The Art of Mathematics
Vincent van Gogh
Since his death, Vincent van Gogh has become one of the most famous painters in the world. Between November 1881 and July 1890 he painted almost 900 paintings, but sold only one of them, The Red Vineyard, just a few months before he died. He worked at such a feverish pace that he had no time to pursue any other source of income. He died at the age of 37.
Born on 30 March 1853, Vincent grew up in Holland. He worked for a firm of art dealers for a while before teaching in England. After short periods as a Methodist minister's assistant, working in a bookshop and studying theology, van Gogh attended the Académie Royale des Beaux-Arts in Brussels. He studied anatomy and perspective in his quest to become an artist. Van Gogh firmly believed that to be a great painter you had to first master drawing, which he clearly did, only then could you add colour. He did not begin his first painting until November 1881, after spending at least a year focusing on his drawing. His legacy includes more than 1 100 drawings and sketches. One of the most recognizable aspects of van Gogh’s paintings is his bold use of colour.
In March 1882, he wrote to his brother Theo, “Although I find myself in financial difficulties, I nevertheless have the feeling that there is nothing more solid than a ‘handicraft’ in the literal sense of working with one’s hands. If you became a painter, one of the things that would surprise you is that painting and everything connected with it is quite hard work in physical terms. Leaving aside the mental exertion, the hard thought, it demands considerable physical effort, and that day after day.”
Van Gogh’s feverish working pace caused him both mental and physical stress. There is much discussion on how much his bouts of mental illness influenced his work. Van Gogh did not begin painting until his late 20s and most of his best-known works were produced during his final two years. When he moved to the south of France, he was captivated by the strong sunlight he found there. His work grew brighter in colour and he developed his unique and highly recognisable style.
It was during one of his bouts of depression that he cut off his ear. He had earlier stopped himself from attacking another artist, Paul Gauguin, with an open razor. He tried to give his ear to one of the prostitutes at the local brothel, but she reported the incident to the police, who went to van Gogh’s house where they stopped him from bleeding to death.
On 29 July 1890, at 37 years old, van Gogh shot himself in the chest. He died two days later. His fame grew in the years after his death. Today, he is widely regarded as one of history’s greatest painters and an important contributor to the foundations of modern art. Many of his pieces are among the world’s most recognisable and expensive works of art.
About a week after his death, van Gogh’s brother Theo wrote to his sister Elizabeth about Vincent’s legacy as a great artist, “In the last letter which he wrote me and which dates from some four days before his death, it says, ‘I try to do as well as certain painters whom I have greatly loved and admired.’ People should realize that he was a great artist, something which often coincides with being a great human being. In the course of time this will surely be acknowledged, and many will regret his early death.”
Activities for Sunflowers
During August and September 1888, van Gogh painted four pictures of sunflowers. They were to decorate Paul Gauguin’s room in the Yellow House that van Gogh rented in Arles in the South of France. Van Gogh wrote to his brother Theo in August 1888, “I am working at it every morning from sunrise on, for the flowers fade so quickly. I am now on the fourth picture of sunflowers. This fourth one is a bunch of 14 flowers...it gives a singular effect.”
Show the children Sunflowers at The National Gallery. Are there 14 flowers? Can the children order the flowers for age? Do all van Gogh’s paintings of sunflowers have 14 flowers? The National Gallery image allows you to zoom in on parts of the painting. Compare close-up images with a real sunflower to explore how van Gogh achieves the effects he wants.
If you are able to obtain mature sunflowers, estimate then count the number of seeds in each head. The flower head can be 30 to 40 centimetres across, with well over 100 seeds, so sorting the seeds into piles of ten (or into small pots) could be a useful support.
In the document Social and Emotional Aspects of Learning (SEAL): Improving behaviour, improving learning, the Red Resource sheets, pages 14-16 in Relationships include a story about a boy growing a sunflower and a set of pictures which could be ordered.
Use Ten Seeds by Ruth Brown (ISBN 0862648491) to explore the life cycle of the sunflower. You could also plant ten sunflower seeds, as in the book, and observe what happens to them. Photograph daily to develop a sunflower timeline. Transfer to a scrap book when it gets unwieldy.
