# The Beauty of Mathematics

CAN MATHEMATICS BE BEAUTIFUL?

If you take a look inside a child’s math jotter you will most likely find some numbers written on parallel lines to form equations and answers. But, is it possible to use math to form or create something which is not numbers based? Can we create something more exciting and creative other than stereotypically dull equations found in a child’s maths textbook?

Using Maths to Enhance Art

To my surprise, we can! We can actually use maths to ENHANCE and IMPROVE our abilities within the creative arts sector. Barrow (2014) suggests that maths and art are subjects which can be seen as coming in ‘hand in hand’ with one another. He also emphasises that patterns – which are the fundamental basis of art – are all based upon mathematical concepts (Barrow, 2014), such as symmetry, angles, rotation, shape etc – what Ma (2010) describes as the basic ideas of a fundamental understanding of maths. Buck (2011) agrees with this, saying that the patterns that artists create all have their individual algorithms, a mathematical set of instructions, which they must follow in order to correctly create the pattern.

Rule of Thirds

Even photographers can use maths to enhance their ability to capture aesthetically pleasing images. By splitting their lens into nine equal squares/rectangles, they can position the main subject of their photo along the intersecting lines of the squares. This opens up space behind or around the subject which the eye is then drawn to, meaning there is more than just the subject of the photo that is attractive to the eye at first glance.

Image 1 – Rule of Thirds

Self-Portraits

We can also use maths to transform ourselves into expert portrait drawers (ish)! By implementing basic concepts of shape and fractions into a portrait piece, we can enhance the end product. Using these concepts increase the likelihood of the features of the face being proportionate to each other, and therefore, making it more realistic than a piece that has not used maths. These basic concepts can be implemented when portrait drawing due to the symmetrical nature of the face, which serves as a source of beauty in itself (Zaidel and Hessmian, 2010).

For example, through splitting the outline of the face into quarters we can correctly identify where each of the facial features should be placed in respect of each other. Using maths, we can work out that the eyes should be positioned half way up the face and a fifth of the width of the face in from the outline (See picture below).

Image 2 – Using maths to sketch a face

I attempted to use this technique to draw a portrait of a face. Here is the before and after…

It really amazed me how different and how much better my second attempt at drawing a face was using just a little bit of maths! Being someone whose art ability is incredibility limited, it was surprising how easy the maths made drawing an in proportion and to scale face. Thus, this small adjustment to the way I approached this task, in my opinion, increased the aesthetic nature of my work.

Using Maths to Create Art

But it doesn’t just stop there! Maths can also be beautiful when used in solitude, not in conjunction with other subject areas – we can use maths alone to CREATE art.

Curves of Pursuit

By repeating a shape at the same interval multiple times, we can create even more shapes and beautiful patterns.

For example, using the square. By drawing a square and then drawing another square within it by measuring 1cm away from the right of each of the corners and then jointing these points up, we can create another square within it. When you repeat this action, you end up with something like this…

As you can see, I have ended up with a spiral motion within the original square, as well as individual triangles running through the curves. This type of mathematical phenomenon demonstrates how using one simple shape can create a very dynamic new image which is very pleasant to look at. I think that is amazing that we can use maths to create such intricate patterns, all from using a simple shape.

From my research into maths and art, I now understand the importance of being able to apply mathematical knowledge and skills to wider areas of society. I will no longer view maths as an isolated discipline of which numbers are the underlying fundamental basic idea (Ma, 2010). I hope to gain a better understanding of how maths can influence our society (other than in the creative arts) by exploring other sectors which it is intrinsically connected with, such as science and engineering.

In conclusion, the end result of mathematics does just have to include formulae, numbers and equations. It may result in beautiful aesthetics such as patterns, painting, images, photographs, tiling and much more. We can use maths to enhance our ability within the arts such as through using fractions and shapes in portrait drawing, we can increase how realistic the end drawing looks. You can also use maths alone to create art. Again using the basic idea of shape, Ma (2010), we can create beautifully aesthetic patterns from just one simple shape, for example, in curves of pursuit images.

References

Barrow, J.D. (2014). 100 Essential Things You Didn’t Know You Didn’t Know About Maths and the Arts. London: The Bodley Head. Available at: https://www.vlebooks.com/vleweb/Product/Index/673669?page=0 [Accessed 2 November 2018].

Buck, G. (2001). MATHEMATICS AND ART: Algorithms of Boundless Beauty. Science, 292(5516), pp.445-446.

Ma, L (2010) Knowing and Teaching Elementary Mathematics. Oxon: Routledge.

Zaidel, D. and Hessamian, M. (2010). Asymmetry and Symmetry in the Beauty of Human Faces. Symmetry, 2(1), pp.136-149.

