Category Archives: Uncategorized

Consider the Riemann sphere, obtained by adjoining a ‘point at infinity’ to the complex plane. The conformal maps from the Riemann sphere to itself form a group, the Möbius group, which is abstractly isomorphic to (and also the proper orthochronous … Continue reading →

I apologise for the sporadicity of recent cp4space posts, but I do have several legitimate excuses (including MOG marking, which occupied a significant portion of yesterday). Naturally, it would be improper for me to prematurely release the results, so you’ll have to … Continue reading →

The Tammes problem asks for an arrangement of n points on the surface of a sphere, which maximises the minimum distance between any two points. This can be regarded as the classic problem of circle packing, but on the sphere (endowed with … Continue reading →

Any fluid dynamicist would be able to tell you that fluids obey partial differential equations such as the Navier-Stokes equations. This macroscopic behaviour should, and indeed can, be derived from applying Newton’s laws of motion to the individual molecules in the … Continue reading →

The first instance of the concept of a symbolic mathematical equation is usually attributed to Robert Recorde, a Welsh mathematician, in a 1557 book with the rather verbose title ‘The Whetstone of Witte, whiche is the seconde parte of Arithmeteke: containing the … Continue reading →

Since the conception of the European Girls’ Mathematical Olympiad (henceforth abbreviated to EGMO), the British Mathematical Olympiad Committee has run an annual national olympiad specifically for aspiring female mathematicians. The third edition of the Mathematical Olympiad for Girls (MOG) takes place … Continue reading →

It is straightforward to position a cube such that its vertices are all integer coordinates. For instance, we could choose its eight vertices to be (±1, ±1, ±1). Similarly, the vertices of a regular octahedron can be positioned at cyclic permutations … Continue reading →

Suppose you were cast away on a desert island. You’re only allowed to take a maximum of eight known theorems with you, along with rudimentary results such as ZFC axioms together with ‘boring stuff’ such as mathematical induction over the naturals, commutativity … Continue reading →

In the not-too-distant future, people are going to be celebrating the 100th birthday of Bill Tutte. He’s not quite as well-known as Alan Turing, which is a shame since they were both equally invaluable in the cryptanalysis at Bletchley Park. You … Continue reading →

The Perrin sequence is defined by a recurrence relation, and is qualitatively similar to the Lucas sequence. The initial terms are and subsequent terms are defined by , and summarised in the following spiral of equilateral triangles: As you can … Continue reading →