Category Archives: Uncategorized

Assuming everything has gone to plan, I am now introducing myself at the British Mathematical Olympiad training camp at Trinity. I’ll be assisting the future IMO team by making tea and providing biscuits (integral, if somewhat overlooked, roles in the administration … Continue reading →

The usual method of generating the primes below N is to use a prime number sieve, such as the Sieve of Eratosthenes. This requires O(N log log N) operations for a random access machine, but can be reduced to O(N) … Continue reading →

In 2010, Evangelos Kranakis and Danny Krizanc published an academic paper with a rather bizarre title. The Urinal Problem investigates a particular mathematical model arising from the behaviour of men selecting urinals in a bathroom arrangement. Rather atypical of mathematical publications, … Continue reading →

Suppose we have a unit square ABCD. Is it possible to place a point P in the plane of ABCD, such that PA, PB, PC and PD are all rational? It’s not too difficult to show that such a point … Continue reading →

Euler’s formula famously relates the number of vertices, edges and faces of a polyhedron. Specifically, it gives , where V, E and F are the numbers of vertices, edges and faces, respectively. For example, the dodecahedron has 20 vertices, 30 … Continue reading →

It’s a well-known fact that the harmonic series (i.e. the sum of the reciprocals of the natural numbers) diverges to infinity. There are at least two reasonably straightforward ways to prove this, the first being the Cauchy condensation test. Essentially, … Continue reading →

Firstly, I would like to announce that today is the Ides of March. Secondly, I was alerted on two semi-recent occasions to this beast of a puzzle, namely the regular expression crossword. Like a normal crossword, you populate the empty cells of a grid … Continue reading →

(Sorry about the recent dearth of cp4space postings; I’ve been rather busy in real Euclidean 3-space, .) Quite a large class of self-similar geometrical objects can be expressed as iterated function systems. For instance, the Sierpinski triangle is composed of three … Continue reading →

The determinant of a matrix can be regarded, most naturally, as the volume scaling factor of the corresponding linear map. However, one of the formulae for finding the determinant of a square matrix is to compute , where we sum over … Continue reading →

The connect sum of two knots is obtained by joining them together in the obvious way. There is, however, one small detail. If you define this naïvely, then you won’t necessarily obtain an unambiguous connect sum. For instance, consider the … Continue reading →