If you had told me that maths was in art, I would have probably liked maths a lot more when I was a child. Maths can be seen everywhere in the world but I would never have thought that it was in art as well! To be honest, I would never have thought of the two subjects having any sort of connection.
If we take into consideration Liping Ma’s profound understanding of mathematics, it is mentioned that a teacher should have “connectedness.” This now makes sense to me as this I can now connect the two subjects together.
In a recent lecture, we spoke about Mondrian and created our own versions of these in class. At first, I did not see the relevance of this and thought to myself that this was just another piece of artwork that was displayed in the primary classroom.
The next part of the lecture was the interesting part. We were shown a sequence of numbers: 1, 1, 2, 3, 5, 8, 13…and asked what the next number and the rule was. I grasped this quickly as I have seen a sequence like this before. The next number is 21. Why? Because each term is formed by the sum of the 2 preceding terms. These numbers can go on and on to create much larger numbers.
The Golden Spiral
We were then given some instructions to draw a series of rectangles:
- Imagine the origin and put a dot in the center – this represents zero and is our starting point…
- Draw a 1cm square from this starting point.
- Draw a 1cm square adjacent to it, sitting on top.
- Draw a 2cm square adjacent to the first two squares.
- Draw a 3cm square adjacent to the three squares.
- Continue with a 5cm square, am 8 cm square
- Use a compass. The pencil should sit at 0, the point should sit above. Draw a half circle through the two 1cm squares.
- Move the point to 0 and continue the line through the 2cm square.
- Move the point and continue the line through the 3cm square.
At first, I was completely baffled by this and had to start my example again. Once I had drawn the spiral within the rectangles I was left with a very aesthetically pleasing visual but still was not completely sure on the point of this example. We were told to pick out a rectangle within the visual and asked to divide the length by the width to see what number we ended up with. The number that we were all left with was the same, even though we did not all pick the same rectangle. This number was 1.6.
This is called the ratio of Phi or the golden ratio. In 1509, Italian mathematician Luca Pacioli published by Divina Proportione, a piece of work on a number that is now widely known as the “Golden Ratio.” This ratio, symbolised by Phi and it appears in nature and mathematics (Pickover, 2009, p.112). Could Mondrian have used the Fibonacci sequence to create his most famous piece of artwork?
After further reading on this, I have discovered Fibonacci’s sequence and the Golden spiral can be seen in many different pieces of artwork. If we look at famous geometric shapes, many can be found in works of art such as the Fibonacci pine cone. This is a three-dimensional image, in which the petals of the pinecone are counted in a spiral downwards from the top of the cone. The Fibonacci numbers can be seen highlighted on this cone.
Fibonacci in Nature
One of the most interesting thing that I learnt about the Fibonacci sequence and the golden spiral is that it can be seen in nature. The fact that this sequence of numbers can be seen in in the world around us and in nature is fascinating! This spiral can be seen in shells, flowers, pine cones and even pineapples. I feel that this sequence must have a huge significance if it’s naturally occurring.
Fibonacci Sequence in Famous Art
As well as nature, the Fibonacci sequence can also be seen in works of art. This is because the sequence is considered a naturally graceful number sequence and using it is to create very aesthetically pleasing works of art or images, so many artists have used it to increase the visual appeal of their artwork. An example of this would be the Mona Lisa, which is one of the most famous paintings in the whole world. If you look at the image below, you can clearly see how the golden spiral fits in the painting. Mona Lisa’s face traces out the Fibonacci sequence.
Another piece of artwork that this sequence can be seen in is Leonardo Da Vinci, The Vetruvian Man. However, this is seen in a different way from the previous piece of art. The ratio of the distance from the man’s feet to his stomach to the distance from the man’s stomach to his head is approximately the golden ratio of 1.6. Again this is shown in the image below.
Fibonacci in Famous Architecture
The ancient Greeks, Romans, Egyptians, and many others knew about the golden ratio. The Parthenon, which the Greeks constructed, has the golden ratio existing in many different places. The ratio of the width to the height of the building and the ratio of the height of the building to the height of the roof are both golden. Plus, the pillars in the front are placed so that the width of the building is split into a golden segment. The Egyptians used the golden ratio to build the famous Pyramids. The ratio of the side length of the pyramid to half the length of the base is the golden ratio.
Fibonacci around the house
Believe it or not you can see this sequence around your own house! As the golden ratio can be used in artwork to so that it is more visually pleasing, furniture designers use this sequence in their work to not only make it aesthetically pleasing, but also functional.
After having researched the Fibonacci sequence and the golden spiral, I am fascinated to see that it not only occurs in artwork to make it visually pleasing, but in the world around us!
Liping (2010) Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in china and the United States. 2nd edn. New York: Taylor & Francis.