Make a sunflower using a paper plate or a yellow circle of stiff card. Paint the plate yellow. Spread glue thickly on the central circle of the plate and quickly glue sunflower seeds in place. Use scraps of yellow paper and card to add short petals to the outer rim of the plate. When dry, count the sunflower seeds and label the back of the sunflower with that number. You could display the sunflowers with questions such as ‘Which sunflower has 15 seeds?’ and ‘Which sunflower has the most seeds?’
Why not ask the children to paint their own copy of Sunflowers? They could practise some ratio and proportion as they mix shades of yellow to match as closely as possible those that van Gogh used. As they mix, encourage them to write down the ratios of different paints they used e.g. one teaspoon of yellow and two of white 1:2. Later they could work them out as proportions e.g. 1/3 yellow, 2/3 white.
The Fibonacci sequence is an example of efficiency in nature. As each row of seeds in a sunflower or pine cone, or petals on a flower grows, it tries to put the maximum number in the smallest space. Fibonacci numbers are the whole numbers which express the golden ratio, which corresponds to the angle which maximises the number of items in the smallest space. The seed head and petals of a sunflower, daisies and pine cones have two sets of spirals, one radiating clockwise and the other anti-clockwise. Find some pictures of sunflowers, daisies or pine cones on the internet. Copy and enlarge them. Ask the children to examine the pictures closely. How many clockwise spirals in each plant? How many anticlockwise spirals in each plant? Are they Fibonacci numbers? For more information on Fibonacci, go to A little bit of history in Issue 20 of the Primary Magazine.
Look at van Gogh's Chair. Which tessellating shapes can you see? Explore tessellation through the Tile Designer on the Victoria and Albert Museum website. You can design your own tile and tessellate that design in blocks of 2 x 2, 4 x 4 or 6 x 6. The tool also allows you to rotate and reflect the tile to get different effects in the tessellation. It is very simple and intuitive to use. More ideas on how you might use it in the classroom from Issue 51 of the Secondary Magazine.
Two Crabs was painted soon after van Gogh’s release from hospital in Arles in January 1889. Despite its name, it is probably the same crab shown both on its back and upright. If the crab started on its back, one way to describe its repositioning could be, flip side to side, translate forward and right. Can the children think of other descriptions? Explore wrapping paper patterns. Can the children find any that could be called ‘crab patterns’ because one image has been used to create another as in Two Crabs? Describe how each pattern has been made, using rotation, reflection and translation. Revisit the Tile Designer to help with descriptions.
Starry Night was painted in 1889. Ask the children to paint their own starry night using thick paint and their fingers. Alternatively, use pastels on black paper. The same swirling, flowing movements will give the desired effect in both media. ‘Less is more’ in this kind of activity. Each child could roll a dice (1 to 10 if the paper is big enough) to decide how many stars they can create. Display the paintings in groups with questions such as ‘What is the same about this group of paintings?’ and ‘How is this group different to the other groups?’
Wikimedia Commons has categorised Vincent van Gogh’s work as self-portraits, portraits, sunflowers, irises, potatoes and other. Ask the children if they agree with this categorisation, particularly the ‘other’ category. Could this be broken down further, and if so how? Ask the children to present their final results as a pie chart, block graph or pictogram. Compare the different representations and discuss which is more suitable for a particular purpose.
Vincent van Gogh Gallery offers a chronology of van Gogh’s most famous paintings. Ask the children to find out which were van Gogh’s best years, that is, the years when he painted more famous paintings. They should choose which type of diagram or graph to use to present their findings clearly. For a more challenging activity, use the Catalog of Paintings and find his more prolific years.
There are several YouTube slideshows of van Gogh's work which might inspire the children as they work.
Further information from these sites:
The images of the works of art depicted in this article are courtesy of Wikimedia Commons. These images are part of a collection of reproductions compiled by The Yorck Project. The compilation copyright is held by Zenodot Verlagsgesellschaft mbH and licensed under the GNU Free Documentation License.