but I had people who were better at numbers than I, checking where we were with the budget. If I used a computer, I could generally understand what had happened to all the dollars spent and talk about how much was left over; or talk to the purse string holders and explain where we expected to spend all the money in the next year. But Please, Please don’t ask me to explain the mathematical aspects of the Golden Rectangle to you. There are several people much better at it and if you just Google these terms, you will find some mathematical explanations if you should so desire.

The question that is important to me is, how does it apply to art? Why is it important to even think about these complicated mathematical relationships when all we really want to do is draw? Why would we go to a lot of trouble to create a grid underneath our images in order to artificially bend a composition into it?

First of all, it’s been used as a principle of structuring, both in two dimensional and three dimensional art and in architecture, for thousands of years. It behooves us to at least be aware of it and understand that it’s not too bad a way to go about designing things. It has been declared universally pleasing in many different cultures which makes me wonder if it isn’t also a part of our own make up – an archetypal pattern in the Jungian sense of a inherited pattern or thought or symbolic imagery derived from the past collective experience and living in the present unconscious .

Secondly, during the Renaissance in the 14th and 15th Century, Greek geometry texts were rediscovered and using the Golden Mean for proportions became a leading-edge art fad. The heightened interest led to its being used in a formulaic way in the structuring of all paintings. By the Nineteenth Century, it was considered the only way to compose pictures and became a confining, imprisoning idea and all other forms of composition were mocked as primitive or decorative. However, the idea of geometric composition is still taught in Art History to explain Renaissance and Neo-Classic Artist methodology. Some modern day artists are again finding the concept a useful one for compositional balance.

In the photographers’ or artists’ life, most of the standard sizes of photographs (i.e. 4 x 6) and the manufactured canvases, frames, artist’s watercolour blocks and drawing pads conform to the Golden Rectangle proportion. As a result of starting with a Golden Rectangle in photography, it is evident that the Rule of Thirds also complies to the Golden Ratio principle.

If you go back to my post titled “Today’s Offering” I’ve already talked about some of the periods of art where the slavish attention to this principle of composition was rejected by artists who wanted to free their thinking and find new, fresh ways of making images. In the Twentieth Century, there was an enormous upheaval in society engendered chiefly by two horrendous, cataclysmic wars. The forefront of the art world reflected these upheavals by challenging all the rules and eventually, there were Art movements that chose to toss out all the previously cherished formulas for art.

By the time I was studying Art in the late ‘Sixties, our professors were still teaching drawing and painting, but there were lots of forms of Art or trends that didn’t seem like Art at all. Some artists challenged the notion that art was for museums and for homes. Longevity of art was not deemed desirable nor necessary. It was felt that Art should be brought to the streets and the masses.

One of the performances that I remember entailed the artist erecting a platform on which his piano was placed. After a rather wild and agitated performance of some non-harmonic piano bashing and much gyrating and ranting on the part of the artist, he turned from the audience and attacked his piano, beating it into smithereens. A strong sense of Anihilism reigned as the North American populace struggled with the futility of American involvement in Viet Nam. A whole generation of brave and intelligent young men were being conscripted off to a war that few Americans believed in. Art of the time reflected a disaffection with society in some creative and also some destructive manners.

One of Vancouver’s artists took reels and reels of discarded film and knit it into an amorphous pile that surrounded her in the Vancouver Art Gallery. Her artwork was this pile of knitted film. Another built a low wall of bricks that snaked through one room of the the Art Gallery. One installation had lines of various kinds of string and other tangible, touchable items hanging inside a built passageway that the “observer” to the gallery, was invited to walk through, encouraging the gallery’s guest to think of art as a sensation as much as a visual experience. Installation Art, as this mode of expression became named, has not run it’s course still – fifty years after.

In my early years while I was studying at University, we still were taught drawing and painting, basics of design, sculpture and ceramics. Our professors were trained in the first half of the Twentieth Century and many were still products of the Nineteenth century teaching philosophy and training, for which I am eternally grateful. But they were reaching out to understand and incorporate the modern trends that were exploding around us in a maelstrom of creativity and reaction to the political atmosphere of the time. I am equally thankful for that exposure to Found Art, Op Art, Pop Art and other leading edge forms of that time.

