Category Archives: Uncategorized

Sam Cappleman-Lynes noticed the seemingly remarkable fact that at least one of the interior angles of a triangle being equal to π/3 is equivalent to the linear relation between the semiperimeter, circumradius and inradius. He provided a clever synthetic solution, and I … Continue reading →

The card game Set is played rather regularly at gatherings such as the MathsJam events held nationwide on a monthly basis. The original game involves trying to identify sets of three cards which form lines in the affine hyperspace . … Continue reading →

This is breaking news, by the way; hence, the article is somewhat rushed. (If you haven’t heard of Conway’s Game of Life, there is a summary on Wikipedia.) As of a few minutes ago, Mike Playle discovered a π/2 stable reflector with a … Continue reading →

Twelve years ago, Kontsevich and Zagier published an enlightening exploration of a set of real (or, more generally, complex) numbers known as periods. Firstly, let’s have a look at which sets are subsets of which other sets: The integers  are a … Continue reading →

With basic calculus, it’s possible to solve the problem of two masses orbiting under gravitational attraction. In particular, the only solution is for them to follow conic sections, sharing a common focus (the barycentre of the two particles). For example, Pluto and … Continue reading →

I have returned from assisting at the Easter olympiad training camp at Trinity College, Cambridge. After we marked a selection test (the results of which I am not at liberty to divulge), a preliminary squad of nine people were selected, which … Continue reading →

Hall’s marriage theorem is well-known and frequently useful, but it’s a nightmare from a computational perspective. The standard proof can be turned into an algorithm which finds a matching, but it’s impracticably slow. The reason for this is that the … Continue reading →

The ordinary game of Noughts and Crosses, also known as Tic-tac-toe, features a board on which two players alternate placing symbols (O for the first player, and X for the second player) in unoccupied squares, attempting to form a line of three … Continue reading →

The Gamma function, Γ, is an extension of the factorial function to the complex plane. Specifically, Γ(n) = (n−1)! for all positive integers n. It is defined, more generally, by analytic continuation of the following integral, which converges for all complex numbers … Continue reading →

Professor Sir Timothy Gowers FRS wrote about the usefulness of a particular proof strategy, known as ‘just do it’. He gives six example problems, providing proofs using this technique. I’ll now give alternative proofs, which use explicit constructions to avoid this idea completely. Problem … Continue reading →