The Art of Mathematics
Auguste Herbin (1882 - 1960)
French artist Auguste Herbin, son of a weaver, was born in the small village of Quiévy, close to the border with Belgium, on 29 April 1882. He studied drawing at the Ecole des Beaux Arts in Lille, from 1898 to 1901, then moved to Paris where he worked in isolation for some years. His work was initially influenced by Impressionism and Post-Impressionism. These influences, visible in paintings that he sent to the Salon des Indépendants in 1906, gradually gave way to an involvement with Cubism after his move in 1909 to the Bateau-Lavoir studios. Herbin’s studio was next to both Braque's and Picasso's, giving him the opportunity to study Cubism at first hand. He created his first Cubist paintings in 1913, and his first abstract paintings in 1917. He moved on to an abstract, geometric phase, before gradually discovering Constructivism. His work forms a bridge between the Cubist movement and post-war geometrical abstract painting.
Herbin's reliefs of simple geometric forms in painted wood and related furniture designs were met with incomprehension and such harsh criticism, even from those critics most favourably disposed towards Cubism, that he briefly followed Léonce Rosenberg's advice to return to a representational style, including landscapes, portraits and still life. Herbin later disowned these works. He returned to abstraction in 1926 and was co-founder of the group Abstraction-Cr-23ation in 1931.
From 1938, his interest in the Italian, Trecento, led Herbin to a more concrete, two-dimensional painting style with simple geometric forms. He was one of the great pioneers of geometric constructivist art in France. His later work became highly abstract, but he always worked with geometric forms. Although these sometimes suggest people or objects, they are not representational. He discovered his own geometrically abstract language of forms in 1943. The pure geometric shapes and positive colours of his later abstract works had considerable influence on younger abstract painters. In 1946, he developed the unique Alphabet Plastique, a compositional system based on the structure of letters. He assigned colours and shapes to each letter. This was not meant to be art alone, but a puzzle to unlock. His code reveals an unexpected depth and complexity which adds a particular attraction to his paintings. However, in spite of his strict adherence to his coding principles, Herbin also allowed himself a great deal of freedom in the conception of his pictures.
Herbin published this compositional system, as well as his colour theories, in his 'L'art non-figuratif non-objectif' in 1949. A lateral paralysis in 1953 forced him to learn to paint with his left hand. He was active in the 1950s as a designer of tapestries.
Herbin's typical architectural approach and his colour effects made his pre-war work widely known in the international art world – a success which continued after the war. Herbin died in Paris on 31 January 1960. One painting remained unfinished – it was called 'Fin'.
Alphabet Plastique 2, 1950
The Arithmeum opened in Bonn in 1999. It offers a rich mixture of science, technology, mathematics and art and aims to convince you of the fascination, excitement, beauty and fun that these disciplines offer.
A recent children’s TV programme asked, What is constructivist art? and focused on the work of Auguste Herbin and his Alphabet Plastique. Children studied several of his originals to develop an understanding of the Alphabet Plastique. They then encoded their own name and turned it into a work of art.
National Curriculum links
These activities will address aspects of the learning objectives in the Primary Framework Using and applying mathematics, Understanding Shape and Measuring strands. Pupils in Key Stage 1 and 2 can learn to recognise circles, semi-circles, ovals, triangles, squares and rectangles, as well as crescents. They will explore using 2D shapes, position and symmetry as they create pictures.
Although the following activities are suggested for a particular stage, most could be adapted for use in any key stage.
Activity using ‘Nude’
You will need:
- pre-cut coloured circles, semicircles, triangles and thin rectangles
- black paper for the background
If the children are able to draw around a shape and cut out reasonably accurately, you may prefer to offer the children a range of shapes to draw around on different coloured papers.
Work in small groups of around four children. Show the children a copy of ‘Nude’. Ask them what they notice – look for observations on shape, colour and the arrangement of the shapes. Observations may include suggestions such as ‘the circles are like traffic lights’ or ‘there’s a circle cut in half’.
Invite the children to create their own version of the picture. Encourage each child to move pieces around until they are happy with the final result, then stick in place. As they work, discuss the shape used and the position in which it has been placed.
Display the creations alongside a copy of the original picture.
Key Stage 1
Activity using ‘Nu’
You will need:
- black paper for the background
- white paper and various shades of blue paper
- a range of shapes to draw around on different coloured papers.
You might like to provide some thick and thin strips of white paper for the children to use for rectangles and squares.
Show the class a copy of ‘Nu’. Ask them what they notice – look for observations on shape, colour and the arrangement of the shapes. Children may ‘see’ scales – is the white circle being weighed? Is the thin blue triangle balancing the white square and darker blue small circle?
Ask the children to choose a piece of measuring equipment, such as weighing scales, ruler, trundle wheel, jug etc. Explain that you would like their picture to suggest that item, but not be a picture of it. Look at the equipment and ask the children to suggest which shapes might best represent it.
The children must limit themselves to only two colours, though they may use shades of those colours and any geometric shapes they wish. Encourage the children to move their pieces around until they are happy with the final result before sticking in place. As they work, discuss the shapes used and the positions they have been placed in. When complete, look at the children’s work together. Can you see the piece of equipment each child was aiming to represent?
Display the pictures with the equipment used for inspiration.
Key Stage 2
Activity using ‘Soleil’ and ‘Pape’ initially, then any of the other pictures.
You will need:
- a copy of each painting
- access to a computer for each child
- black or grey background paper and a range of coloured papers.
Begin by showing the whole class ‘Soleil’ and ‘Pape’, complete with their titles. What is the same and different about each picture? Invite observations. Explain Herbin’s Alphabet Plastique. Return to ‘Soleil’. This is a six-letter word and the picture appears to split into six blocks. Could each block represent a letter? If so, which block represents which letter? Ask the children to explain their thinking. Move on to Pape. Could there be one or more colours and a group of shapes for each letter? Can the children use the same ideas to pick out parts of this picture?
Explain that they are going to create their own alphabet code, using colours and geometric shapes. They will need to set up a 5 x 5 grid on the computer and split the last cell. To avoid confusion, each cell should be labelled with the appropriate letter of the alphabet. Once their template is ready, the children can create their own alphabet, using the shapes provided by the particular computer programme. They will need to consider the size, orientation and colour of each shape as well as the combinations used for each letter. Once complete, preferably on one sheet of A4 for ease of handling, the alphabet should be saved and printed.
Using their own alphabet, children move on to create a picture of their own name or another word. It is useful to have a possible word in mind when designing the alphabet since the word may influence the colours, as in Soleil. Display the names or words with the relevant alphabet, inviting observers to ‘read’ each picture.
Round off the activity by inviting children to share their work with the rest of the class and explain their choices. You might also like to show the children one of the more complex constructions such as Composition with the word ‘Vie’, or ‘Napoléon’. What does the title of the piece suggest? Can the children recognise possible representations for any of the letters used in the title?
And finally: take a look at John Dabell’s blog I spy with my little maths eye... for some further ideas.
Follow these links to find the paintings referred to in this article: