Recently I friend and I wrote a semi-serious paper called "The geometry of impossible objects" to be delivered at a mathematics technology conference. The reviewer was not hugely complimentary, saying that there was nothing new in the paper. Well, maybe not, but we had fun pulling together some information …

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 …

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 …