Ten years after I finished University and my art teaching degree, I was frustrated with my own abilities to draw and I sold everything I had so that I could go to Art school for a year. It turned into four years, thankfully, because that period of concentrated learning and discovery made the difference in me becoming a good artist instead of a really bad wannabe. Amongst other things, I had time to focus on different means of composition and internalize them.

I got caught up on the principles of the Golden Rectangle which I had only heard of briefly in a Math class in Grade 10 or 11. I thought it might be the magic answer for composing landscapes that people would have an inherent connection to, whether they realized it or not. The compositions would be familiar to them because of the underlying structure. They would then fall in love with my pictures and want to buy them. It was a little naive, and spurious at the same time. Of course, any time I’ve tried to make pictures with make-money-quick as the end goal, I’ve always failed miserably. I still have them all stored in my basement. It may work for some people, but it doesn’t work for me.

Nevertheless, I got quite apt at planning out pictures with this classical method as the underpinning for composition. I gained a much better understanding of all the Renaissance, Classical and Baroque Art. Even the Impressionists were steeped in the use of geometrically designed compositions. While they were breaking away in colour and subject, they just couldn’t shake their early classical training in composition. Once learned, you start noticing it everywhere. It’s hard to dismiss it and it is hard to erase it from your compositions. Certainly, you will begin to realize which artists use it as a formula in their work and those who don’t.

Here’s how it works:

Step One

4 x 6 inch golden rectangleI

I’m using a 4 x 6 watercolour block, the kind one does post cards for this illustration.

You will see that I have divided it into three equal rectangles. The two on the left, combined, make square. The two on the right when combined also make a square.


Now I’ve used a black line to put a large diagonal cross in black on the two left rectangles. The intersecting point halves the common side of these two rectangles. I’ve done the same on the two right-hand rectangles but in red so that you can see the difference. I filled in the resulting square with a pale blue so that you could take special notice of it.

In classic composition, the subject of the painting should be focused in some way in this important square. If someone’s arms come through this space, they should align with one of the side of the square; or if there is a head that is important, it should be placed fitting in this area. If it doesn’t, according to this geometric method of composition, you change your composition so that it does fit. You bend your images to fall on important lines and this square is the key focal point that needs to have something interesting going on in it.

Step Two

Stage 2i

Now I’ve reinforced the Step One lines in black. For Step Two, using red, I’ve drawn a vertical line between intersecting points and carried them on to top and bottom of the picture surface (the picture plane); then I’ve done this horizontally as well. In yellow, I’ve drawn lines from corner to corner. If you are completely accurate in your drawing, then you have defined dead centre, smack dab in the middle.

Step Three

I have changed all of those Step 2 lines to black so that you will be able to see what happens next.

Step Three defines more diagonals, creating more intersecting points.


In Step Three, I’ve taken diagonals from the midpoints of each side and drawn them down to the corners, shown in red. Then I looked for intersecting points and connected them, continuing the lines out to the sides. There are vertical and horizontal ones. And then more intersections occur and more connections can be made ad infinitum until you have a real (but very geometrical) spider web of lines.

I’ve done this in a variety of colours so that you could distinguish the progression of connections, but in a preparation drawing for composition, this would most likely be done in light pencil, or on a canvas, in sanguine chalk or willow charcoal that would easily erase or blend in with the paint as you start to add in pigments.

Step 4

Next, I’ve drawn a rather primitive drawing on top of the geometric grid. I’ve done this all with the mouse in cyberspace (no pencil or paper), so enjoy the directness of it. It’s rather rough. You’ll wonder what I was doing all those years in art school!

For some reason that I wasn’t willing to spend a lot of time on, the computer wouldn’t let me fill in colours in enclosed shapes today. In order to add colour to this drawing, I ended up doing a lot of switching between Adobe Photoshop and the Accessories program that comes with every PC called Paint. It has made for some interesting textures and colour choices that I found rather interesting.


You can see that I’ve chosen the grid lines to define the couch mattress, I’ve chosen a right hand vertical to prop the pillow against; the breasts lie on either side of one wall of the middle square; the knees are at strategic points as are the hands. The window with trees outside is a rectangle that is bordered on vertical and horizontal lines provided in the grid; I tried to get the centre of the body, the torso, into the important middle square. It didn’t quite fit that way, but with this drawing it was too hard to go back and change it.

Now here’s the same drawing developed a little more. Particularly, I’ve tried to erase the grid lines as much as possible while still leaving a trace of them underneath (for demonstration purposes only).


