October | 2017 | Brodie's Teaching ePortfolio

I have never really been overly enthusiastic about maths and I have most defiantly never been enthusiastic about art. The two as individuals give me much anxiety and I often believe the myth that your either good at maths or literacy, the two never hold the same value. I also had this view towards art and so, when I realised we were going to be receiving a lecture on maths and art together, I must say I felt a strong sense of dread. However, I was amazed and how simply maths and art could be connected. My original thoughts were that we would be using our mathematical knowledge to create large portraits, how one would do this I do not know.

Piet Mondrian is one artist who bring maths and art together. He was famous for creating geometric abstract pieces of work (Piet Mondrian 1877 – 1944, no date). This abstract style he created was quite simple, he would create a grid of black and white horizontal lines on white paper. The black lines would create a variety of different sized squares and rectangles which he coloured in using only 3 primary colours; he called this piece of art Neo – Plasticism (Piet Mondrian 1877 – 1944, no date).

A mathematician whose work has artistic connections was Fibonnaci. Fibonnaci created different sequences, one of his most famous was the golden spiral. Fibonnaci created a mathematical sequence that if you start at 1 and add the two numbers before it you will create the Fibonnaic’s sequence (Meinser, 2015). Doing this myself I found that the sequences goes in the order of 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144 etc. Fibonnaci discovered that using this sequence as dimensions for squares he would be able to create a perfect spiral inside of them; today this spiral is known as the golden spiral (Meinser, 2015).

The golden spiral can be seen most of all in nature. FIbonnaci’s sequence can be seen in sunflower seeds, pinecones and pineapples (Meinser, 2015).

“Is God a mathematician? Certainly the universe seems to be reliably understood using mathematics. Nature is mathematics. The arrangements of seeds in a sunflower can be understood using Fibonacci numbers. Sunflower heads, like those of other flowers, contain families of interlaced spirals of seeds – one spiral winding clockwise, the other counter clockwise. The number of spirals in such heads, as well as the number of petals in flowers, is very often a Fibonacci number.”

(Pickover, 2009, p.100)

A progression from Fibonnaci’s golden spiral was that from using this sequence a golden ratio could be determined for line segments. This special ratio will appear when a line is spilt into two segments. 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 (Pickover, 2009, p.112). The ratio is determined by using the formula:

(a + b) / b = b/a

The golden ratio is 1.61803, however not every line segment will equate to this, it will only occur if the numbers used appear in Fibonacci’s Sequence.

I started off by creating my own golden spiral, then by using the dimensions of the rectangular boxes and substituting these into the golden ratio formula I was able to determine the golden ratio. I also done this using the dimensions for my Mondrian drawing, however I was unable to determine the golden ratio in these, meaning that the dimensions did not occur in FIbonnaic’s sequence.

Maths is often used when creating patterns. Maths can be used to determine the length of the line or the size of the boxes within a pattern. One example of this is fractals, a fractal is a never ending pattern which is self-similar across different scales (Robb, 2017).

I went into the lecture on maths and art with the feeling of dread and came out in amazement. I had no idea about the variety of ways that maths could be linked with art and that I could do it. I now feel passionate about bringing maths and art together and it is something I plan on researching further to take with me onto to placement and in my career as a teacher to ensure that children do not feel the same feeling of dread I first had when I saw the title Maths and Art.

References:

Meisner, G (2015), Spirals and the Golden Ratio, Available at: https://www.goldennumber.net/spirals/ (Accessed on: 27^th October 2017)

Pickover, C. A. (2009) The Math Book From Pythagoras to the 57th Dimension, 250 Milestones in the History of Mathematics. London: Sterling.

Piet Mondrian 1877 – 1944, (No Date), Available at: http://www.tate.org.uk/art/artists/piet-mondrian-1651 (Accessed on: 27^th October 2017)

Robb, A (2017) ‘Maths and Art’, [PowerPoint Presentation], ED21006 Discovering Mathematics, Available at: https://mydundee.ac.uk (Accessed on: 27^th October 2017)

1, 2, 3, 4, 5 is almost everyone’s first memory of maths, the enjoyment of being able to count. However, I have been very naive in my thinking and believed that number systems and counting have been around forever. I have recently discovered that this is not the case.

Some of the earliest evidence of mankind considering mathematically thinking can been seen on marked bones from Africa dating back to around 20,000 years ago (The Story of Mathematics, 2010). It is thought that mankind could identify the difference between having one of something and having two but they had not discovered a way of communicating this through words or symbols. It has been suggested that early mankind made markings on bone to track occurrences such as the phases of the moon, the seasons and time (All Worlds, 2015).

The first steps made towards the mathematical systems we have now were suggested to have been made for bureaucratic needs and the development of agriculture. A shared mathematical system was needing to measure land and work out taxes (The Story of Mathematics, 2010).

This video explains mankind’s first signs of mathematical thinking by looking at the Ishango Bones.

I have read through many articles while writing this post to see if there has been any final determination of what the markings on the Ishango Bones mean, however it is still unknown. The most commonly found assumption I have read is that early mankind were making these markings to track the phases of the moon but again, whether or not this is true is still unknown.

References:

All Worlds (2015) PREHISTORIC MATHEMATICS, Available at: https://www.youtube.com/watch?v=TsLqTfKtpCA (Accessed on: 6^th October 2017)

International Organization for Chemical Sciences in Development (2015), The Ishango Bone. An enduring symbol of mankind’s intellectual progress and a star of archaeology from the heart of Africa, Available at: http://www.iocd.org/v2_PDF/IOCD-IshangoBrochure2015bp.pdf (Accessed on: 6^th October 2017)

The Story Of Mathematics (2010), Prehistoric Mathematics, Available at: http://www.storyofmathematics.com/prehistoric.html (Accessed on: 6^th October 2017)