In last week’s input with Anna we were looking into the relationship between maths and art. We looked at Mondrian, Fibonacci and the Golden Ratio – Phi.
Piet Mondrian was a Dutch artist who focused on Pointillism and Cubist art. His art was very geometric and is seen a lot in modern day art. – https://www.guggenheim.org/artwork/artist/piet-mondrian?gclid=CjwKCAjwssvPBRBBEiwASFoVd_XWXluR5gKRvWAB9ZhvVXuoW08LlVXAJYz3SyyIHQROWYoqqD5VpBoCdMYQAvD_BwE
When creating my Mondrian style art I wasn’t exactly sure how it related to maths as I wasn’t focusing on any maths concepts when doing it. I think this would need to be brought in explicitly so that children were actually learning some key maths concepts for example using the art to look at angles. However, I do think this is a good way to relax the pupils as when doing it I felt very calm and at ease which can enable learning (Hayes, 2010).
Next we went on to look at Fibonacci. This was something I had heard of before as I had done it in school myself. The sequence begins at 0 and 1, naturally, and goes on by adding the two numbers before it. E.g. 0 1 1 2 3 5 8 13 21 34 etc. The numbers of the Fibonacci sequence can be used to draw squares on graph paper in a spiral or circular direction. As you can see on the picture (ignore the blue lines – mistakes made by me along the way) the sequence begins in the centre with 1cm square then to the right another 1cm square is added. This is because in the Fibonacci sequence 0 + 1 = 1. The sequence is then continued, 1 + 1 = 2 so a 2cm square is added and so on.
This can then be used to draw a spiral from the middle of the first square and through the centre of every square on the page. This is known as the golden spiral or the golden ratio which can be symbolised by Phi. This video clip explains the spiral and how it’s seen in nature.
Phi denotes a special ratio of line segments. This ratio results when a line is divided in a special way. The lines are seen in the rectangles created on the graph paper. For example, the squares of 1, 1, 2 and 3 beside each other show a rectangle. Pickover (2009) said “we divide a line into two segments so that the ratio of the whole segment to the longer part is the same as the ratio of the longer part to the shorter part”.
(a+b)/b = b/a
The formula can be used with any rectangle in the sequence and the answer will come out to 1.6 every time or very close. This answer is seen by artists to be the number of beauty. This might explain why it’s seen in so many beautiful natural and living things on the planet, or maybe it’s another phenomena with no explanation which makes our planet so wonderful.
Hayes, D. (2010). Learning and Teaching in Primary Schools. Exeter: Learning Matters.