MATHS SOCIETY 2017/18
Dr Lawley on the Philosophy of Science


The Great Christmas Maths Off
Congratulations to Mr Salimbeni who raised £50 for his Charity of Choice, Mind.


Lecture Series
Dr Peter Jones spoke about General Relativity


Ms Copin spoke on Boring Maths in Bad Art


Mr Stuart Haring spoke on Solving Problems by Colouring


Mr TaylorWest spoke on Gödel's Incompleteness Theorem


Ms Copin spoke on The Lion and The Christian Problem

Ms Copin spoke on Fractals and Dimensions for a Christmas lecture



Factorial Magazine  Articles from Michaelmas 2017
Who Discovered Pi?
There are many things we have not yet discovered about pi: how it was found, and indeed, who discovered it first. The most we can do is trace it back. Geometers from ancient civilizations, dating back to around 1900BC, were aware that the circumference of a circle is just over 3 times the diameter, however they could not accurately calculate pi. The first known individual to calculate pi, to a relatively good level of accuracy, was Archimedes. He drew a square on the outside of a circle, and then another square on the inside of a circle. The perimeters, of these squares, created upper and lower bounds for the circumference of the circle, therefore deducing that pi was between 2.83 and 4. By using shapes with more and more sides and therefore closer to a circle [see below], mathematicians were able to find more accurate measurements for pi. Archimedes persevered and was eventually able to use 96sided shapes, to deduce that pi was between 3.141 and 3.143. Many mathematicians used this technique to refine the value of pi further. In the 5th century AD Zu Chongzhi used 12288sided polygons to estimate pi to 7 decimal places: noone improved on this for 1000 years! In the seventeenth century, Ludolph van Ceulen used 4billionbillion sided shapes to calculate pi to 35 decimal places, and when he died his tombstone gave tribute to this. There is no one particularly credited with “discovering pi”, however. Its value has been estimated by a series of mathematicians, each carrying forth the previous work to better the accuracy of this very important constant. Saachi Sennik 
How Come Imaginary Numbers Are Useful in Life If They Aren’t Real?
A number is “imaginary” when it is expressed in terms of the square root of 1, usually denoted as i. However, being “imaginary” is not to say that it does not exist or have any use. In fact, it can be argued that no number truly exists – they are merely a concept invented by mathematicians. Yet I’m sure you’ll agree that numbers are still an extremely important tool in our lives. In the early ages of mathematics, the ancient Greeks worked solely with whole numbers. These were thought to be the only type of numbers. With the idea of ‘debt’, however, negative numbers were introduced. This essentially extended the number line to the left, providing us with a larger toolbox to work with. Imaginary numbers can be thought of in a similar way – they add another dimension to our number system, kind of like extending the number line upwards, which allows us to solve even more problems, like solving x2+1=0. With this in mind, we can hopefully be less unsettled by the concept of imaginary numbers, and begin to understand that they can be utilised just like any other type of number. For example, a complicated electronic signal can be made much simpler by splitting it into the smaller components which make it up. This is known as Fourier transform, and is done with the help of complex numbers, which are numbers containing a mixture of real and imaginary parts. Fourier transforms have applications in modelling the flow of fluids through pipes, or the movement of oscillating objects (including some stars), or the positions of particles in quantum mechanics. All these theories provide insight into things from the real world, such as how to pump oil in oil rigs, how earthquakes shake buildings, and how electronic devices work on a quantum level… it even helps understand how your own brain processes light and sound! Clearly, complex numbers are therefore invaluable to mathematicians, scientists, and engineers alike. Without them, we would not be living in the same world. Mengyao Xu 
IB vs A Level Maths
When studying mathematics in the Sixth Form, there is a range of different options to choose from. Below the Maths Society have created an overview of each course in the hope of helping those interested: A LEVEL FURTHER MATHEMATICS: 2 Pure Mathematics papers, covering topics such as complex numbers, hyperbolic functions, differential equations, matrices, polar coordinates. 2 additional papers from a choice of Further Pure, Statistics, or Mechanics. 12 periods per week, 4 exams at the end of Y13. AS LEVEL FURTHER MATHEMATICS: 1 Pure Mathematics paper, and another paper from a choice of Further Pure, Statistics, or Mechanics. 8 periods per week, 2 exams at the end of Y12 (distinct from A Level Further exams). A LEVEL MATHEMATICS: 2 Pure Mathematics papers, covering topics such as proof, algebra, trigonometry, calculus, vectors. 1 Applied Mathematics paper, covering Statistics and Mechanics. All exams are taken at the end of Y13, and lessons take up 8 periods per week. AS LEVEL MATHEMATICS: 1 Pure paper, 1 Applied paper (weighted 63%, 37% respectively). 2 exams are taken at the end of Y12. IB higher leveL: This takes up 8 periods each week. the depth is comparable to Further Maths and the list of topics is slightly different. There is a calculator, noncalculator and an options paper (where the class decides what they want to study) as well as an exploration: many IB students say their maths explorations are the high point of their time here. IB Standard level: this is the IB equivalent of A level maths. It is made up 20% of coursework, one calculator paper and one noncalculator paper. Coursework is completed on a topic of interest related to one’s choice of university course (such as the link between gender inequality and murder). Maths takes up 4 periods each week. IB STUDIES: Students complete exams and coursework, with 4 periods of Maths each week. the focus of Maths Studies is on topics which are useful in the ‘real world’, like percentages, logic, and statistics. The course is a lot of fun and suits humanities specialists really well. Georgia Benson Fun Maths Websites
Here are three maths websites you can try out if you get bored, or are looking for a “productive” way to procrastinate :)) Brilliant.org: With thousands of fun exercises on anything from number theory, to machine learning, to quantum mechanics, ‘Brilliant.org’ is great for anyone who has an interest in mathematics and science. You can work through engaging and interactive online courses, which are expertly written by leading instructors and researchers to help you master foundational concepts to topics far beyond the standard curriculum. The weekly challenges (complete with discussions of the solutions from the community) are also a great way brush up on problem solving skills! Mengyao Xu 
An Interview with Mr Cockerill
Let’s start by getting to know you, where are you from? Alaska. What is your favourite number and why? 36 because it is easily divisible. Tell me a maths joke. Life without geometry is pointless. What is your favourite flavour of Pi? It’s got to be a traditional American apple pie. What is your favourite thing so far about NLCS? How nice everyone is, I know that sounds lame but it’s true! Were you good at maths when you were younger? Yes. When did you realise that you wanted to become a maths teacher? I was just finishing my degree and reflecting back on my experience when I realised that what I enjoyed the most was tutoring. I tried teaching but I wasn’t sold until after a full year as at first, I was nervous about teaching big classes. However, now I love teaching big classes! What is your favourite maths topic to teach and why? Differentiation because it is very tricky to understand the asymptotic nature of how you would calculate the tangent at a single point. And finally, what is your best piece of advice for anyone struggling with maths? You are definitely not alone, keep at it and try your best to enjoy it. Faridah Otulana Maths in the News
On the 24th August 2017, ‘The Independent’ published an article called, “Babylonians developed trigonometry 'superior' to modern day version 3,700 years ago.” The article explains how Hipparchus, a Greek astronomer who lived in about 120 BC, is traditionally regarded as the founder of trigonometry. But two professors discovered that a Babylonian table called Plimpton 322 predates Hipparchus by more than 1,000 years. Plimpton 322 was discovered in southern Iraq by the early 1900s by archaeologist, diplomat and antique dealer Edgar Banks. The tablet has numbers written in cuneiform script in four columns and 15 rows. There were suggestions in the 1980s that the numbers showed knowledge of trigonometry, but this had been dismissed more recently. However Dr Mansfield said their research revealed it was a “novel kind of trigonometry” that was based on ratios, rather than angles and circles. On the 15th July 2017, ‘BBC News’ published an article called “Maryam Mirzakhani, first woman to win maths' Fields Medal, dies.” Maryam Mirzakhani was the first woman, and first Iranian to receive the prestigious Fields Medal for mathematics. Nicknamed the "Nobel Prize for Mathematics," the Fields Medal is only awarded every four years to between two and four mathematicians under 40. It was given to Prof Mirzakhani in 2014 for her work on complex geometry and dynamical systems. Born in 1977, Prof Mirzakhani was brought up in postrevolutionary Iran and won two gold medals in the International Mathematical Olympiad as a teenager. She earned a PhD at Harvard University in 2004, and later worked at Princeton before securing a professorship at Stanford in 2008. Sarah Lewis 
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Factorial from 2014