Author Archives: apgoucher

There are several mathematical heuristics (it’s difficult to call them proofs), which are non-rigorous in the best of cases and sometimes seemingly insane. For example, Euler’s ‘proof’ that the sum of the reciprocals of the primes diverges at an asymptotic … Continue reading →

In Einstein summation convention, repeated indices are summed over. For example, . If a Kronecker delta has two different suffices, we can ‘contract’ them as follows: , whereas . Vishal Patil considered contracting English words in this manner. For example, … Continue reading →

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 →