The Art of Mathematics
Georgia Totto O’Keeffe was born in Wisconsin, US on 15 November 1887. Her parents, Francis Calyxtus and Ida Totto O’Keeffe were dairy farmers. Her father was of Irish descent and her mother was the daughter of a Hungarian count who came to the US in 1848. Georgia was the second of seven children and the eldest daughter.
By the time she was ten, Georgia had decided she wanted to become an artist. She and her younger sister were taught art by a local water colourist. In 1902 her family moved to Virginia but she stayed in Wisconsin with her aunt to continue her studies for a year before joining her family again in 1903. During her childhood she went to several schools sometimes as a day pupil and sometimes as a boarder.
From 1905 to 1906, Georgia went to the School of the Art Institute. In 1907 she attended the Art Students League in New York, where she studied under William Merritt Chase, an American impressionist painter and teacher. In 1908, she won the League's William Merritt Chase still-life prize for her oil painting ‘Dead Rabbit with Copper Pot’. Her prize was a scholarship to go to the League's outdoor summer school at Lake George, New York.
In the same year, she went to a Rodin watercolour exhibition at the famous art gallery 291 on Fifth Avenue, New York which was owned by photographer Alfred Stieglitz, her future husband. At this time she began to feel that the techniques and styles she had been taught during her studies were at odds with the vision she had for art which was based on finding essential, abstract forms in nature. She therefore decided to give up the idea of becoming an artist. She took a job as a commercial artist in Chicago and didn’t paint her own works again for four years. However, in 1912 she attended a class at the University of Virginia Summer School and was inspired when her tutor encouraged her to express herself using line, colour, and shading harmoniously. She began to paint landscapes, flowers and bones which recorded subtle nuances of colour, shape and light. All her images were drawn from her life experiences and related generally or specifically to places where she lived,
In 1914 she went to the Teachers’ College of Columbia University where she took classes from Arthur Wesley Dow, the man whose work inspired her at the summer school she went to in 1912. She spent a few years as a teaching assistant and then a teacher of art. It was while she was teaching that she was first noticed by the New York art community. The art works that caught their attention were large paintings of enlarged blossoms as seen through a magnifying glass and paintings of New York buildings.
During this time Alfred Stieglitz exhibited ten charcoal drawings that she had made. He considered them to be the ‘purest, finest, sincerest things that had entered 291 in a long while’. He also organised Georgia’s first solo show at his gallery in 1917 which included oil paintings and watercolours. With his encouragement and promise of financial support, Georgia left teaching and began a career as an artist. The two soon fell in love and became inseparable, despite Alfred being 23 years older than her and a married man with children.
In 1924, after Alfred’s divorce came through, he and Georgia were married. They both continued working in their individual fields. In 1923, he began to organise annual exhibitions of her work. By the mid-1920s, Georgia had become known as one of the most important American artists.
In 1938, when Georgia was 51 and her career appeared to be stalling, for various reasons, an advertising agency offered her work creating two paintings for the Hawaiian Pineapple Company to use in their advertising. This seemed to be the opportunity she needed and as a result she went to Hawaii for nine weeks. She visited several islands one of which was Maui. On Maui, she was given complete freedom to explore and paint. She painted flowers, landscapes, and traditional Hawaiian fishhooks. When she arrived back in New York, she completed a series of 20 paintings of what she had seen on Maui, but not the requested pineapple! The Hawaiian Pineapple Company eventually sent a plant to her New York studio and she finally completed her work for them.
Sadly, in 1946, Alfred died after suffering from a cerebral thrombosis. In the years after his death she continued painting and continued to make a name for herself.
|Ghost Ranch Valley
In 1972, Georgia's eyesight suffered macular degeneration and left her with only peripheral vision. She stopped oil painting, but continued working in pencil and charcoal until 1984. In 1973 Juan Hamilton, a young potter, appeared at her ranch house looking for work. She hired him for a few odd jobs but soon employed him full-time. He became her closest confidante, companion, and business manager until her death. Juan taught Georgia to work with clay, and with assistance, she produced clay pots and a series of works in watercolour.
In 1976, she wrote a book about her art and, in 1977, allowed a film to be made about her. In this year she was presented with the Presidential Medal of Freedom by President Gerald Ford. This was the highest honour awarded to American citizens. In 1985 she was awarded the National Medal of Arts.
In 1984, in her late 90s, Georgia, who was by now quite frail, moved to Santa Fe, where she died on 6 March 1986 at the age of 98.
Information sourced from:
Now for some mathematics!
Show Above the Clouds 1
This painting was completed in 1963. Ask the children to work out how long ago that was by plotting that year and our current year onto a number line and counting on. Alternatively, ask them to use their number pairs to 10 and 100 and make jottings.
The dimensions of the painting are 361⁄8 by 481⁄4 inches. You could discuss why the painting is measured in imperial units and not metric (we only used Imperial in the days Georgia was living). You could explore the fractions 1⁄2, 1⁄4 and 1⁄8. This could involve folding strips of paper into 2, 4 and 8, labelling the fractions, comparing and ordering them and finding equivalences. You could also use the strips to find halves, quarters and eighths of quantities.
You could ask the children to convert these inches into centimetres using the conversion 1 inch = 2.45cm or round to 2.5cm. They could then work out the perimeter of the painting. Encourage them to use the formula 2(l + w). They could use a calculator to work out the area of the painting or round the measurements to the nearest whole number and use a mental calculation strategy. This would be a good opportunity for discussing the most efficient strategies. They could then scale the measurements down by a fraction such as 1⁄4 or 1⁄8 and draw a frame of that size. Once they have they could then recreate Georgia’s painting inside their frame.
You could ask the children to estimate the number of clouds that they can see and discuss why it is difficult to be exact. What do the clouds in the front of the painting remind the children of? Ask for their suggestions. If arrays are not suggested bring these to their attention. Can they see the 4 by 2 array? Ask them to write down the four multiplication and division sentences that describe this. You could ask them to work with a partner and make cloud arrays of the same size on paper, for example one each that is 8 x 7. Once they have they could use straws to explore different ways of working out how to find 8 x 7, for example:
They could then put their arrays together to make either 16 x 14 or 14 x 16 and create a model for grid multiplication.
Discuss what might be seen above the clouds, for example stars and planets…and the Aurora Borealis (Northern Lights). You could show this video clip and ask them to look for the patterns that they can see. They could estimate the length of time that the video lasts for. The video was taken in Iceland. You could ask the children to research Iceland and make a fact file about the country which includes population, temperature, rainfall, currency, heights of the volcanoes and anything else with a mathematical flavour!
Show From the River - Pale
You could repeat the second and third activities from the previous painting. This painting is 411⁄2 by 313⁄8 inches.
Ask the children to tell you what they can about rivers. You could cut out the information about the world’s 25 longest rivers and distribute copies to pairs and ask them to order these from longest to shortest. They could also convert the measurements from miles to kilometres. You could ask them to work out the difference between the Nile and the other rivers using a counting on strategy.
Give each child a piece of string and a copy of the painting and ask them to measure the river from where they think the source might be to the mouth. You could give them a scale, for example, 1cm is approximately 5km and ask them to work out how long the length of river they measured is. If using this scale, encourage them to multiply by 5 using the strategy multiply by 10 and halve. First discuss why this strategy works.
You could ask them to measure and compare the lengths of the tributaries that they can see. You could ask them to draw, colour or paint their own river, similar to Georgia’s and make up a scale. They could then work out its length. As a class order these lengths and find out who has the longest and why, for example, did they draw a longer river or use a greater scale?
Show Series 1 White and Blue Flower Shapes
Can the children recognise the parts of the flower in this painting? How many petals can they see? Discuss the symmetry of the flower and where the line of symmetry is. They could create their own painting with one or two lines of symmetry.
Again, you could repeat the second and third activities for the first painting. This one is 197⁄8 by 153⁄4 inches. You could develop some good fractions activities from these measurements!
You could copy the painting and cut it into small rectangles – one for each member of your class. Scale the size up so that each part can be drawn on A4 paper. Once the children have drawn their piece to the scale given, you could then put all the pieces together to make a very large version of the painting. Alternatively you could ask the children to make their own copy after scaling the size down.
Show Ram’s Head, Blue Morning Glory
This painting is 20 by 30 inches. Repeat the activities relating to converting to centimetres and finding its perimeter and area.
Discuss the symmetry of the ram’s head. What needs adding/taking away to make it perfectly symmetrical? You could give each child a picture of half an animal’s head and ask them to stick it onto a piece of paper and then draw the other half, making it as symmetrical as possible.
Look at the flower. Can the children identify its shape? If you look closely you will see that it is a decagon. You could ask the children to draw flowers that are shaped like equilateral triangles, squares and other regular shapes. Of course, as always, you will need to name and discuss the properties of regular and irregular shapes.
Show Morning Sky with Houses
This painting is 77⁄8 by 12 inches. You could repeat the activities previously mentioned relating to fractions, conversion of units and perimeter and area.
You could explore the shape of the house. What 3D shapes do they think it is made from? You could then explore the properties of cuboids and triangular prisms and discuss their similarities (for example, they are both prisms) and their differences. They could make these shapes with plasticine or something similar and then work out how to make them with card. Depending on the age of the children, they could explore nets or, if you give them actual shapes, they could draw round the faces and stick them together.
You could do a paint mixing activity which involves finding the ratio of two different colours of paint to make a colour similar to one that Georgia has used. If small groups children work together and each takes a particular colour they could write a ‘recipe’ for the ratios made – using the correct notation. They could then copy the painting using their new colours.
Show Pink Shell with Seaweed
This painting provides a great opportunity to explore the Fibonacci sequence. You could try Making Spirals from NRICH.
You might be interested in sharing some information about Fibonacci and also some Fibonacci-style number puzzles, which can be found in A Little bit of History from Issue 20 of the Primary Magazine.
The ideas here are just to give you a taster of the mathematical activities that could be involved when looking at artists such as Georgia O'Keeffe. We know you can think of plenty of others! If you try out any of these ideas or those of your own, please share them with us!
If you've enjoyed this article, don't forget you can find all the other Art of Mathematics features in the archive, sorted into categories: Artists, Artistic styles, and Artistic techniques.
Page header by Ron Cogswell, some rights reserved
Georgia O'Keeffe courtesy of Wikimedia Commons, in the public domain
Ghost Ranch Valley by Artotem, some rights reserved