Despite the inaccuracies of form, despite the roughness of this mouse-drawn sketch, you can see that the composition is pleasant. There is a balance to it. There are sufficient directional changes to make things interesting.

That’s the end of this demonstration on geometric composition using Divine Proportions.

If you would like to explore this further, I suggest that you take a look at some Renaissance paintings – Leonardo da Vinci; Michelangelo; or some from the Neo-Classical period – Jacques-Louis David (The Death of Marat;The oath of the Horatii). Some other artists clearly using geometric compositions are Jean-Baptiste-Simeon Chardin, John Constable, Dominique Ingres, Jean-Honore Fragonard and Nicholas Poussin. These are some of the artists who embraced this compositional method during a time when it was still a fresh idea, not an overused and restricting one. The structure of their images is easily seen when you know that this geometric grid is responsible for the placement of figures and objects within them.

You might try printing this grid and making drawings right on it so that you can try fitting compositional elements into it. Or you might photocopy some famous Renaissance and Classical art works, then draw the grid on top to see what objects and figures align with the principle shapes of the grid.

A last word:

I enjoyed working with this type of composition for a long period of time. Later, though I decided to explore many different types of composition, I would often come back to this principle. I no longer had to draw the grid to know good placements for the picture elements of my drawings.

I find that, looking at art, the Divine Proportion pervades all European painting prior to Twentieth Century. Knowing that someone has taken such care over his composition makes me marvel at the final result; and equally, for such a structured method, I’m always awed at how much variety there is in composing with it. It’s much like a musician uses a Sonata form or a Concerto to structure their creations but there are thousands of different ones.

Rules are made to be broken so feel free to go ahead and break rules. The only caveat? You need to know the rules first in order to work with them and then bend them to your will.


10 Responses to “Divine proportions”

  1. suburbanlife Says:

    Good overview, LFB. A painter, still alive, who uses the Golden Mean proportions, is the Canadian Alex Colville. If you take a reproduction of any of his paintings, you are able to overlay a sheet of plastic and with felt pen and ruler make study of the divisions and arrangements over the format space. A sense of rightness, a frozen moment, characterizes this manner of classical compositions. There is nothing serendipitous or accidental about them and therein lies their attraction – stability, predictability and measure. g and GEM

  2. lookingforbeauty Says:

    Thanks GEM
    Thanks for your suggestions of El Greco and Alex Colville. I bet Ken Danby and Christopher Pratt used math and ratios in their paintings as well.

  3. forestrat Says:


    Thanks for taking all the time and trouble to create this post.

    Since photography is such a recent form and since it is relatively accessible to the average Joe, I suppose the rule of thirds came along as a sort of common man’s golden mean.

    I wonder how many of the big name photographers have followed this system and whether it was a conscious decision or just a feel for composition? Maybe it depends on if they went to art school or were self taught.


  4. lookingforbeauty Says:

    Thanks MDW
    You pose an interesting question. It’s a chicken-and-egg kind of question – which came first? An understanding of composition or just a feel for it? Is it an innate ability some have and others have to learn?
    In photography, I can see that the full blown methodology of geometric proportions is really inapplicable. You can move your camera’s location to bend things to your composition, but you can’t remove a tree if it’s in the way, or bend a branch of it if it doesn’t fall along an important axis of the geometric grid. And you can’t be carrying around a grid on mylar or plexiglas to see what part of the landscape fits into it before you pull the trigger.
    The rule of thirds allows for more photographic flexibility, a generalization that is harmonious and fortuitously (or maybe not) conforming to the Golden Rectangle.
    There are photographers that take great pains to compose their pictures. Jeff Wall is one of these. He spends hours structuring his subjects and makes a cult of explaining all the references and glorifying the preparations. His photos seem like snaps that anyone could take, but the apparent effortlessness is misleading. Everything is calculated, prepared, managed, staged.
    Others base their success on taking thousands of pictures and chucking 95 percent of them in order to get a few publishable ones that appear effortlessly natural, a slice of life caught on the lam, compositionally perfect. In fact, the photographer has taken a hundred photos of the same subject and culled ones where some little thing went wrong – a head with the top sliced off, a full length figure with no feet, a face with eyes that closed or a smile that was forced. Portrait photography for grads and weddings works on this basis. The photographer offers a hundred shots or more and then the subjects choose which ones they want reproduced.

