Category Archives: Uncategorized

It is widely acknowledged that an infinite number of monkeys sitting at computers typing randomly will almost surely produce a properly-LaTeXed copy of the complete works of Shakespeare. This statement, known as the ‘infinite monkey theorem’, has received a wide amount of … Continue reading →

Knot theory is a branch of topology which considers the different embeddings of a cycle into three-dimensional Euclidean space, R^3. The simplest type of knot is the unknot, which is just an ordinary circle (which can be ‘thickened’ to form … Continue reading →

My colleagues marked the first round of the British Mathematical Olympiad in Sidney Sussex College, Cambridge. You can view the leaderboard on Joseph’s website; well done to everyone who featured. There are quite a few new names on that list, … Continue reading →

The sinc function is important in signal processing for removing noise and reconstructing the original signal. It’s defined rather simply as sin(x)/x, so it’s surprising that it actually has its own special name (you have to be careful at x … Continue reading →

Quite a few things are described as ‘X-ing the Y’, where X and Y are the interiors of piecewise algebraic curves. Probably the most famous of these is ‘squaring the circle’, which refers to the impossible task of constructing a … Continue reading →

A particularly useful result in real analysis is, remarkably, applicable to combinatorics problems where reals are not even mentioned. It is the fabled Bolzano-Weierstrass theorem. The statement of the theorem is that ‘every bounded sequence has a convergent subsequence’. It … Continue reading →

Unfortunately, I am currently being invaded by millions of microscopic icosahedra (at least, I hope this is the common cold). I apologise on their behalf for any slight lapse in the frequency of CP4space postings. Don’t worry; the sixth cipher was made ages … Continue reading →

The ordinary Cantor set is obtained by removing the middle third of a unit line segment and iterating. The resulting set of points is uncountable, nowhere dense and has zero measure. It transpires that the construction can be modified to give … Continue reading →

In 2001, Lee Sallows generalised the concept of a magic square, replacing the integers in each cell with subsets of the plane. He calls such a configuration a ‘geomagic square’ if the subsets in every row, column and diagonal can … Continue reading →

Tsukamoto and Miyazaki of Kyoto University have discovered that three states are sufficient to enable gliders to exist on a Penrose tiling, rather than four. The following video demonstrates their discovery together with a periodic emitter in an augmented rule: [youtube=http://www.youtube.com/watch?v=6xVLpP25DRQ] On … Continue reading →