Appreciating art through Maths

Appreciating art through Maths

This painting by Mondrian entitled  ‘Composition with Grid 8: Checkerboard Composition with Dark Colours’ (1919) is on display over the summer at the Turner Gallery in Margate. It is reputedly the first ‘grid painting’ in the history of art. What gives it its impact? The contrasts of the colours and their juxtaposition? The patterns formed of single colours and their arrangements within the space?  

At first sight it reminded me of the mundane 10 x 10 number square or percentage grid that I sometimes give to students, who shade them in in order to get a visual sense of proportions like 10% or a fifth etc. and also learn how proportions can be disposed within the borders in an infinite variety of ways.

Of course, in the Mondrian I could see immediately that his shapes were rectangles, not squares, and that there were a lot more than 100 of them. How many rectangles are there precisely? A count reveals sixteen each way, so 16 x 16 or 256. Sixteen is itself interesting, being 4 x 4 or ‘two to the power of four’ (2 x 2 x 2 x 2). 256 is therefore ‘two to the power of eight’, which is 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2. So, when the eye rests on, say, one of the blue rectangular blocks of 4 in the upper half of the painting, it is looking at exactly one 64th of the canvas.

Not everyone may be won over by this way of responding to an abstract painting, but for me it became more and more productive of questions. What was the ratio of width to length of the rectangles, and therefore of the dimensions of the painting as a whole? (It proves to be about 14:17). Which colour, blue, red or orange (the orange is really ochre – all the colours are darker in the original than in this reproduction), is used most for the rectangles? The answer: orange (94). Where, and how large, is the largest rectangular area without blue?  How long is the longest ‘chain’ of same-coloured rectangles joined side to side? What is the longest straight stretch of rectangles without one of the three colours? (Answer: There’s a vertical of 15, six columns along from the bottom left corner, without a red).

Is this being obsessive about numbers and measures and losing sight of the overall quality of the painting? I don’t think so. Most works of art do not lend themselves to analysis of this kind – but clearly as this one does, why not make the most of it?

Anyway I have just bought a print for the centre, and will have available a set of questions for a thorough mathematical investigation. But I shan’t insist that students follow it through. I shall be curious to see if ‘Composition with Grid 8’ by its own power captures anyone’s interest.