The Beautiful Math Hidden in Paintings

man in museum

This is a photograph I took of a man looking at a painting in the Norton Simon Museum. I loved seeing him sitting there for a long time. And the longer I watched him (watching the painting), the more I realized that there was a mathematical beauty in not only the composition of the painting, but in the new composition created by the man sitting on the bench looking a the painting.

Some months later, I noticed myself enjoying this calendar image on our refrigerator, in much the same way as the man was enjoying the painting in my photograph. I’d be waiting for the water in our tea kettle to boil and feel myself pulled into the angles and colors of Scottish artist F.C.B. (Francis Campbell Boileau) Cadell’s “The Blue Fan” (1922).

Cadell on fridgeA few months later, I noticed the same thing when a new month revealed another painting by F.C.B. Cadell: “The Green Bottle.” Indeed, I wasn’t the only one having this reaction. Natalie came home from college one weekend and said, “I can’t stop looking at that painting. Each time I walk into the kitchen, I find my eye drawn to it.”

Cadell #2 on fridge

I decided to share our reaction with our friend Andy McEwan, who introduced us to the work of F.C.B. Cadell (along with the other artists in the group known as the Scottish Colourists, who included F.C.B. Cadell, J.D. Fergusson, S.J. Peploe and Leslie Hunter). A week later, I was delighted to receive Andy’s beautiful and detailed analysis of “The Green Bottle,” which allowed me to better understand why I was never impatient waiting for the water in the tea kettle to boil, as long as I was standing next to a Cadell painting. Andy’s diagram demonstrates the beautiful math hidden in paintings.


F.C.B. Cadell’s The Green Bottle (mid-1920s) National Gallery of Scotland

A Brief Analysis by A.G. McEwan

At first sight Cadell’s The Green Bottle seems a simple, if pleasing, still life, an apparently straightforward depiction of commonplace objects – bowl, fruit, bottle, glass, napkins – casually arranged on a table with a picture hanging on the wall behind. Why, one may ask, is this ostensibly simple picture so pleasing? The answer, I believe, lies in the fact that this painting is anything but straightforward or simple in its composition and execution. I would go so far as to say it is a masterpiece of composition by Cadell. Let us look at how the artist has put the picture together. To assist in that analysis, I have superimposed some black, red and green lines on a reproduction of the picture.

Screen Shot 2017-01-02 at 10.18.44 PM

The green bottle, which gives the picture its title, is literally, or more correctly pictorially, the focus of the painting, being set directly in the centre of the picture (App.line A-A), the top and bottom of the bottle being the same distance from the top and bottom respectively of the canvas (App. lines B1 & B2). The strong verticals of the bottle are echoed by the straight sides of the drinking glass and the picture frame on the wall, which itself has another frame depicted within it. Intriguingly, Cadell thus depicts his picture as containing another two pictures. Might we suppose that, were we able to see all of the smallest picture behind the blue vase, it might too contain another picture and so on ad infinitum? I am sure that Cadell fully intended that the viewer’s gaze would be led into the composition through the pictures within a picture.
Of course the main picture, and those depicted within it, form rectangles and indeed rectangles are a fundamental element of Cadell’s compositional strategy in The Green Bottle. In addition to the background picture’s rectangular echo of the entire painting, the dark brown foreground rectangular tabletop (App. R1 )is replicated in the picture behind the bottle (App. R4). The wall area behind the bottle and below the depicted picture frame forms another rectangle (or two, if you see them as separated by the bottle (App. R2 & R3). In the background pictures, rectangles are formed in the blue areas (App. R5 & R6). A vertical rectangular area of wall is depicted to the left (App. R7). One might even say that the background pictures are even “double rectangles” if their frames and picture surfaces are counted separately. And, of course, the bottle, the focal point of the compostion, is itself rectangular in form.
Although much of the composition is thus based on strong vertical and horizontal elements, Cadell also cleverly uses diagonal elements to lead our eye around the picture. For example, a diagonal line (App. D1) drawn through the left-hand shoulder of the bottle lines up with the top folded napkin edge towards the bottom left of the picture. A diagonal (D2) drawn through the right-hand rim of the glass bisects the two fruits shown in the background picture and a further diagonal bisecting the rim of the glass (D4) lines up with the lower napkin fold. If a diagonal (D3) is drawn through the left-hand rim of the glass, it touches the right-hand edge of the foreground fruit bowl. Finally, a shorter diagonal (D5), through the centre of the tulip in the background painting, bisects the yellow fruit in that picture at just the point that it is also bisected by the line (D2). I am sure these strong diagonal axes are not there by chance: I am confident Cadell deliberately used them in constructing his painting.

Neither should we overlook the circular aspects of the composition. Particularly obvious is the visual echo between the paired fruits in the foreground bowl (itself of circular form) and the two in the bckground picture. However, the rim and base of the glass, the circular mouth of the bottle and even the cropped image of an apple and its reflection to the left of the glass, as well as the tulip flower near the top of the painting, all contribute circular elements. Furthermore, if we see the bottle as the focal point of the picture, then most of the other objects depicted are arranged in a broadly circular manner around it.

Complex though these geometrical elements of the compostion are and masterful though Cadell’s use of them is, another aspect must not be ignored, the artist’s use of colour. F.C.B. Cadell, after all, is known primarily as one of the Scottish Colourists, that group of artists comprising himself, J.D. Fergusson, S.J. Peploe and Leslie Hunter. In The Green Bottle, he demonstrates his masterful use of the palette. The viridian blur-green hue of the bottle forms a strong central focus almost emphasising the coolness of a glass vessel. That cool note is offset against the warm, reddish-brown tabletop on which it sits and again by the juxtapostion of the upper part of the bottle with the similarly-hued tabletop in the background painting. The viridian coolness is also contrasted with the hot orange of the folded napkin, the tulip flower and the cooler, but not cold, hues of the fruit. Echoes of the bottle’s coolness are provided by the dark blue vase and lighter blue foliage, as well as the shadow on the yellow fruit in the background picture and the deeper blue of the foreground fruit bowl provides another cool element.
So, taken together, Cadell’s use of geometry – rectangles, diagonals, circles – and his bold colours, subtly balanced, create a masterpiece of composition and a pleasure for the eye.

A.G. McEwan December 2016.


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