The Joukowksy Transform is an elegant and simple way to create an airfoil shape. Let \(C\) be a circle in the complex plane that passes through the point \(z=1\) and encompasses the point \(z=-1\). The transform is defined as \[ \zeta=z+\frac{1}{z}. \] We can explore the transform by looking at the circles centred at …

This was a comedy sketch initially performed in the revue "Clowns in Clover" which had its first performance at the Adelphi Theatre in London on December 1, 1927. This particular sketch was written by Dion Titheradge and starred the inimitable Cicely Courtneidge as the annoyed customer Mrs Spooner. It has …

I recently came across some nice material on John Cook's blog about equations that described eggs. It turns out there are vast number of equations whose graphs are egg-shaped: that is, basically ellipse shape, but with one end "rounder" than the other. You can see lots at Jürgen Köller's Mathematische …

JSXGraph is a graphics package deveoped in Javascript, and which seems to be tailor-made for a static blog such as this. It consists of only two files: the javascript file itself, and an accompanying css file, which you can download. Alternaively you can simply link to the online files at the Javascript content …

When I was teaching the binomial theorem (or, to be more accurate, the binomial expansion) to my long-suffering students, one of them asked me if there was a trinomial theorem. Well, of course there is, although in fact expanding sums of greater than two terms is generally not classed as a theorem described by the …

I've been using wordpress as my blogging platform since I first started, about 10 years ago. (In fact the first post I can find is dated March 30, 2008.) I chose wordpress.com back then because it was (a) free, and (b) supported mathematics through a version (or subset) of LaTeX. As I have used LaTeX extensively for …

Election mapping A few weeks ago there was a by-election in my local electorate (known as an electoral division) of Batman here in Australia. I was interested in comparing the results of this election with the previous election two years ago. In this division it's become a two-horse race: the Greens against the …

Presentations are a modern bugbear. Anybody in academia or business, or any professional field really, will have sat through untold hours of presentations. And almost all of them are terrible. Wordy, uninteresting, too many "transition effects", low information content, you know as well as I do. Pretty much …

Programming the Vigenère cipher is my go-to problem when learning a new language. It's only ever a few lines of code, but it's a pleasant way of getting to grips with some of the basics of syntax. For the past few weeks I've been wrestling with Haskell, and I've now got to the stage where a Vigenère program is in fact …

On November 18, 2017, a by-election was held in my suburb of Northcote, on account of the death by cancer of the sitting member. It turned into a two-way contest between Labor (who had held the seat since its inception in 1927), and the Greens, who are making big inroads into the inner city. The Greens candidate won, …