Image 1 – Rule of thirds applied on Mädchen am Strand (2015) Wikipedia. Available at: https://commons.wikimedia.org/wiki/File:Rule_of_thirds_applied_on_M%C3%A4dchen_am_Strand.jpg [Accessed 2 November 2018].

Image 2 – Maths careers. Available at: http://www.mathscareers.org.uk/article/figure-drawing/ [Accessed 2 November 2018].

# A Poor View on Society

After a recent lecture on Socio-Political Perspectives on Poverty, I realised how wrong I was about the ‘type’ of people who find themselves in the ‘lower class’ bracket of society.

http://www.bbc.co.uk/news/uk-32812601

Before going to the lecture, I was asked to write down my views on those who experience poverty; their characteristics, lifestyle, attitude to life etc. I found myself writing words such as ‘scrounger’, ‘homeless’, ‘stealing’, ‘unintellectual’ and the list went on. As I sat up from writing these words, I shocked myself about how easily these demeaning and negative attributes had come from the tip of my pen. I began to feel ashamed as I had always considered myself an open-minded person, able to form my own opinions, and thoughts  about society after considering the perspectives of those within it. How had I come to such a harsh conclusion? Why did these terms appear on the paper without any second thought? Was this really my view of potentially the most vulnerable members of  our society?

After considering my approach to the task for a while, I soon realised that actually, these were NOT my own views; these were my learned views.  But what do I mean by ‘learned views’? I believe that another source has had such prominent views about poorer members of the community that I have unconsciously accepted or abided by these generalisations and stereotypes that they outwardly portray on a daily basis. But what is this incredibly influential source that has dominated my own personal thoughts and beliefs I hear you ask. It is something that is present even when I do not want to look at it, something that is alert even when I am not, something that preys on the weakest and most vulnerable members of  society, and that something is… the media.

The media is notorious for producing ridiculous, one-sided headlines which primarily focus on people who ‘steal’ benefits which they are not entitled to, or are too lazy to go out and find ‘real jobs’. Headlines such as ‘Is Britain a nation of lazy scroungers?’ (2013)and ‘Mother-of-five who pockets £18,000 a year in benefits says she needs MORE handouts because she can’t afford to buy school uniforms for her children (but still manages to spend £20 a week on cigarettes)’ (2016) further the stereotypical view which I adopted in the task around people in poverty, devaluing those who are actually in need and are trying their best to provide for their family.

One particular video which I came across during my research into poverty was ‘I live in real poverty, and it’s not what you think’ in which Kathleen Kerridge illustrates the real life difficulties faced by her and her family in our modern day society.

Kathleen demonstrates how easily it is to fall into poverty without any warning. She challenges people like me who have followed the media’s views and have been coerced into believing that it is their own fault that they are in this situation, that she was to blame. She goes on to explain how none of the events which led to her poverty-stricken status were caused by her actions; her heart attack, losing her job, mastectomy and a bankrupt landlord. I think that this shows that this could happen to any of us, at any time, as she was once in a financially stable position.

Another video which I found which shocked me was that focussing on Shelby’s Story, titled ‘Teenage poverty in the UK’.

I was totally shocked when Shelby revealed she was 17 due to her living AND providing for herself. Being 17 myself, I could NEVER imagine coming home from my work (which I get paid over the minimum wage for) to my home with 2 rooms, no cooker and no bed. It made me realise that anyone can be a victim of poverty – poverty does not discriminate against age, gender or race.

I sat down again after researching Poverty in the UK and wrote down my revised perspective on poverty after seeing and hearing what poverty means to those who experience it daily. ‘Misunderstood’, ‘ordinary’ ‘unfortunate’ and ‘hard working’ were a few that I came up with, what I should of come up with to begin with.

As I sit typing on my laptop that I got for my 14th birthday, in my University flat, with my family and my dog in my 4 bedroom home 40 minutes away, I start to wonder what I will have for my tea. This is not because my cupboards are bare, or because I cannot afford to buy another meal like Kathleen or Shelby, but because I bought too much food when moving into my flat… and this is when I realised what real poverty is.

Poverty isn’t being ‘too lazy’ to go out and get a job. Poverty isn’t people who have spent their live scrounging off of the benefit system. Poverty is ordinary people. Ordinary people who have to count their pennies to see whether they can afford their next meal. Ordinary people who have to sleep on a broken bed because they cannot afford to replace it. Poverty is REAL and it is EVERYWHERE, and it most certainly should not be defined by what we see in the media.

# Racism and Discrimination: My View Before and After

After receiving an input on race, ethnicity, patriarchy, discrimination and prejudice as part of the Values module, my understanding of the topic has significantly changed.

