Face, Maths and Evolution. How does it all mix?

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.


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).

the maths and creativity sandwich.

Never would I have imagined that myself or anyone could sandwich together maths and creativity. Yet what a wonderful sandwich it is! Realistically, the majority of people would strongly argue against this opening statement, my self being one of them, however let me tell you that it is more than possible.

Related image

Like most sandwiches it all begins with the bread and in this case it begins with MATHS and Art. If you wanted to find these breads on a supermarket shelf you would instinctively look at opposite ends. However, this is not true because they could actually be found right next door to each other.  My own experience of maths and art at school was not in anyway this experience. I would have confidently argued during my time at school that art was the elegant French baguette – thick, crunchy and popular-  and on the other hand maths was the sourdough of all breads – bland, odd tasting and for the select few. Although reflecting on this now I think differently. This week in discovering maths we were exposed the creative aspects of this once bland subject.

This adventure was sparked by looking in detail at shapes. We discussed the names, number of side and angles of a variety of 2D shapes such as triangles, squares and hexagons.

You are now wondering how does this relate to maths? And it begins by introducing the idea of tessellation. ‘Tessellation (or tiling) is a repeating pattern of shapes that fit perfectly together without any overlaps or gaps.’ Brown (2018). Simple shapes such as triangle and squares can tesselate because their angles can make a full rotation. But how do you do make it personal?….

  1. Take an original shape, such as a square, and cut segments out of it.
  2. You then take your segments and add them back onto a different side of the square.
  3. You can then repeatedly join this new shape together by repeating, rotating or mirroring it.
  4. Repeat it all over the page, your final result should be a wonderful tessellated pattern.

When this is practiced you can make magnificent patterns and works of art.  Traditionally this commonly used within Islamic art and patterns.

(Please watch this short clip to see many different types of visual tessellations)

Watson, C (2015)

As I discussed this shows that maths can be used in an engaging and exciting way and this is what is extremely important when introducing maths into any classroom. I believe that when you begin a maths lesson you have only a few moments to make it interesting otherwise children will switch off. This what brings me back to the sandwich. Do NOT present maths as the sourdough bread! Within tessellation alone there are hundreds of opportunities for children to put there own creative stamp on their maths sandwich. They can experiment with fillings, experiment with topping, experiment with size and most importantly of all they will understand how the sandwich is made.

This reiterates the concepts of Profound Understanding of Fundamental Mathematics (PUFM). For myself, by investigating this topic of tessellation alone my view of PUFM has evolved because I can see it represented in Maths! The root of tessellation is shape. Children’s basic understanding of shape will be to name the shape they see.  However, if pupils have PUFM  they can understand that if you alter the shape it will still have the same area. In other words pupils will not only be able to name the types of bread, they will   understand how the bread is actually made.

However because of constraints children will not have time to explore this and there for be unable to sandwich maths with creativity. So how do educators step of our this narrow box. Haylock and Thangata (2007) argue that drill like teaching methods which are reused over decades betray creativity. Thus how maths is taught in the classroom can either uplift or damage creative the link between maths and creativity. Similarly Maths needs to be understood by the educator before it can be understood by pupils (Setati, 2011). As a future teacher I will continue to encourage creative thinking and tasks classroom maths topics. If this is done by all it can transform Maths from a bland sourdough into a baguette.


Brown, J. (2018) ‘Maths, creative? No way!’ ED21006: Discovering Maths. Available at: https://my.dundee.ac.uk/webapps/blackboard/execute/displayLearningUnit?course_id=_58988_1&content_id=_5217933_1 (Accessed: 29 September 2018).

Haylock, D. and Thangata, F. (2007)  Key concepts in teaching primary mathematics. London: SAGE.

Setati, M. (2011) Mathematics in Multilingual Classrooms in South Africa: From Understanding the Problem to Exploring Possible Solutions. Dordrecht: Springer Netherlands 2012.

Scottish Government (no date) curriculum  for excellence: mathematics principles and practice. Available: https://education.gov.scot/Documents/mathematics-pp.pdf (Accessed: 29 September 2018).

Watson, C (2015) What is Tessellation? Available at: https://www.youtube.com/watch?v=7GiKeeWSf4s (Accessed: 29 September 2018). 




Hartsford Uniform Conflict

Last year at the beginning of the first school term it became nationwide news when Hartsford High School in Kent had refused to let pupils enter school grounds because of their ‘inappropriate’ uniform which did not follow the school code of conduct.

While the head teacher of Hartsford had received positive feedback from local parents commenting that the code had set ‘high standards’ for school to be a highlight in the local community a small group of parents were out radged. Due to the teenagers being sent home from school parents brought it to the attention of the media that this had a catastrophic effect on their child’s education. The main issues came from a number of people who had ‘skin tight clothes on’, ‘inappropriate’ shoe wear and those who came without their blazers on. Many complained that those caught up in the situation were being prevented from missing the utmost vital education which could damage their studies, especially for those sitting exams. Since becoming local new this has become a conflicting topic of discussion.

Who is in the right?

In my perspective this could be argued from two points of view.

Firstly it is known that the way we dress allows us to express our different personalities. For some people wearing different shoes, clothes, hairstyles and accessories this can be a structure, which adds to their confidence, while they are at school. If this is true then why would it be acceptable to take this away from these young adults? On the other hand one of the main concerns coming from this story is money. In some cases the children’s parents were told to buy new uniform that was more appropriate but just because these things can be easily sourced in shops does that mean that everyone can afford them? Reading about child poverty this week has opened my eyes to the fact that a large majority of families struggle to make ends meet, if so then I don’t think it would be right to dismiss the fact that pupils might not have appropriate uniform because this is what is affordable for their family.

However on the other side of the fence I feel that having a set uniform for everyone in schools provides equality among pupils and their peers. If this code was not implemented it would isolate those from less fortunate backgrounds. All of a sudden school would become a competition of who has the best and most expensive outfit rather than what the real concern is. LEARNING.

As an aspiring professional I believe that the consistent attitude of the Head teacher and his staff has been positive in ensuring that standards will be kept in the school. By maintaining these standards will provide an education to pupils on what to expect in their future careers as the majority of professions have a set standard of how they expect their colleagues to dress. I see it from the perspective that, if you see a nurse on ward wearing a tracksuit or a police officer wearing jeans and a t-shirt while arresting someone, how would you react? How would that be different than wearing the correct uniform to school?

Sometimes building the small pieces of the puzzle first will help create a better idea of the picture. In this case I believe that this was the schools intentions and in the long term it will be worthwhile.