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Maths in a minute: Euler's identity Euler's identity is often hailed as the most beautiful formula in mathematics. People wear it on T-shirts and get it tattooed on their bodies. where is the base of the natural logarithm, is the ratio between a circle’s circumference and diameter, These three constants are extremely important in maths [...]
Tournament Scheduling There are 2 well-known types of tournament formats that sport schedulers use. Single Elimination Tournaments. Round Robin Tournaments. Single Elimination Tournaments. In this format, one defeat is enough to eliminate a team from the tournament. Scheduling a single elimination tournament is relatively easy. The first step is to get the number of teams [...]
Where Do We Get Our Feet Wet? How many high points, low points and passes are there on the island of Crete? I do not know...but I do know a formula which given the number of high points and the number of low points tells me the number of passes. Can you discover it? I [...]
Mouhefanggai This article derives the formula for the volume of a sphere, without using any mathematics more advanced than Pythagoras' theorem. It uses some ideas developed in the article Volume of a Pyramid and a Cone, which you may want to read first. Volume of a mouhefanggai Imagine two identical cylindrical pipes meeting at right [...]
Fourier Series Most of the phenomena studied in the domain of engineering and science are periodic in nature> For instance, current and voltage in an alternating current circuit. These periodic functions could be analyzed into their constituent components (fundamentals and harmonics) by a process called Fourier analysis. Periodic functions occur frequently in the problems studied [...]
Knots Every one knows from experience how to create a knot. We do this all the time, often unwittingly. Knots whose ends were glued together and their classification form the subject of a branch of Topology known as the Knot Theory. On the left there is a picture of the Left Trefoil knot. On the [...]
Curvature of Surfaces How curved is a curve? How curved is a surface? When is a 'curved surface' flat? We shall only briefly mention curves in the plane and then move on to discuss positive and negative curvature of surfaces. Imagine tracing out the ellipse shown in the diagram. How does the curvature change as [...]
Ding Dong Bell If you wear a different coloured T-shirt every day someone may say that you are "ringing the changes". This expression simply means that you plan for variety rather than keeping things the same. It comes from the the custom of ringing churchbells. In East Anglia, as you look across the fens, villages [...]