Before, I believed that was racism was becoming a ‘thing of the past’, which we had acknowledged as a society in order to see past the views of those less kind and stereotypical. However, I have come to realise (after interacting with the slides on the PowerPoint titled ‘Things have moved on haven’t they?’) how incredibly static racism still is in our modern day world. I was terribly shocked by the sheer quantity of case studies, events and news stories (included in the materials shared for student use) which all covered issues based on people committing acts of racism in the 21st century. This included the riots and protests witnessed in Charlottesville USA, where people were, and still are, openly allowed to demonstrate their racial views towards Jews and other ethnic minorities.

Also, I had always seen ethnic groups as being based upon your race, culture, religion or where you were born, for example, British, White, or Christian. I now understand that ethnicity is actually a ‘social phenomenon’ (Giddens, 2013) which is not based upon ascriptive characteristics, but evolutionary devices such as the prohibiting or intermarriage. This shows how easily people can misinterpret words or phrases which we use on a daily basis due to our lack of understanding on the topic.

One of the many statistics which showed how black people are still treated as lesser individuals is that black people are 3 TIMES more likely to be killed by Police than those who are white. I was absolutely appalled by this fact as it highlights how persistent racism is even today. It also shows that our legal systems and governments have failed to provide a duty of care to their black citizens.

Overall, I was seriously taken aback by how common these horrendous acts of racialization still are within our modern day society. I previously thought the government were doing enough to tackle these events, however, I now believe that they (especially America!) need to revise their strategies on tackling racism in order to make the world a safer place for everyone.

# Social Hierarchy – Resource Allocation Task

As part of the first Values Workshop, we were split into 5 groups, each of which received an envelope containing stationary items. The aim of the task was to produce a pack, using the resources in your envelope, for new MA1 students. This would be given to them at the start of their University journey.

My group, Group 1, opened our envelope to see that we had a huge amount of stationary and craft items to use in order to make our pack. We decided to make a ‘Student Starter Guide’. This included the following:

• a personalised timetable;
• a map of the main University buildings;
• tips aimed at the education course;
• a leaflet of all the different social events/aspects of University;
• and a guide to finding your way about the Dalhousie Building.

Derek was extremely enthusiastic towards our group, encouraging us every step of the way – he even offered us biscuits! We thrived off his energy and support for what we were making and felt proud of ur creative abilities. He kept us motivated and engaged in the task by continually checking in on our progress and praising our designs.

When it came to presenting our pack, it came as a great shock to me and the rest of my group to find out that Derek’s praise and the resources given to each group were not shared out equally. It turned out that, actually, this was planned! Some groups had as little as a few post-it notes, a pen and a paper clip in their envelope, whilst my group sat there with piles upon piles of unused paper and other resources. The encouragement each group received from Derek also varied depending on how many resources you had; the more resources you were given, the more praise you received. This was demonstrated right through to the very end of presenting the finished packs, as Derek paid very little attention to Groups 4 and 5 even when they were giving their talks – he even went on his phone during Group 5’s presentation!

We then went on to discuss what this task was really about in relation to the Teaching Profession. The fact that my group did not notice that other groups received less than us illustrates that pupils who come from a wealthy/higher class background and have access to a huge number of resources to aid their learning tend to show a degree of ignorance towards those who are from a lesser background. Also, those who were in the groups which received less equipment did not go to other groups to ask for more. This suggests that those who are from a lower class family and do not have many resources/services available to them feel that they cannot go out and ask for them. It was as if those in Groups 4 and 5 thought that they were not as deserving of the resources as those in Groups 1 and 2, hence why we need to make our pupils aware that no matter what background they come from, they are all equal in the classroom.

As teachers, we need to recognise that not everyone will come to school well-equipped with the skills, tools and support system needed to do well in their educational journey. It is our job to discourage these inequalities amongst children by pushing them to do their best despite the fact that their personal circumstances or social background might be seen as an obstacle which could potentially hold them back.

Another interesting point which was made was the fact that favouring those in your classroom from a higher class background can lead to them excelling and achieving far more than those from a lower class family. This can lead to pupils from deprived areas seeing themselves as ‘less’ than everyone else, therefore, they become unmotivated as they aren’t receiving the encouragement they need to aid success. A member of Group 5 even commented that she “did not see the point” in presenting their finished work as Derek seemed so disengaged in what they had to show, thus highlighting that unevenly distributing praise can have a huge impact on pupils’ motivation.

Overall, I learnt a huge amount during this task and it has opened my mind about the daily struggles we face in erasing the social hierarchy which has been embedded into our system. I thoroughly enjoyed the task and look forward to our next workshop!