    I’m always a bit at odds with the designation “self-taught”. There are many people who have not gone to school to learn their craft. They pick up a camera (or a paint brush) and just start out because they are fascinated by the medium they are working in and they have a burning desire to create some of their own with their own vision. Well and good, up to that point.
    Perhaps they do not go to school, but their fascination with their medium drives them to meet with other photographers to chat about what they are doing; or to get books out of the library and read about what they are doing; or subscribe to magazines with articles about how to manage this point or that concerning their craft.
    They are not living in a vacuum and discovering the wheel for humanity. They are being taught by their colleagues sharing information.
    They are being taught by articles that are instructive.
    They are learning from books and trade magazines. The people who write them are their teachers.
    They seek advice on the Internet – the respondant or the blogger on the other end of this search is their teacher.
    They may even take some night school training or training at the camera shop that helps them hone their craft.
    I’d rather call it self-directed learning.

    Whoops! I went on a rant there! Sorry about that, but the claim of being “self-taught” is one of my pet peeves, especially since, in the art world, it seems to be considered some kind of van Gogh-related claim to excellence (and oft times is not). The thought that van Gogh was self-taught is in itself is a misconception.
    You’ve twigged my curiosity. Look for a new post on a related subject coming to a blog near you soon. I’m thinking that many of the early photographers were closely related to art schools. Many of the artists used photography as reference material for their work – Edgar Degas is one, for sure. Man Ray, earlier in the 20th Century, and the Dadaists were also interested in photography. I believe they were products of art school education.
    Certainly, photography was originally conceived as a substitute for portraiture in painting, amongst other things. It was the poor man’s access to posterity and, in looking at early portraiture in photography, the poses are classic, in imitation of paintings which would have been structured carefully using the geometric composition methodology of the times.

    Most art schools have photography departments. Photography is considered a branch of the Ats these days. Besides, photography is essential to the advertising trade and there is an expectation that the photographers will have a strong basis of visual concepts in their work that have nothing to do with the technical side of the craft; or, rather should I say, is an equal component of the craft.
    Thanks for your thoughtful responses. They always trigger more reflections on my part. And that’s a very good thing.

  5. sarsen56 Says:

    One of most remarkable exercises is to look at how prehistoric communities experimented with geometry, those interested in this fascinating topic, and how it may be used to enthuse students today may like to look at : http://sarsen56.wordpress.com/solve-this

  6. lookingforbeauty Says:

    Your blog is very interesting. I hope you get lots of visitors.
    Thanks for adding your views.

  7. Rodney Chesley Mackay Says:

    I came to Mount A in 1954 as a “mature student.” I had already had a long apprenticeship, formal and informal, under a number of artists who are now better known. I was very pleased to read what you have written and to see the comments. I studied Life Drawing and Design with Colville and what you say is correct. I have been a full-time painter since 1972, and excepting the year 2008, have always had the support of a number of patrons. Galleries are never enough! At the age of 76, I am trying to deduce how I ended up in this strange business, and am writing about my collisions with Thomas Acheson Jr., Sinclair Healy, Lucy Jarvis, Alfred Pinsky, Fritz Bandtner and the Mount A Three. I love your compositional grid. Can I please pirate it with credit of course? On my walls I have a couple of paintings featuring equal divisions of sky and water, and one has a triangular objecvt at dead centre. I am not totally sold on the golden ratio although I do use it by accident. By the way exactly who should be credited?

    • lookingforbeauty Says:

      HI Rodney,
      Thanks for your comments.
      I had a long look through your web-site and enjoyed your life story and your art work as well.
      When you mentioned Sinclair Healy, I went back to the blog to see what I had written (since I wrote it a longish time ago. I hadn’t remembered mentioning him, but I studied with him at UBC in the 60’s; as well as Sam Black, Gordon Smith, John Macdonald (JAS Macdonald), Bob Steele, Penny Gouldstone, Doris Livingstone and others. And actually, I hadn’t mentioned them, so it’s interesting to see we have a connection in our respective art education.

  8. Anne (Healy) Hall Says:

    It is actually Sinclair Healy – no e in the last name!

  9. lookingforbeauty Says:

    Thank you Anne,
    It’s always important to spell names right, especially in a business like art where one’s signature is a key part of success.
    I looked through the post and could not find it, but it is twice in comments above. I don’t know if I can edit them, but I will try.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: