# The Significance of Maths in Science!

“There is a strong relationship between science and mathematics.  Science is about exploring, describing, understanding and explaining our Universe.  To do this scientists have used mathematical tools for analysis of natural phenomena and describing the relationship  between natural phenomena in succinct and predictive ways.  Today many of our more abstract advanced ideas of nature can currently only be expressed in mathematical terms e.g. aspects of quantum physics, string theory and Dark Matter/ Dark Energy.” – Neil Taylor

Recently, we had an input in Discovering Maths from Neil Taylor, who is a Science Lecturer at the University of Dundee. He first of all asked us to write down every aspect of maths that we think is used in science. We came up with quite a lot:

Having done Higher Chemistry and Physics myself I felt very aware of the maths used in science, but didn’t quite realise how much!  In science, everything is measured. And I mean EVERYTHING; volume, density, speed, temperature and time are all to name a few. All equally studied in maths separately as well as under the term of measurement. The use of formulae in equations, for example in the top right of the photo is Distance=Speed/Time – a very useful and renowned formula that Science wouldn’t work without.

The use of graphs, charts and tables to display data is a huge one. This is important in science as all findings are tend to be shown in the form of a line graph, scatter graph, bar graph, or shown in various types of tables and charts. It is the easiest way for us to understand scientific findings, and its all down to maths! – E.g of my own graph from the input:

Even the use of positive and negative numbers that maths gives us – makes it easy to understand temperature, not only in Celsius but in Kelvin scale. Another couple of big ones are shapes, ratios, and converting numbers. Who could be bothered writing 1nm (nanometre 1×10^-9) as 0.0000001m every time? Not me! Not anyone in fact.

It just goes to show that our knowledge of maths is used in other areas, and are very important in these areas. This links in with a fundamental knowledge of maths, as it is allows us to revisit basic ideas from our early learning in maths and adapt these to suit the situation. For example, we all learned to do a very simple bar graph in primary school, a line graph maybe by p6/7, but never really used them again, or never used them for a purpose, only to answer a questionIn science, it is essential these graphs are used to display your OWN findings, so we are conducting a real mathematical activity.

It also allows us to form links between different subjects in maths. I must say I found the use of formulae easy in Higher maths as I had been regularly using it in Physics and Chemistry. Although they were used in completely different contexts, the concept remains the same and allows you to develop your skills in using these specific things.

Maths is extremely important, fundamentally, and every other aspect of it, especially in science. Science is one of the most progressive fields out there, and splits up into hundreds of different categories, where Maths is apparent and important in each. One part that is extremely important to the future of our society is energy – renewable energy. The use of turbines for wind energy, wave turbines for wave energy, and solar panels for solar energy are all on the rise in terms of popularity due to our finite resources such as oil and gas suspected to run out in the next 100 years or less. This means that the most efficient means of renewable energy must be implemented and this is all done by scientists and scientific technicians.

Also, in terms of the health sector, hundred of biologists and chemists research every day in order to find and improve medicines for our society. This could be done by carrying out tests which requires estimation, measuring quantities and displaying results on graphs – all areas of maths.

By having a fundamental awareness of maths we are able to use and apply mathematics in different contexts and relate the different concepts to form one body of knowledge. I feel as though this is done in Science to a degree, and science is crucial to our future. Therefore a knowledge of fundamental maths is also significant to the future of our wider society.

# Musical Maths

Music and Maths – two subjects you rarely think of as being connected with each other. One deals with numbers, the other with sounds. Well, actually, they identify with each other more than you think.

“Rhythm depends on arithmetic, harmony draws from basic numerical relationships, and the development of musical themes reflects the world of symmetry and geometry.  As Stravinsky once said: “The musician should find in mathematics a study as useful to him as the learning of another language is to a poet.  Mathematics swims seductively just below the surface.”

– Marcus du Sautoy (2011)

So, maths is related to the rhythm of the music. Not only this but it is related to the beats in a bar, the chords, the tuning of the instruments and the scales. Specifically when tuning the instruments, we use frequency which is a mathematical term. Without the use of this, the instruments would not be able to be successfully tuned and we would be listening to some awful, awful music.

Personally, I use rhythm and the beat of a music a lot in dancing as I dance very regularly. We count in sets of 8 and generally choreograph a dance and speak of the dance in terms of sets of 8. For example, “We’ve learned four sets of 8 and only have another two sets until we reach the chorus”. Most, if not all, songs work in sets of 8, which repeat themselves over and over until the songs finish. This, fundamentally, is repetition which is an area of maths. Now every set of 8 is not the same pitch wise –  it varies, which links in with variation. Now because I know a lot more about dance than I do about music and its instruments, I’m going to focus more on this.

Again, society would probably argue against any correlation between a tango for instance and a higher maths topic, however it is not the specific topics in maths but the fundamental concept which is important in the world of dance. –

“Mathematics is present in dance. It is not the mathematics of simple number manipulation; we do not attempt to add or integrate through movement, instead we would like to employ abstract mathematics and various methods of analysis to understand dance at a deeper level.” – http://archive.bridgesmathart.org/2012/bridges2012-453.pdf

If we move on from the aspects of music in dance we find ourselves in the types of dances. Of these, there are hundreds, but probably the most mathematically equipped are line dancing, Scottish dancing, and even hip hop. I am going to try and bring to light the fundamental maths which lies within dance.

Line dancing (although I am not an expert), tends to be done in lines, with very abrupt changes perhaps turning 90 degrees or 180 degrees, perhaps moving in a square or rectangular fashion. This obviously associates with shape and angles which you must be aware of whilst dancing this type of dance.

As for Scottish dancing, in most dances, especially with a partner, you are mirroring exactly what your partner is doing – my personal favourite is the Canadian Barn Dance. As you are mirroring what your partner is doing, you are in fact practising symmetry, which of course is a mathematical concept.

Lastly, some hip hop moves are extremely technical, with precise movements of the limbs, head and body to create different shapes. Hip hop is also one of the hardest types of dance to master as you have to work intricately with the beat of the music, sometimes dancing off beat. Now in order to do this you must have a strong understanding and concept of the beat in music, which relates to simply being able to count in your head and hold this count in your head (harder than it looks may I add!).

Lots of extra points on the matter here.

# The hidden secret of The Simpsons

The Simpsons is one of the most popular TV shows in the USA and the UK, but did you know that its actually one of the most mathematically sophisticated TV show ever made?! Me neither!

“Most people are unaware that The Simpsons’ writing team is bristling with maths PhDs, and that the programme contains a huge amount of mathematics in its content.”  – http://www.bbc.co.uk/news/entertainment-arts-24344912

These writers, one of whom went to Harvard to study maths at 16, hide hundreds of maths references throughout The Simpsons’ 581 episodes. This includes a joke about Fermat’s last theorem, the most notorious equation in the history of mathematics!

Another example of hidden maths is in an episode involving a baseball game. On the way in, the camera shows a board with a list of numbers that show the possible attendance.

These digits might seem pretty random, normal, good guesses in fact, but they actually represent a perfect number, a narcissistic number and a Mersenne prime. (!!!!!!!!) What does this even mean!?!?

Im not even going to go into what they mean as it is generally far too confusing. But it just goes to show that something that millions of people have probably turned a blind eye to whilst watching their favourite dinner time show, actually means something – something very complicated but also very true! These mathematicians have almost got too much time on their hands. It just goes to show that maths is literally right under our noses without even noticing.

Simon Singh has even released a book called ‘The Simpsons and their Mathematical Secrets’.

Here is him discussing the numbers of attendance I have just spoken about, he probably explains it better than me…

I could literally be here all day talking about The Simpsons and its hidden maths, but that isn’t the point. The point is the maths hidden within the show. This scenario happens in our every day life, where maths is actually concealed behind things we would never expect! Although we do not notice it I still feel it is really important as it means mathematics is still around us and even whilst we are watching the Simpsons we are still getting a taste for numbers and sometimes, extremely difficult mathematical equations.

# Logistics and maths and supply chains!

Recently in maths we were introduced to the idea of logistics and supply chains. Richard asked us to think about the food we eat, how it grows, where it grows and how it gets to us. It’s something that is an extremely important process yet one that I rarely ever think about! I just walk into Tesco and buy a bunch of bananas, not blinking an eye as to what their journey to the supermarket might have been like. Many things need to be taken into consideration; the shape of the product, the weight, how far it has to travel, how long it takes till it goes out of date, the temperature the product must be held at (we don’t want the ice cream to melt!), the packaging it comes in, how many are delivered and where they are delivered. The list could go on further, but it just goes to show you how we must mathematically use our brains even just thinking of factors of a food’s journey! Another example of how maths is all around us.

An interesting example of how the shape of the product can prevent the full potential of products being shipped is the watermelon. Because they’re round, lots of air is left in the packaging which is basically lost money for the distributors! So Japan came up with these,

http://news.bbc.co.uk/1/hi/world/asia-pacific/1390088.stm

Squared shape watermelons so they pack more easily! The Japanese using their mathematical knowledge and applying it to food distribution… However, it didn’t catch on.

On the receiving end of the food, are the supermarkets! Where a majority of us will buy our messages from and expect to find everything we need, in their usual place in the same aisle every week. However, the supermarkets don’t just receive a random amount of food and hope for the best – this is where demand planning comes in. Demand planning is something I have never particularly heard of or new existed, but something that supermarkets and retailers – any business actually – can simply not survive without! It’s when someone estimates how much of each product they must order in to their store that they aim to sell, not wanting to end up with too little stock which will reduce profit, and too much stock which will increase waste as it will go off. They must use their estimation skills, and knowledge of the market, their customers and general common sense in order to come to these conclusions.

In pairs, we went off and did our own demand planning, starting with a budget of 5000 euros and a list of products to choose from – Team ‘Synergy’ got started! We chose 5 products over a 3 month period, so over the summer season we opted for crisps, juice, beer – summer holiday essentials! The Christmas season brought turkeys, selection boxes and biscuit trays to mind, and these were reflected in the sales which were around 90 to 100% for all of these products throughout December. It is this problem solving and abstract thinking which is the fundamental maths we use when coming to these conclusions as we have to reason with ourselves and use our knowledge of the world to solve problems. In the end, we made a healthy profit of 25000 euros in 9 months, and only lost about 25 euros worth of bananas, which turned brown (yuck). Not too bad at all!

# Maps and Maths

The other day in Discovering Mathematics we were learning how to incorporate outdoor learning with Maths, but not your typical kind of maths (numbers and sums). Will asked us to discuss how everyday objects, buildings and activities involve maths. For example, a building site – the maths needed to measure the size of parts needed, the machines needed to carry the weights, the way in which the building is built, the design of the building itself… it all is centred around maths!

We then moved on to focus on maps and map skills, something I am completely rubbish at. I realise now how important having a basic knowledge of how to read a map and how to work a compass is, and why children should be learning this in school. It is also something you can do outdoors! Something that is encouraged in Curriculum for Excellence and of course that children love doing.

To practise, we were given the task to draw the classroom we were in as a map from above.

Later in the lesson, we were given another task to create a resource or a lesson based on maps and using maths/maps skills. I decided to use my drawing of the map of the classroom as I was pretty proud of it!

In partners, we decided to use the map as a kind of treasure hunt. We were going to hide clues in different places in the classroom and mark these on the map given. The children would then have to figure out where in the classroom the clues were by adjusting and associating themselves with the map. Once they got the clue, which is actually a puzzle (or anything along those lines), they must figure it out. Once they have the answer, they return to their base point and add answer to chart. (Returning to base point is a very basic but extremely important factor with orienteering as it ensures that you never get lost and keep an eye on your surroundings).

Here was our notes for the task…

Before hand, I would probably introduce the idea of maps to the children. Possibly get them to draw their own maps, of their bedrooms, living room, their classroom etc. This ensures they will get the gist of reading this type of map. This is a fun activity and can be used as a follow up activity of possibly some textbook work, or as an initial activity of which you can follow up on. Either way its incorporating maths with an activity that doesn’t feel necessarily like maths, and makes it fun for everyone involved by actively learning.

# Number Systems

Yesterday in the Discovering Mathematics elective we were discussing number systems and investigating patterns and sequences. We were asked why we have numbers, which – to me – is one of those questions that just makes your mind go completely blank. So, why DO we have numbers? Some say for time and distance – measuring if something is twice as far away, others say numbers are used to make things fair by halving between two people. I think there are far too many possibilities to fit in one answer. Numbers are around us all of the time, from our phone numbers to telling the time, to watching the speed at which you are driving your car. Numbers allow humans to compare, with some anthropologists suggesting that trading created a need for numbers.

Instead of focusing on numbers, we looked at the actual numerals themselves. Numerals as we know them, 1 2 3 4 5 6 7 8 9 0, is only one form used, although probably the most popular, in the world. There are also –

ARABIC NUMERALS

http://portlandcoins.blogspot.co.uk/2012/03/reading-arabic-numbers-and-dates.html

ROMAN NUMERALS

http://inotiq.pev.pl/roman-numeral-number-answers.php

CHINESE NUMERALS

http://www.chinese-word.com/numbers_1_100/html/

Considering the different numerals used worldwide, our activity was to create our own numeric alphabet from scratch. Each numeral’s symbol, the name of the individual numeral and the name of the numeric alphabet had to be completely made up. So we got to work…

We started off with a triangle theme, because we felt like it!

Then when we got to 5, we turned our 1 – 4 numerals upside down..

Then we decided our numerals would simply be called the same as ours, but backwards. The result – Slaremun!

We decided our numerals would take the same form as ours, e.g, number 10 is made up of a 1 and 0, and 11 out of 1 and 1.

We then put slaremun into a quadratic equation..

..and it worked! We were so proud of ourselves we had to give our group a round of applause. I definitely think slaremun could be the future number system used worldwide.