Pythagoras’ theorem is one of the beauties of mathematics. Something so simple as being able to work out sides of a right angled triangle has had pretty much unlimited use in practical engineering as well as very theoretical linear algebra and calculus. For those of you less mathematically inclined, I’ll explain briefly what the theorem says and then show you a nice real-world application of it. The Theorem If your years of mathematics are long gone and forgotten, then Pythagoras’ […]

In keeping with the football spirit, I’m going to use the format of the FIFA World Cup as an example to show you how to calculate the total number of matches/games played in a tournament. There are two cases that we need to consider: 1. The league stage – where every team plays every other team in a group 2. The knockout stage, which follows a structure like that shown in the picture above, until one team is declared the […]

Before we get down to the maths, let me digress to explain why there is a still from BBC’s motoring magazine Top Gear at the top of this page. In the last few series of the show, I have noticed an interesting tendency for BBC to include attractive women in the camera shot whilst the presenters are sitting in the foreground. The image above shows a prime example of this. Whether this is a conscious attempt at subliminal messaging targeted […]

Modes. They seem to be difficult for many musicians to get the hang of. Fortunately, I’ve found that the easiest way to understand them and to explain them lies in a nice bit of maths. A quick note on Cycles Cycles are a neat piece of mathematics, lying as a part of permutations within the realms of combinatorics and algebra. Despite its simple nature, it has very powerful applications. Let me give you a short introduction. A permutation of a […]

Maths and music. Probably my two favourite subjects, and yet, two things that are often considered as mutually exclusive. But this is very, very far from the truth. Much research has been done to show that logicians and mathematicians are often very talented musicians. History also supports this fact (I have linked to a couple of interesting articles at the end of this one that go into more detail about this). There are more direct mathematical links to be found […]

One of my favourite proofs in the maths world is actually a very simple one. The reason that I love it so much is that it highlights the difficulty us humans face when trying to understand the concept of “infinity”. Everything that we know of seems to have a beginning and an end. We die after a finite period of time. Pluto is extremely far away, but it is a finite distance away, meaning that it can be reached given […]

A Quick Introduction to Basal Numbers Our number system has evolved a lot over the years, but for a while now, we have established the base 10 number system (the decimal system) as being the norm. It’s great because calculation becomes very easy due to it being something our brains can deal with quite efficiently. Base 10 means that each position in a written number represents a quantity of a specific power of 10. We start from the right hand […]