Spotting Asset Bubbles Asset bubbles are formed when a service, product or company becomes massively over-valued only to crash, taking with it most of its investors’ money. There are many examples of asset bubbles in history – the Dutch tulip bulb mania and the South Sea bubble are two of the most famous historical examples. […]

Measuring the Distance to the Stars This is a very nice example of some very simple mathematics achieving something which for centuries appeared impossible – measuring the distance to the stars. Before we start we need a few definitions: 1 Astronomical Unit (AU) is the average distance from the Sun to the Earth. This is […]

The Remarkable Dirac Delta Function This is a brief introduction to the Dirac Delta function – named after the legendary Nobel prize winning physicist Paul Dirac. Dirac was one of the founding fathers of the mathematics of quantum mechanics, and is widely regarded as one of the most influential physicists of the 20th Century. This […]

The Rise of Bitcoin Bitcoin is in the news again as it hits $10,000 a coin – the online crypto-currency has seen huge growth over the past 1 1/2 years, and there are now reports that hedge funds are now investing part of their portfolios in the currency. So let’s have a look at […]

This post is inspired by the Quora thread on interesting functions to plot. The butterfly This is a slightly simpler version of the butterfly curve which is plotted using polar coordinates on Desmos as: Polar coordinates are an alternative way of plotting functions – and are explored a little in HL Maths when looking at […]

A geometric proof for the Arithmetic and Geometric Mean There is more than one way to define the mean of a number. The arithmetic mean is the mean we learn at secondary school – for 2 numbers a and b it is: (a + b) /2. The geometric mean on the other hand is defined […]