Category Archives: Uncategorized

Here’s the post I promised you a while ago. I wrote the first part of this in an e-mail on Burns’ Night of 2011, and the main idea (which Alex Bellos termed the ‘Goucherian calendar’) was mentioned in the Guardian. … Continue reading →

The Mandelbrot set, as you’re probably aware, is the set of points c in the complex plane such that iterating f(z) = z² + c repeatedly doesn’t escape to infinity. By invoking the triangle inequality, it can be shown that a point … Continue reading →

In Albrecht Dürer’s 1514 engraving Melancolia I, there is a famous 4×4 magic square. In addition to the rows, columns and main diagonals summing to 34, so do various other arrangements such as the quadrants and four corners. We can transform this into an … Continue reading →

There have been several recent items of news, either related to or inspired by the recent postings on Complex Projective 4-Space. Rather than mention them separately, I have collected them in this ‘digest’ format. Jigcypher solved I received an anonymous e-mail … Continue reading →

One of the qualities of a quintessential British mathematician is the ability to invent crazy and contrived functions to satisfy particular properties. For instance, John Conway’s base-13 function was designed as a counter-example to the converse of the Intermediate Value … Continue reading →

Studies have shown that bilateral symmetry in female humans is linked to attractiveness. Also connected with attractiveness is the presence of the golden ratio (the positive real root of the quadratic equation x² – x – 1 = 0, approximately 1.618034). Earlier, … Continue reading →

What’s the cheapest calculator you know of? Basic calculators are much cheaper than their scientific counterparts, and you can probably get one for £2. A slide rule is even cheaper: you could strap together two plastic rulers with logarithmic scales … Continue reading →

There is a plethora of polyhedra. One way to classify polyhedra is based on their symmetry, transitivity and other properties. An alternative, constructive approach, by John Conway, involves specifying sequences of operations to turn one polyhedron into another. Quite a … Continue reading →

I expect you’re tired of hearing about the centenary of Alan Turing’s birth. His automated machines for cracking the German Enigma and Lorenz ciphers have enjoyed quite a lot of recent press, as has his pioneering work on the theory … Continue reading →

For my first post on this blog, I’ve decided to stay away from complex projective 4-space, but instead write about something equally mathematical and just as interesting: pathological functions. The ideas may be more familiar to you in the form of fractals, although the … Continue reading →