Would you believe me if I said that mathematics can judge your facial proportion? Well unfortunately it can in a very accurate and understandable way. In our most recent input for our Discovering Mathematics module we unearthed how to draw a face accurately. For myself I have always had a creative ambition and enthusiasm, but I can say that I consciously – and even happily – avoided ever drawing an accurate face to gain my Higher Art and Design Qualification. It wasn’t until this input that I have ever successfully accomplished my avoided dream.

##### Introducing ‘The Golden Ratio’

Initially we were instructed to draw a face on one side of an A3 piece of paper. As you can imagine this triggered a few negative responses along with ironically a small part of art anxiety rather than maths anxiety. Like myself you will begin to wonder how on earth drawing a face has any connection to maths. It wasn’t until we were indulged on the beauty of drawing an accurate facial proportion. Everyday countless people have looked in the mirror and ridiculed there physical appearance. I would argue that at this moment in time there has never been a greater pressure worldwide to look, rather than be, your best. However, without knowing it you are judging the mathematical proportions of your facial features rather than your face itself.

To break it down simply, the shape and size of your face can be segmented into different groups. This discovery can unfold the ground breaking realisation that the human face is like a jigsaw. There are many different parts which aline and fit together to construct each of our individual faces. This is make clear by what is know as the Golden Ratio. This discovery by Dr. Stephen Marquardt identifies the proportions and measurements of each facial feature that would form the desirable face (Meisner, 2014) . In most cases this discovery has influenced reconstruction in cosmetic surgeries of people world wide. This is exactly what we considered when redrawing our original face. Ideally the stature of a perfectly sculpted face would include;

- The inner and outer corners of the eyes to be in line with the center of the nose
- The outer edge of each nostril to be in line with the inner corner of each eye
- The center line of the chin to a line with center of the upper lip
- The tops of the ears to be in line with the center line of the eyes
- The bottom of the ears to be in line with the bottom of the nose

As seen in the picture above, when considering these proportions and measurements it made it dramatically easier to redraw our original portrait. The contrast when considering and understanding proportions is undeniable. Understanding the relationship between features meant that shape, scale and proportion became much more understandable. Mathematics has made this possible through comparing measurements of facial features, without this an ever-growing cosmetic would not be able to function. By segmenting features together and build considerable knowledge of these proportions, the end result has greater accuracy. It achieves realistic dimensions of the human face.

##### The golden ratio vs. primates

Studying this topic immediately fueled my interests to link the facial proportions of The Golden Ratio to the facial structure of primates. Science has generously allowed us to explore the connections and evolution of humans themselves. Without delving to much into scientific theory, the theory of evolution devised by Charles Darwin concludes that all species have devolved from a small string of lifeforms (BBC, 2014). This is where the link between humans and primates can be made. Over time genetic differences have reshaped our species both physically and mentally. The theory of evolution has brought to life scientific evidence that humans are derived from primates. Using my new profound knowledge of facial proportion I thought this may provide and enciteful comparison.

Neverse (no date)

Looking at the pictures above you can see how some proportions of The Golden Ratio can seen within the facial structure of these primates. Although there are some physical difference such are the ears, there is a clear connection between our faces and these primates. By showing that these primates do not have a the structure of The Golden Ratio this can in fact relate to the differences between physical appearance among humans. Our eyes don’t match. Our ears don’t match. Everything about our faces are different yet we all have small common forms of facial structure, just like primates. As explained by Burrow et al. (2014) humans and primates can be physically compared because of the way our muscles are positioned in our faces. It is this connection which makes it possible to see similarities between ourselves and primates using The Golden Ratio.

In terms of the bigger picture in depth exploring mathematical concepts within the primary school will open rather than close the mind of children. By weaving concepts together and making cross curricular links children will be able to access the world around them through a new lens. This will allow them to use imagination and fun within the world of maths rather than be tied to textbook procedural work. A key concept which drove the Profound Understanding of Fundamental Mathematics according to Ma (2010) is Basic Ideas. This allows teacher to craft they’re approach in a way the takes a component of maths (in this case proportion and measurement) and spark by guiding children through its exciting structure. Therefore, the maths curricula will not inhibit but expand children’s approaches and interests in the world we are a part of. Furthermore, this also signifies the importance of competence within teachers themselves. Unless and educators work individually, and together as a body, to acquire profound understanding of fundamental mathematics how can we expect pupils to feel the same? The level of understanding which educators are capable of mimic the level of understanding which their pupils can achieve (Bregner and Groth, 2006). Building on mathematical knowledge and relating it to other concepts throughout the education curriculum will only encourage children to achieve in maths rather than be limited by teachers’ deficiency’s. This attitude should be established both nationally and internationally in order to provide children with the opportunity achieve with flexible and stable knowledge and understanding.

References

BBC GCSE Bitesize (2014) *Science: Evolution. *Available at: http://www.bbc.co.uk/schools/gcsebitesize/science/edexcel/classification_inheritance/evolutionrev1.shtml (Accessed: 29 October 2018).

Bregner, R. Groth, J. (2006) *Preservice Elementary Teachers’ Conceptual and Procedural Knowledge of Mean, Median and Mode.* Available at:* https://www-tandfonline-com.libezproxy.dundee.ac.uk/doi/abs/10.1207/s15327833mtl0801_3 *(Accessed: 29 October 2018).* *

Burrows, A. et al. (2014) *Humans Faces Are slower than Chimpanzees Faces.* Available at: http://europepmc.org/backend/ptpmcrender.fcgi?accid=PMC4206419&blobtype=pdf (Accessed: 26 October 2018).

Neverse (no date) Available at: https://www.stockfreeimages.com/29164140/Pair-of-monkeys.html (Accessed: 29 October 2018).

Ma, L. (2010) *Knowing and teaching elementary mathematics: teachers’ understanding of fundamental mathematics in China and the United States. *Available at: https://ebookcentral.proquest.com/lib/dundee/detail.action?docID=481154. (Accessed: 25 October 2018).

Meisner, G. (2014) Available at: https://www.goldennumber.net/face/ (Accessed: 25 October 2018).

Meisner, G. (2014) Available at: https://www.goldennumber.net/beauty/ (Accessed: 25 October 2018).