measuring | A Time for Reflection

Its that time of year again when the lights are up, songs are being sung, decorations are being hung and joy is absolutely everywhere. What is this time you ask? it is indeed Christmas. It is obvious that Christmas is a time for giving and thinking of loved ones, but after a recent blog post from Andy Hughes (titled ‘Christmaths’), I have been inspired to blog about how maths can be incorporated into Christmas in fun and inventive ways. In addition, it has made me want to uncover the fundamental principles of mathematics in Christmas.

Hughes (2015) in his blog post ‘Christmaths’ describes mathematics in Christmas. He states that snowflake’s are a ‘fractal (a fractal is a shape that contains similar patterns which recur throughout the shape on a smaller scale)’. In addition he identifies that zooming in on a snowflake just produces more details and can splurge up fundamental processes such as scaling, shape and ratio – very fundamental processes. On a larger scale, lets take the fundamental process of shape. As I have mentioned numerous times before, maths is all around us. In a seasonal sense, we only need to look at our Christmas trees to see that shape is evident. For example, Christmas baubles. These are spherical in shape. The star on top of the tree also shines bright, but is still a shape. However, what is the maths behind a Christmas tree? It could be suggested that there is maths in assembling a Christmas tree (especially and artificial one. For example, you will need to have the right length of Christmas tinsel to pass around the tree – the mathematical concept of length and measurement. In addition, you will need to have enough Christmas baubles in order for the tree to be symmetrical. Talking about symmetry, this can be used widely as examples to help children understand this concept. For example, trees are symmetrical, as are snowmen, stars, snowflakes.. the list goes on. This can be used as a consolidation activity and it effectively ties Christmas into mathematics.

Moreover, Christmas time in the classroom should be an exciting and engaging time for children. So why can’t we use maths within Christmas? Even if it is not directly from a maths lesson. Board games are a fantastic way to do this and they challenge a range of mathematical concepts. Take monopoly, for example. Now, I am not going to lecture you on how to play monopoly as I am sure we all have a ‘profound understanding’ of how to play it. However, what does monopoly all boil down to? Money. In order to play this game, children must have a basic knowledge of money and will have to subtract or add together money when they land on someone’s property or even if they pass go! I find this to be pretty incredible – its fun and engaging, but you are learning at the same time… Do you see where I am going with this? Take snakes and ladders – counting is the fundamental principle there. Cluedo – problem solving to find out who really committed the crime. Even in dominos there is a basic element of counting. Probability is also another fundamental principle that can be seen in games that use dice – what is the probability of landing on a six? Lets be honest, which games do not have dice in them?

It is obviously apparent that maths is incorporated into Christmas profoundly. If you even think about presents under your tree – some are cuboidal and some are spherical. Shape is such a common theme within Christmas. So when your opening your presents this year, have a second thought about how maths is incorporated into Christmas – it may even inspire you to write a blog post!!!!

reference:

Hughes, A. (2015) Christmaths. In a Class of my Own. Last accessed 06/12/15. Available at https://blogs.glowscotland.org.uk/glowblogs/ajhportfolio/2015/12/02/christmaths/

When we think of mathematics, we often think numbers, formulas, data handling and a whole host of other mathematical concepts. However, have you ever just looked around you whilst out in the outdoors and thought ‘maths is beautiful?” I guess its a thought that never springs to mind. However, mathematics is actually in everything we see in the outdoors (believe it or not) and this blog post aims to highlight how beautiful maths is within the context of the outdoors.

To see mathematics in the outdoors, we do not need to look far. It is in the very buildings that you see walking up and down the street. Here is a building that should all be too familiar:

For those of you who don’t know, this is the Dalhousie Building at Dundee University. I don’t know about you, but I feel believe that this is an architectural masterpiece. Firstly, if you look at the design, it is very visually appealing and it incorporates squares and curves to create a building that is grand in size. Where does the maths come into this? Well if we think back the original plans of the building, it had to be measured accurately in order for it to come together. Of course, there would have been slight room for error, but it had to be pretty accurate. If we think about the windows, the architects had to create enough space so they can tessellate perfectly. This absolutely astounds me. When looking back to a lecture on the golden ratio, you can almost see it happening here. To elaborate, the golden ratio was a ratio used since the 1500’s as it was perceived to be aesthetically pleasing. It uses the formula:

$\frac{a+b}{a} = \frac{a}{b} \ \stackrel{\text{def}}{=}\ \varphi,$

This can be best described using this square:

Basically, A golden rectangle (in pink) with longer side a and shorter side b, when placed adjacent to a square with sides of length a, will produce a similar golden rectangle with longer side a + b and shorter side a. This illustrates the relationship $\frac{a+b}{a} = \frac{a}{b} \equiv \varphi$ .

This all together makes this pattern which can be recognised in Fibonacci’s sequence:

This is seen to make an aesthetically appealing design:

Picture Courtesy of apple.

So where does our Dalhousie building come into this? Well if we look at the elevation of the building (the front of building consisting with the front entrance and the classrooms in the second block, we get a (block two) and b the entrance which would create this perfect spiral. I find this absolutely intriguing. This is not just the case for Dalhousie, However, this is the case for most things in our world. If we look at this plant:

we can see the golden ratio coming into play along with Fibonacci’s sequences. This officially ties nature and mathematics together and the results are absolutely breath taking. In this image above, not one segment of the flower is out of place. They all spiral in the same direction towards the centre of flower which makes it symmetrical.

And here it is again (sorry, I couldn’t resist). Everything in this world is tied into mathematics and this is why maths is beautiful. Whether its looking at buildings or looking at flowers, the fundamental mathematics is there. With buildings, its all do with measuring and being precise and I guess with flowers you could say pattern. Whatever the outcome, just have a look at the world around you and it might amaze you like it has me. Maths is beautiful.

Christmas in Mathematics – ideas for the classroom

Beautiful Mathematics – an Outdoor Perspective